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1*
2* $Id$
3*
4* $Log$
5* Revision 1.1.1.1 1996/03/08 17:48:06 mclareni
6* Pdf
7*
8*
91***********************************************************************
10 * *
11 * CERN *
12 * *
13 * W5051 PDFLIB 1995.03.15 *
14 * *
15 * --------------------------------------------------------------- *
16 * *
17 * PDFLIB: Nucleon, Pion and Photon Parton Density Functions *
18 * and alpha(s) Calculations *
19 * *
20 * User's Manual *
21 * *
22 * Version 6.06 *
23 * *
24 * *
25 * H. Plothow-Besch/CERN-PPE *
26 * *
27 * CH-1211 Geneva 23 *
28 * BITNET/EARN address: PLOTHOW@CERNVM.CERN.CH *
29 * Tel.: +41 - 22 - 767 39 80 *
30 * *
31 * A complete manual in PostScript format exists on a separate file *
32 * Requests can be addressed to the CERN Program Library Office *
33 * *
34 * Copyright by H. Plothow-Besch *
35 * *
36 * Abstract *
37 * *
38 * This document describes an integrated package of Parton Den- *
39 * sity Functions called PDFLIB which has been added to the CERN *
40 * Program Library Pool W999 and is labelled as W5051. In this pack- *
41 * age all the different sets of parton density functions of the *
42 * NUCLEON, the PION and the PHOTON which are available today (about *
43 * 100 different sets) have been put together. All these sets have *
44 * been combined in a consistent way such that they all have similar *
45 * calling sequences and no external data files have to be read in *
46 * anymore. A default set has been prepared, although those prefering *
47 * their own set or wanting to test a new one may do so within the *
48 * package. The selection mode, the program parameters as well as *
49 * the possibilities to modify the defaults and to control errors *
50 * occured during execution are described. *
51 * *
52 * The package offers as well a program to calculate the strong *
53 * coupling constant alpha(s) to first or second order (default). *
54 * The correct Lambda(QCD) associated to the selected set of struc- *
55 * ture functions and the number of allowed flavours with respect to *
56 * the given Q**2 is automatically used in the caculation. For those *
57 * structure functions where the evolution has been performed to *
58 * leading order only, an alpha(s) value fixed to first order is re- *
59 * turned. *
60 * *
61 * The package is written in standard FORTRAN-77 and is avai- *
62 * lable on all CERN system areas. *
63 * *
64 * Submitter: H. Plothow-Besch/CERN-PPE *
65 * Language: FORTRAN 77 *
66 * Library: PDFLIB *
67 * *
68 ***********************************************************************
691***********************************************************************
70 * *
71 * *
72 * _______________________________________________________________ *
73 * | | *
74 * | PDFLIB - User's Manual | *
75 * | | *
76 * | CERN Program Library entry W5051 | *
77 * | | *
78 * | Copyright CERN, Geneva 1990, 1991, 1992, 1993, 1994, 1995 | *
79 * | | *
80 * | Copyright and any other appropriate legal protection of | *
81 * | these computer programs and associated documentation re- | *
82 * | served in all countries of the world. | *
83 * | | *
84 * | These programs or documentation may not be reproduced | *
85 * | and/or redistributed by any method without prior written | *
86 * | consent of the Director-General of CERN or his delegate. | *
87 * | | *
88 * | Permission for the scientific usage of any programs des- | *
89 * | cribed herein is granted apriori to those scientific in- | *
90 * | stitutes associated with the CERN experimental program or | *
91 * | with whom CERN has concluded a scientific collaboration | *
92 * | agreement. | *
93 * | | *
94 * | Commercial utilisation requires explicit a priori per- | *
95 * | mission from CERN and will be subjected to payment of a | *
96 * | licence fee. | *
97 * | | *
98 * | These statements are without prejudice to any rights that | *
99 * | third parties may hold in these programs. | *
100 * | | *
101 * | | *
102 * | Requests for information should be addressed to: | *
103 * | | *
104 * | CERN Program Library Office | *
105 * | CERN-DD Division | *
106 * | CH-1211 Geneva 23 | *
107 * | Switzerland | *
108 * | Tel. +41 22 767 4951 | *
109 * | Fax. +41 22 767 7155 | *
110 * | Electronic Mail address: | *
111 * | | *
112 * | EARN/Bitnet: CERNLIB@CERNVM | *
113 * | DECnet: VXCERN::CERNLIB ( node 22.190 ) | *
114 * | Internet: CERNLIB@CERNVM.CERN.CH | *
115 * |_____________________________________________________________| *
116 * *
117 * *
118 * *
119 * *
120 * *
121 * *
122 * *
123 * *
124 * *
125 * *
126 * *
127 * *
128 ******************************** - 1 - ********************************
1291***********************************************************************
130 * *
131 * Table of Contents *
132 * page *
133 * *
134 * PROGRAM SUMMARY .......................................... 3 *
135 * *
136 * 0. Major Differences compared to earlier Versions 4 *
137 * 0.1 The actual Version 6.06 wrt Version 5.00 ............ 4 *
138 * 0.2 Version 5.00 wrt Version 4.00 ....................... 4 *
139 * 0.3 Version 4.00 wrt Version 3.00 ....................... 4 *
140 * 0.4 Version 3.00 wrt Version 2.00 ....................... 6 *
141 * 0.5 Version 2.00 wrt Version 1.00 ....................... 7 *
142 * *
143 * 1. Introduction 8 *
144 * *
145 * 2. The Structure Functions Package PDFLIB 10 *
146 * 2.1 Parameter Setting and Selection of sets ............ 10 *
147 * 2.2 The Calling Sequence: PDFLIB Format ................ 12 *
148 * 2.3 The Calling Sequence: PDG Format ................... 14 *
149 * 2.4 Error Handling ..................................... 14 *
150 * 2.5 Features ........................................... 15 *
151 * 2.6 PION Structure Functions ........................... 16 *
152 * 2.7 PHOTON Structure Functions ......................... 17 *
153 * 2.8 How to find PDFLIB ................................. 18 *
154 * *
155 * 3. alpha(s) Calculation 18 *
156 * *
157 * 4. Conclusions 19 *
158 * *
159 * 5. Acknowledgements 21 *
160 * *
161 * 6. Appendix 22 *
162 * A : Example of how to use PDFLIB ........................ 22 *
163 * B : List of subprograms and COMMON blocks in PDFLIB *
164 * which are relevant to the user ...................... 25 *
165 * C : Complete list of subprograms in PDFLIB .............. 26 *
166 * *
167 * 7. References 32 *
168 * *
169 * 8. List of Tables 34 *
170 * *
171 * *
172 * *
173 * *
174 * *
175 * *
176 * *
177 * *
178 * *
179 * *
180 * *
181 * *
182 * *
183 * *
184 * *
185 * *
186 * *
187 * *
188 ******************************** - 2 - ********************************
1891***********************************************************************
190 * *
191 * PROGRAM SUMMARY *
192 * *
193 * *
194 * Titel of Program : PDFLIB, version 6.06 *
195 * *
196 * Catalogue number : W5051 in the CERN Computer Program Library *
197 * *
198 * Program obtainable from : CERN Computer Program Library Office *
199 * *
200 * Computer for which the program is designed and others on which it *
201 * has been tested: *
202 * Computer : IBM 3090, VAX, IBM-RISC, DECS, SUN, APOLLO, HP-UX, *
203 * Silicon Graphics, NEXT, CDC, CRAY, IBM-PC *
204 * *
205 * Operating systems : VM/CMS, VAX/VMS, ULTRIX *
206 * *
207 * Programming language used : FORTRAN 77, program is available also *
208 * in the PATCHY and the CMZ format *
209 * *
210 * Number of lines in distributed progam, *
211 * including test data, etc : 99 000 *
212 * *
213 * Memory required, *
214 * including testprograms and some documentation : 5 700 000 bytes *
215 * *
216 * No. of bits in a word : 64 *
217 * *
218 * Peripherals used : line printer (optional) *
219 * *
220 * Keywords : parton density functions, structure functions, W5051, *
221 * nucleon-, proton-, pion-, photon density parametrisa- *
222 * tions, Altarelli-Parisi equation, strong coupling *
223 * constant alpha(s) *
224 * *
225 * Nature of physical problem : *
226 * All theoretical calculations of cross sections involving the *
227 * hadronic structure of the incoming particles, i.e. protons, pions *
228 * or photons, use the parton density at a given longitudinal momen- *
229 * tum X of the parton and at a given momentum transfer Q**2. There *
230 * is a variety of parametrisations available, but each of them has *
231 * its own structure for input and/or output. *
232 * *
233 * Method of solution : *
234 * Collection of all available parton density parametrisations and *
235 * application in an identical format for all of them, regardless of *
236 * the author's convention or of the particle type. *
237 * *
238 * References : *
239 * [1] H. Plothow-Besch, 'PDFLIB: Structure Functions and alpha(s) *
240 * Calculations', User's Manual - Version 1.00, W5051 PDFLIB, *
241 * 1991.03.21, CERN-PPE. *
242 * [2] H. Plothow-Besch, 'PDFLIB: a library of all available parton *
243 * density functions of the nucleon, the pion and the photon and *
244 * the corresponding alpha(s) calculations', *
245 * Comp. Phys. Comm. 75 (1993) 396-416. *
246 * *
247 * *
248 ******************************** - 3 - ********************************
2491***********************************************************************
250 * *
251 * 0. Major Differences compared to earlier Versions *
252 * *
253 * 0.1 The actual Version 6.06 wrt Version 5.00: *
254 * *
255 * The following major changes compared to version 5.00 of PDFLIB *
256 * have been implemented: *
257 * *
258 * Several NUCLEON structure function sets have been added: *
259 * - the NLL sets A' and G of Martin, Roberts and Stirling (MRS-Ap) *
260 * and (MRS-G) of February 1995 with grid data as well as in its *
261 * parametrized version (MRS-Ap-F) and (MRS-G-Fit), *
262 * - the version 3 of the CTEQ group of October 1994 as NLL parame- *
263 * trisation in the MS_bar as well as in the DIS renormalisation *
264 * scheme and as LO (CTEQ3M, CTEQ3D, CTEQ3L), *
265 * - the new sets of GRV of November 1994 as NLL in the MS_bar as *
266 * well as in the DIS renormalisation scheme and as LO GRV *
267 * (GRV94-MS, GRV94DI, GRV94-LO), *
268 * *
269 * a NEW group of PHOTON structure function sets have been added: *
270 * - the six NLL sets of the WHIT group (WHIT1-G to WHIT6-G). *
271 * *
272 * Please note that as new the default set the MRS set (G) has been *
273 * chosen (NPTYPE = 1, NGROUP = 3, NSET = 41). *
274 * *
275 * More details can be found on the next pages of this updated *
276 * User's Manual. *
277 * *
278 * The response from the Physics community has been very satis- *
279 * factory, which is encouraging us to keep up-to-date with the *
280 * latest developments in this area. The author will be pleased to *
281 * learn about new parton density functions, as well as to receive *
282 * suggestions to improve both, the usage and the documentation. *
283 * *
284 * *
285 * 0.2 Version 5.00 wrt Version 4.00: *
286 * *
287 * The following major changes compared to version 4.00 of PDFLIB *
288 * have been implemented: *
289 * *
290 * NUCLEON structure function sets have been added: *
291 * - the NLL set A of Martin, Roberts and Stirling (MRS-A) and the *
292 * parametrized version (MRS-A-Fit) *
293 * PHOTON structure function sets have been added: *
294 * - the NLL set of Aurenche, Fontannaz and Guillet (AFG-G). *
295 * *
296 * *
297 * 0.3 Version 4.00 wrt Version 3.00: *
298 * *
299 * The following major changes compared to version 3.00 of PDFLIB *
300 * have been implemented: *
301 * *
302 * NUCLEON structure function sets have been updated or added: *
303 * - the updated NLL sets of Martin, Roberts and Stirling (MRS) of *
304 * November 1992, the sets S0', D0' and D-' in the MSbar as well *
305 * as the sets S0', D0' and D-' in the DIS renormalisation *
306 * scheme. Please note that the previous S0, D0 and D- sets have *
307 * *
308 ******************************** - 4 - ********************************
3091***********************************************************************
310 * *
311 * been retracted by the authors. The new MRS(H) set in both *
312 * schemes have also been added, *
313 * - the NLL and LO sets of the CTEQ collaboration (CTEQ) in its *
314 * parametrised form of January 1993. These are the sets 1M, 1MS *
315 * and 1ML in the MSbar, the set 1D in the DIS renormalisation *
316 * scheme and the LO set 1L, *
317 * - the new NLL sets A and B of Berger and Meng (BM) of *
318 * February 1993 with special gluon distributions, and finally *
319 * - the new NLL and LO sets of the CTEQ collaboration (CTEQ) in *
320 * its parametrised form of August 1993. These are the sets 2M, *
321 * 2MS, 2MF and 2ML in the MSbar, the set 2D in the DIS renorma- *
322 * lisation scheme and the LO set 2L. The revised CTEQ2 version, *
323 * CTEQ2p, of November 1993 is recommended by the authors. *
324 * *
325 * Please note that the default set has been put to the GRV set HO *
326 * (NPTYPE = 1, NGROUP = 5, NSET = 3 / former MODE = 72). *
327 * The MOST DRASTICAL change of the package has been, however, the *
328 * NEW FORMAT of PARAMETER SETTINGS. Instead of using only ONE para- *
329 * meter (MODE) to select a set of parton density functions (PDF), *
330 * each PDF set is now identified by THREE parameters. These are *
331 * NPTYPE, NGROUP and NSET, for PARTICLE TYPE (Nucleons, Pions or *
332 * Photons) AUTHOR GROUP (f.ex. MRS, CTEQ, GRV, etc) and the PARAME- *
333 * TRISATION SET within the group. Therefore the user should provide *
334 * THREE parameters (NPTYPE, NGROUP, NSET) to the subroutine PDFSET, *
335 * each time a PDF set shall be selected. But to make life nice and *
336 * easy, it is also possible to select a PDF set by transferring only *
337 * ONE parameter to PDFSET as before: this parameter should then *
338 * identify the NAME of the author group in an unequivocal way; the *
339 * selection of the PDF set within the author group is made by the *
340 * corresponding VALUE value (f.ex. PARM(1) = 'MRS' with VALUE(1) = *
341 * 29.0D0 would select the 29th set of the Nucleon PDFs of MRS, and *
342 * f.ex. PARM(1) = 'GRVph' with VALUE(1) = 1.0D0 would select the *
343 * first set of the Photon PDFs of GRV). As a suggestion, the NAME for*
344 * each PDF set can be found in the NEW COMMON block /W505110/SFNAME, *
345 * where SFNAME is a CHARACTER*8 array with dimension SFNAME(NPTYMX, *
346 * NGRMAX,NSETMX), and NPTYMX, NGRMAX, NSETMX are defined by the *
347 * parameter sequence, +SEQ, W5051P2. In case the user wants to se- *
348 * lect the DEFAULT, it is sufficient to transfer as the ONLY parame- *
349 * ter PARM(1) = 'Nset' with VALUE(1) = 0.0D0. This change of format *
350 * had been necessary to take into account the inflationary growing *
351 * number of PDFs until now and to foresee already the possibility of *
352 * adding new PDFs in a more flexible way. Please note that in case *
353 * of any INCONSISTANCY of parameter settings, it is always chosen *
354 * the DEFAULT settings !
355 * Please also note that the internal COMMON block /W50511/ has been *
356 * modified to /W50511/ NPTYPE,NGROUP,NSET,MODE,NFL,LO,TMAS. *
357 * *
358 * Full backward compatibility with previous versions is ensured !! *
359 * This means that old programs using PDF sets up to version 3.00 of *
360 * PDFLIB should run without ANY change. To ensure this, four new *
361 * COMMON blocks have been added: *
362 * - /W50519/ NEWVER : to flag the NEW/OLD version with the *
363 * LOGICAL variable NEWVER, *
364 * - /W505120/ NPGSMX(NPTYMX,NGRMAX),NSETFL(NPTYMX,NGRMAX,NSETMX) : *
365 * to provide the actual maximum number of parametrisation sets *
366 * per particle type and author group, and to flag the retracted *
367 * *
368 ******************************** - 5 - ********************************
3691***********************************************************************
370 * *
371 * PDF sets (NSETFL(I,J,K) = 0), *
372 * - /W505121/ NPTYCR(MODEMX),NGROMX(MODEMX),NSETCR(MODEMAX) : *
373 * to provide the cross reference to the NPTYPE, NGROUP and NSET *
374 * value (NEW format) for a given MODE value (OLD format), *
375 * and *
376 * - /W505122/ MODECR(NPTYMX,NGRMAX,NSETMX) : to provide the *
377 * cross reference to the MODE value (OLD version) for a given *
378 * NPTYPE, NGROUP and NSET value (NEW format). In case of the *
379 * above added PDF sets NO MODE value is available; in that case *
380 * MODECR(I,J,K) = -1 is returned. *
381 * *
382 * *
383 * 0.4 Version 3.00 wrt Version 2.00 *
384 * *
385 * The following major changes compared to version 2.00 of PDFLIB *
386 * had been implemented: *
387 * *
388 * NUCLEON structure function sets had been updated or added: *
389 * - the NLL set of Aurenche et al. (ABFOW), *
390 * - the updated NLL set of Kwiecinski, Martin, Roberts and *
391 * Stirling (KMRS) set B0 with u_bar not equal to d_bar *
392 * of April 1992, *
393 * - the new NLL sets of Martin, Roberts and Stirling (MRS) *
394 * set S0, D0 and D- with u_bar not equal to d_bar of April 1992. *
395 * Please note that the default set had been put to the MRS set S0 *
396 * (MODE = 45). *
397 * *
398 * PION structure function sets had been added: *
399 * - the new LO and NLL sets of Gl"uck, Reya and Vogt (GRV-P) *
400 * of August 1991, *
401 * - the new sets 2 and 3 of Aurenche et al. (ABFKW-P). *
402 * Please also note that the ABFKW set had changed MODE number from *
403 * 110 -> 180, as well as the SMRS sets from 120ff -> 130ff, and *
404 * that earlier inconsistencies in the parton density definitions *
405 * had been corrected. *
406 * *
407 * For the first time also PHOTON structure function sets had been *
408 * added to the package. These sets were the following: *
409 * - the old Duke and Owens (DO-G) LO and NLL sets, *
410 * - the old LO sets 1 to 4 of Drees and Grassie (DG-G), *
411 * - the new LO sets 1 to 3 of Abramowicz, Charchula and Levy *
412 * (LAC-G), *
413 * - the new LO sets 1 and 2 and the NLL set of Gordon and Storrow *
414 * (GS-G) of July 1991, *
415 * - the new LO and NLL sets, as well as the leading term of the *
416 * NLL calculation of Gl"uck, Reya and Vogt (GRV-G) *
417 * of December 1991, *
418 * - the new NLL sets of Aurenche et al. (ACFGP-G) of April 1992. *
419 * *
420 * Some improvements in the usage of the package had been made: *
421 * - more protections had been implemented and inconsistencies *
422 * had been corrected to make the package more robust and *
423 * available on ALL system areas, and finally *
424 * - the subroutine STRUCTM had been added. STRUCTM is basically *
425 * the same routine as the old steering subroutine STRUCTF apart *
426 * from ONE additional parameter in the argument list which had *
427 * *
428 ******************************** - 6 - ********************************
4291***********************************************************************
430 * *
431 * been added to transfer separately the parton densities for *
432 * u_bar and d_bar. The argument list of the subroutine STRUCTF *
433 * was as before; in case of STRUCTF sea = (u_bar + d_bar)/2 is *
434 * transferred. The subroutine PFTOPDG, which is the sterring *
435 * routine in PDG format, was unchanged; this routine always *
436 * transferred u_bar and d_bar separately. *
437 * *
438 * *
439 * 0.5 Version 2.00 wrt Version 1.00 *
440 * *
441 * The following major changes compared to version 1.00 of PDFLIB *
442 * had been implemented: *
443 * *
444 * New parton density functions of the NUCLEON had been added: *
445 * - the old LO set of Buras and Gaemers of 1978 (BEBC) for com- *
446 * pleteness, *
447 * - all the LO sets of Diemoz, Ferroni, Longo and Martinelli (DFLM)*
448 * including their parametrisation for the NLL average fit, *
449 * - the new LO set 1.1 of Owens (DO 1.1) of June 1991, *
450 * and finally *
451 * - the new LO and NLL sets of Gl"uck, Reya and Vogt (GRV) of *
452 * May 1991. *
453 * *
454 * PION structure function sets had been added to the package: *
455 * - the old Owens (OW-P) sets 1 and 2, *
456 * - the newer Aurenche et al. (ABFKW-P) set and *
457 * - the new Sutton, Martin, Roberts and Stirling (SMRS-P) sets 1, *
458 * 2 and 3. *
459 * *
460 * Some improvements in the usage of the package had been made: *
461 * - COMMON block names had been changed to avoid interference *
462 * to those defined by the user (/IMODE/ -> /W50511/, *
463 * /ALAMB/ -> /W50512/), *
464 * - three new COMMON blocks had been added: *
465 * a) /W50513/ XMIN,XMAX,Q2MIN,Q2MAX : *
466 * to provide the minimum and maximum values of X and Q**2 for *
467 * each set of structure functions, *
468 * b) /W50510/ IFLPRT : *
469 * to provide a print flag at different levels to print *
470 * b.1) the variables of the three COMMON blocks *
471 * /W50511/, /W50512/ and /W50513/ at job initialisation *
472 * b.2) error messages during job execution *
473 * c) /W50514W/ PDFWGT : *
474 * to take into account the event weight for error counting *
475 * - a subroutine PDFSTA had been added to allow at job termination *
476 * for a summary how often X and Q**2 limits have been exceeded, *
477 * - the MODE number of some structure functions had been changed *
478 * to keep consistensy, *
479 * - the number of parameters which can be set through the sub- *
480 * routine PDFSET had been extended to 20, *
481 * - more protections had been implemented and inconsistencies *
482 * had been corrected to make the package more robust, *
483 * and finally *
484 * - a subroutine PFTOPDG had been provided as an interface for *
485 * those users who prefer the flavour code convention of the PDG *
486 * instead of the PDFLIB format. *
487 * *
488 ******************************** - 7 - ********************************
4891***********************************************************************
490 * *
491 * 1. Introduction *
492 * *
493 * *
494 * The number of useful sets of parton density functions of the *
495 * NUCLEON available today is about 70 and is still growing. The ol- *
496 * der sets are leading order evolutions only, like *
497 * *
498 * - Buras and Gaemers (BEBC) [1], *
499 * - Owens and Reya (OR) [2], *
500 * - Baier, Engels and Petersson (BEP) [3], *
501 * - Gl"uck, Hoffmann and Reya (GHR) [4], *
502 * - Duke and Owens (DO) sets 1 and 2 [5], *
503 * - Eichten, Hinchliffe, Lane and Quigg (EHLQ) sets 1 and 2 [6], *
504 * - Diemoz, Ferroni, Longo and Martinelli (DFLM) with *
505 * Lambda_4(QCD) = 200 MeV for soft and hard valence quark and *
506 * soft and hard gluon distributions [7], and finally *
507 * - the new LO paramerisation of Owens set 1.1 (DO 1.1) [8]. *
508 * *
509 * Most of the sets, essentially the more recent ones, are *
510 * next-to-leading order evolutions, like *
511 * *
512 * - Diemoz, Ferroni, Longo and Martinelli (DFLM) with *
513 * Lambda_4(QCD) = 160, 260, 360 MeV [7], *
514 * - Martin, Roberts and Stirling (MRS) sets 1 to 3, sets E and B *
515 * and sets E' and B' [9], *
516 * - Harriman, Martin, Roberts and Stirling (HMRS) sets E, E+, E- *
517 * and B [10], *
518 * - Kwiecinski, Martin, Roberts and Stirling (KMRS) [11] sets B0 *
519 * and B-, and for the B- set with different radii for shadowing, *
520 * - Martin, Roberts and Stirling (MRS-B Lambda) [11] for the B0 *
521 * set also with different values of Lambda_4(QCD) = 135, 160, *
522 * 200 and 235 MeV, *
523 * - Martin, Roberts and Stirling (MRS) [12] sets S0, D0 and D- *
524 * as well as the upgraded KMRS set B0, all having u_bar not *
525 * equal to d_bar, *
526 * - Morfin and Tung (MT) sets 1 to 6 [13], *
527 * - Gl"uck, Reya and Vogt (GRV) [14] including their new para- *
528 * metrisation from August 1991, *
529 * - Aurenche et al. (ABFOW) [15], *
530 * - the upgraded Martin, Roberts and Stirling (MRS) [16] sets *
531 * S0', D0' and D-' in the MSbar renormalisation scheme and MRS(H)*
532 * - the upgraded Martin, Roberts and Stirling (MRS) [17] sets *
533 * S0', D0' and D-' in the DIS renormalisation scheme and MRS(H), *
534 * - the sets 1M, 1MS and 1ML in the MSbar and the set 1D in the *
535 * DIS renormalisation scheme of the CTEQ collaboration (CTEQ) *
536 * [18] in its parametrised form, *
537 * - the new sets A and B of Berger and Meng (BM) [19] with special *
538 * gluon distributions, and *
539 * - the new sets 2M, 2MS, 2MF and 2ML in the MSbar and the set 2D *
540 * in the DIS renormalisation scheme of the CTEQ collaboration *
541 * (CTEQ) [20] in its parametrised form which superseed already *
542 * the previous CTEQ sets 1M, 1MS, 1ML and 1D. The CTEQ collabo- *
543 * ration provides also parametrisations to leading order, the *
544 * sets 1L [18] and 2L [20]. *
545 * *
546 * *
547 * *
548 ******************************** - 8 - ********************************
5491***********************************************************************
550 * *
551 * There is also a limited number of parton density functions of *
552 * the PION available. These are the old set to leading order evolu- *
553 * tion of *
554 * *
555 * - Owens (OW-P) [21], sets 1 and 2, *
556 * *
557 * and the newer and the very new next-to-leading order evolutions of *
558 * *
559 * - Aurenche et al. (ABFKW-P) [22], sets 1, 2 and 3, *
560 * - Sutton, Martin, Roberts and Stirling (SMRS-P) [23], sets 1, 2 *
561 * and 3 and *
562 * - Gl"uck, Reya and Vogt (GRV-P) [24], the LO and NLL sets. *
563 * *
564 * In addition there are also a few parton density functions of *
565 * the PHOTON available. These are the old sets to leading order evo- *
566 * lution of *
567 * *
568 * - Duke and Owens (DO-G) (and the NLL) [25] using an asymptotic *
569 * solution of the Altarelli-Parisi equation, *
570 * - Drees and Grassie (DG-G) sets 1 to 4 [26] using a full solu- *
571 * tion of the Altarelli-Parisi equation, *
572 * *
573 * the new leading order evolution of *
574 * *
575 * - Abramowicz, Charchula and Levy (LAC-G) [27] sets 1 to 3 using *
576 * a full solution of the Altarelli-Parisi equation, *
577 * *
578 * and the new next-to-leading order evolution of *
579 * *
580 * - Gordon and Storrow (GS-G) [28], the LO sets 1 and 2 and the *
581 * NLL set, *
582 * - Gl"uck, Reya and Vogt (GRV-G) [29], the LO, NLL and the *
583 * leading term of the NLL sets, and *
584 * - Aurenche et al. (ACFGP-G) [30] sets 1 and 2, without and with *
585 * massive charm. *
586 * *
587 * The different sets differ also in the renormalisation scheme *
588 * they use. The DFLM series, the sets 1 to 6 of the MT series, the *
589 * new MRS sets S0', D0' and D-' and the new CTEQ sets 1D and 2D are *
590 * performed in the DIS renormalisation scheme [31]. If the LO evo- *
591 * lutions of these authors are ignored, all the other sets are *
592 * performed in the MS_bar renormalisation scheme. All sets are made *
593 * using four flavours in the initial state (NF = 4). The value of *
594 * the QCD scale factor, Lambda_4(QCD), ranges from 45 to 500 MeV. *
595 * *
596 * We have put together all these different sets of parton density *
597 * functions in one single package [32]. We have modified the sets *
598 * such that no external data files for the grids have to be read in *
599 * anymore. All these structure function sets have been combined in a *
600 * consistent way such that they all appear in an IDENTICAL STRUCTURE *
601 * to the user. The selection is made via THREE parameters, NPTYPE, *
602 * NGROUP and NSET, which identify a PDF set by its PARTICLE TYPE *
603 * (Nucleon: NPTYPE = 1, Pion: NPTYPE = 2, Photon: NPTYPE = 3), its *
604 * AUTHOR GROUP (f.ex. MRS: NGROUP = 3, CTEQ: NGROUP = 4, *
605 * GRV: NGROUP = 5) and its PDF SET WITHIN THE GROUP (NSET = 1,2,3 *
606 * etc.). It is also possible to select a PDF set by transferring *
607 * *
608 ******************************** - 9 - ********************************
6091***********************************************************************
610 * *
611 * only ONE parameter to PDFSET as before: this parameter should then *
612 * identify the NAME of the author group in an unequivocal way; the *
613 * selection of the PDF set within the author group is made by the *
614 * corresponding VALUE value (f.ex. PARM(1) = 'MRS' with VALUE(1) = *
615 * 29.0D0 would select the 29th set of the Nucleon PDFs of MRS, and *
616 * f.ex. PARM(1) = 'GRVph' with VALUE(1) = 1.0D0 would select the *
617 * first set of the Photon PDFs of GRV). As a suggestion, the NAME for*
618 * each PDF set can be found in the new COMMON block /W505110/SFNAME, *
619 * where SFNAME is a CHARACTER*8 array with dimension SFNAME(NPTYMX, *
620 * NGRMAX,NSETMX), and NPTYMX, NGRMAX, NSETMX are defined by the *
621 * parameter sequence, +SEQ, W5051P2. The parameters should be, *
622 * NPTYPE, NGROUP, NSET or the 'NAME' of the PDF set with their VALUE *
623 * values should be set with a call to the subroutine PDFSET at the *
624 * initialisation phase. A simple SUBROUTINE call, which is IDENTICAL *
625 * for all applications (nucleons, pions, photons) returns the parton *
626 * densities for all partons (u, d, s, c, b, t, gluon and their anti- *
627 * quarks) at a given X value (where X is the fraction of the longi- *
628 * tudinal momentum carried by the parton) and the Q-scale SCALE (in *
629 * GeV). A default set has been prepared, in which case it is suffi- *
630 * cient to transfer as the ONLY parameter PARM(1) = 'Nset' with *
631 * VALUE(1) = 0.0D0, although those preferring their own private set *
632 * or wanting to test a new one may do so within the package. Error *
633 * control can be obtained by setting a print flag to obtain output *
634 * either during execution and/or as a summary at job termination via *
635 * a call to the subroutine PDFSTA. In addition, the different parton *
636 * density sets have been modified such that the library can be used *
637 * on all the different computer systems known today. The library has *
638 * been tested on the different system areas to ensure identical re- *
639 * sults within the given machine precision. *
640 * *
641 * Within the same package a program is also provided to calculate *
642 * the strong coupling constant alpha(s) to second order (default) *
643 * or to first order (by user's choice). The correct Lambda(QCD) as- *
644 * sociated to the selected set of structure functions and the number *
645 * of allowed flavours with respect to the given Q**2 is automati- *
646 * cally used in the calculation. For those structure functions where *
647 * the evolution has been performed to leading order only, the *
648 * alpha(s) value to first order is returned. *
649 * *
650 * *
651 * *
652 * 2. The Structure Functions Package PDFLIB *
653 * *
654 * *
655 * In the following the use of and the access to the PDFLIB pack- *
656 * age is described. *
657 * *
658 * 2.1 Parameter Setting and Selection of Sets *
659 * *
660 * *
661 * The user may access his/her preferred set of structure func- *
662 * tions by setting the THREE parameters, NPTYPE, NGROUP and NSET, *
663 * which identify each set of parton density functions via a call *
664 * to the subroutine *
665 * *
666 * CALL PDFSET(PARM,VALUE) *
667 * *
668 ******************************* - 10 - ********************************
6691***********************************************************************
670 * *
671 * at the initialization phase of his/her MAIN program, or use the *
672 * package as a 'black box' with the default values (see below). The *
673 * arguments PARM and VALUE are vectors of dimension 20 and have the *
674 * following meaning *
675 * *
676 * PARM(I) = character*20 variable, which defines in any order *
677 * the variables *
678 * 'NPTYPE', 'NGROUP', 'NSET', 'MODE', 'INIT0', *
679 * 'NFL', 'LO', 'TMAS', 'QCDL4', 'QCDL5' and *
680 * 'XMIN', 'XMAX', 'Q2MIN', 'Q2MAX' *
681 * VALUE(I) = the corresponding numerical value of the variable *
682 * PARM(I) *
683 * (TMAS, QCDL4, QCDL5, XMIN, XMAX, Q2MIN and Q2MAX *
684 * are DOUBLE PRECISION variables), *
685 * *
686 * where *
687 * *
688 * NPTYPE = number of particle type ranging from 1 to 3 *
689 * (Nucleons: NPTYPE = 1, Pions: NPTYPE = 2 and *
690 * Photons: NPTYPE = 3) (Default: NPTYPE = 1) *
691 * NGROUP = number of author group ranging from 1 to 7 *
692 * (Default: NGROUP = 5) *
693 * NSET = number of a selected structure function set within *
694 * the author group ranging from 1 to 34 *
695 * (Default: NSET = 3) *
696 * (MODE = number of a selected structure function set ranging *
697 * from 0 to 281 - OLD format !!) *
698 * (Default: MODE = 45) *
699 * INIT0 = in case of PARM(1) = 'INIT0' PDFSET fills as the *
700 * only action the COMMON blocks /W505110/, /W505120/ *
701 * /W505121/ and /W505122/ *
702 * NFL = desired number of flavours in the alpha(s) calcula- *
703 * tion ranging from 3 to 6 *
704 * (Default: NFL = 5) *
705 * LO = order of alpha(s) calculation; if LO = 1, alpha(s) *
706 * to first order only *
707 * (Default: LO = 2) *
708 * TMAS = the user defined value of the top-quark mass in *
709 * GeV/c**2 (optional) *
710 * (Default: TMAS = 100.0D0) *
711 * QCDL4 = QCD scale, Lambda_4(QCD), in GeV for four flavours *
712 * QCDL5 = QCD scale, Lambda_5(QCD), in GeV for five flavours *
713 * corresponding to QCDL4 *
714 * *
715 * and *
716 * *
717 * XMIN = minimum allowed X value *
718 * XMAX = maximum allowed X value *
719 * Q2MIN = minimum allowed Q**2 value (in (GeV/c)**2) *
720 * Q2MAX = maximum allowed Q**2 value (in (GeV/c)**2) *
721 * *
722 * for each set of structure functions. *
723 * *
724 * If the user wants to select the default settings, it is suffi- *
725 * cient to give PARM(1) = 'Nset' with VALUE(1) = 0.0D0 as the ONLY *
726 * parameter to PDFSET. Please note that a PDF set may also be iden- *
727 * *
728 ******************************* - 11 - ********************************
7291***********************************************************************
730 * *
731 * tified by the NAME of the author group provided in an unequivocal *
732 * way. The selection of the PDF set within the author group is, in *
733 * that case, given by the corresponding VALUE value. The NAME for *
734 * each PDF set can be found in the COMMON block /W505110/SFNAME, *
735 * where SFNAME is a CHARACTER*8 array with dimension SFNAME(NPTYMX, *
736 * NGRMAX,NSETMX), and NPTYMX, NGRMAX, NSETMX are defined by the para-*
737 * meter sequence, +SEQ, W5051P2. Please also note that the variable *
738 * names can be transferred in lower, upper or mixed character modes. *
739 * *
740 * Please also note that PDFSET can be called as often as the user *
741 * likes. In order to redefine the parameters to select other sets of *
742 * structure functions which the user wants to investigate, it might *
743 * be necessary to call PDFSET in an alternating way, but it is al- *
744 * ways mandatory to transfer either the THREE parameters, NPTYPE, *
745 * NGROUP, NSET, or the 'NAME' of the author group with their corres- *
746 * ponding VALUE values. The subroutine PDFSET fills the internal *
747 * COMMON blocks *
748 * *
749 * COMMON/W50511/ NPTYPE,NGROUP,NSET,MODE,NFL,LO,TMAS *
750 * COMMON/W50512/ QCDL4,QCDL5 *
751 * COMMON/W50513/ XMIN,XMAX,Q2MIN,Q2MAX *
752 * *
753 * at the time the routine is called. Please note that in case of a *
754 * multiple call to PDFSET with fewer parameters redefined than in a *
755 * preceeding call, always the last parameters are kept in memory. *
756 * All variables of the three COMMON blocks can be automatically *
757 * printed at job initialisation by setting the print flag IFLPRT in *
758 * the COMMON block *
759 * *
760 * COMMON/W50510/ IFLPRT *
761 * *
762 * to IFLPRT = 2. *
763 * *
764 * *
765 * *
766 * 2.2 The Calling Sequence: PDFLIB Format *
767 * *
768 * *
769 * The main steering routine for a set of structure functions is *
770 * accessed as follows: *
771 * *
772 * CALL STRUCTM(X,SCALE,UPV,DNV,USEA,DSEA,STR,CHM,BOT,TOP,GL) *
773 * *
774 * Please note that all variables are defined as DOUBLE PRECISION. *
775 * The user has to provide the following INPUTs: *
776 * *
777 * X = X value of parton *
778 * SCALE = QCD scale in GeV *
779 * *
780 * The subroutine STRUCTM returns the following OUTPUT: *
781 * *
782 * UPV = up valence quark *
783 * DNV = down valence quark *
784 * USEA = sea (up_bar) *
785 * DSEA = sea (down_bar) *
786 * STR = strange quark *
787 * *
788 ******************************* - 12 - ********************************
7891***********************************************************************
790 * *
791 * CHM = charm quark *
792 * BOT = bottom quark *
793 * TOP = top quark *
794 * GL = gluon *
795 * *
796 * This steering routine has separate arguments for u_bar and *
797 * d_bar-quarks to take into account that some of the new sets of *
798 * nucleon density functions provide separately the densities for *
799 * u_bar and d_bar. In case u_bar is not given separately from d_bar *
800 * it is set USEA = DSEA. *
801 * *
802 * Please note that STRUCTM returns X * parton distribution *
803 * function ! *
804 * *
805 * An older version of the main steering routine
806 * *
807 * CALL STRUCTF(X,SCALE,UPV,DNV,SEA,STR,CHM,BOT,TOP,GL) *
808 * *
809 * is still available. Also here all variables are defined as *
810 * DOUBLE PRECISION. Please note that STRUCTF has only ONE argument *
811 * for the sea-quark, which gives u_bar = d_bar or (u_bar + d_bar)/2. *
812 * The user has to provide as above the following INPUTs: *
813 * *
814 * X = X value of parton *
815 * SCALE = QCD scale in GeV *
816 * *
817 * The subroutine STRUCTF returns the following OUTPUT: *
818 * *
819 * UPV = up valence quark *
820 * DNV = down valence quark *
821 * SEA = sea (up_bar = down_bar or (up_bar + down_bar)/2) *
822 * STR = strange quark *
823 * CHM = charm quark *
824 * BOT = bottom quark *
825 * TOP = top quark *
826 * GL = gluon *
827 * *
828 * Please note that also STRUCTF returns X * parton distribution *
829 * function ! *
830 * *
831 * A list of available sets of NUCLEON structure functions in the *
832 * package is given in Table 1. *
833 * *
834 * The recommended set of structure functions from the different *
835 * authors is indicated with a flash. If NSET is set to zero *
836 * (or if any of the three parameters, NPTYPE, NGROUP and NSET, is *
837 * undefined) a default set is selected which is a nucleon parton *
838 * dennsity set, the set of MRS (G) with Lambda_4(QCD) = 255 MeV *
839 * (NPTYPE = 1, NGROUP = 3, NSET = 41). *
840 * *
841 * *
842 * *
843 * *
844 * *
845 * *
846 * *
847 * *
848 ******************************* - 13 - ********************************
8491***********************************************************************
850 * *
851 * 2.3 The Calling Sequence: PDG Format *
852 * *
853 * *
854 * To allow the use of the package with the flavour code conven- *
855 * tion of the Particle Data Group (PDG) an interface has been writ- *
856 * ten which translates the PDFLIB format (see Section 2.2) into the *
857 * PDG format. Instead of calling the subroutine STRUCTM the user *
858 * preferring the flavour code convention of the PDG accesses the *
859 * package via a call to the subroutine *
860 * *
861 * CALL PFTOPDG(X,SCALE,DXPDF). *
862 * *
863 * All variables are defined as DOUBLE PRECISION as before, and *
864 * X and SCALE are INPUTs provided by the user having the same *
865 * meaning as above (see Section 2.2). *
866 * *
867 * The subroutine PFTOPDG outputs a vector DXPDF(-6:6) of which *
868 * its variables have the following meaning: *
869 * *
870 * DXPDF(0) = gluon *
871 * DXPDF(1) = sum of down valence + down_bar quark *
872 * DXPDF(2) = sum of up valence + up_bar quark *
873 * DXPDF(3) = strange quark *
874 * DXPDF(4) = charm quark *
875 * DXPDF(5) = bottom quark *
876 * DXPDF(6) = top quark *
877 * and DXPDF(-1) to DXPDF(-6) are the corresponding antiquarks. *
878 * *
879 * DXPDF(-1) = DXPDF(-2) stands for down_bar = up_bar or *
880 * (down_bar + up_bar)/2 in almost all parametrisations. In case *
881 * where u_bar is not equal to d_bar (like for the retracted MRS S0, *
882 * D0 and D- sets, the updated MRS S0', D0' and D-' in MS_bar and DIS *
883 * renormalisation scheme as well as the upgraded KMRS set B0 and one *
884 * of the MT series) DXPDF(-1) = d_bar and DXPDF(-2) = u_bar. In all *
885 * sets is DXPDF(3) = DXPDF(-3), DXPDF(4) = DXPDF(-4), *
886 * DXPDF(5) = DXPDF(-5) and DXPDF(6) = DXPDF(-6) so far. *
887 * *
888 * Please note that also PFTOPDG returns X * parton distribution *
889 * function ! *
890 * *
891 * *
892 * *
893 * 2.4 Error Handling *
894 * *
895 * *
896 * A note of caution should be addressed here. All structure *
897 * functions are limited in X and Q**2 which range for most of the *
898 * sets from *
899 * *
900 * 4 - 10 < Q**2 < 10**6 - 10**8 (GeV/c)**2 *
901 * 10**{-5} - 10**{-4} < X < 1. *
902 * *
903 * If the user wants to extend the X or Q**2 ranges, it is pos- *
904 * sible for some of the structure function sets, but the result *
905 * should be looked at with great caution. If in doubt, please check *
906 * with the authors of the structure function set. The program is *
907 * *
908 ******************************* - 14 - ********************************
9091***********************************************************************
910 * *
911 * protected against calculations of Q**2 values below Q2MIN (in this *
912 * case Q**2 = Q2MIN) and of X values in unphysical regions (X < 0 or *
913 * X > 1). The execution of the program is stopped in the later case. *
914 * *
915 * A COMMON block can be accessed *
916 * *
917 * COMMON/W50513/ XMIN,XMAX,Q2MIN,Q2MAX *
918 * *
919 * where *
920 * *
921 * XMIN = minimum allowed X value *
922 * XMAX = maximum allowed X value *
923 * Q2MIN = minimum allowed Q**2 value (in (GeV/c)**2) *
924 * Q2MAX = maximum allowed Q**2 value (in (GeV/c)**2) *
925 * *
926 * is given for each set of structure functions. To control how often *
927 * the X or Q**2 ranges have been exceeded during execution of the *
928 * user's program a call to the subroutine *
929 * *
930 * CALL PDFSTA *
931 * *
932 * at the termination phase of his/her MAIN program allows to print *
933 * a summary of these errors. If the COMMON block *
934 * *
935 * COMMON/W50514W/ PDFWGT *
936 * *
937 * where *
938 * *
939 * PDFWGT = weight *
940 * *
941 * is filled by the user on an event-to-event basis the statistics *
942 * in the error summary takes into account this weight. *
943 * *
944 * The print flag in the COMMON/W50510/IFLPRT may be set to *
945 * IFLPRT = 3 to print an error message EACH TIME a limit is exeeded *
946 * during job execution. Please note that setting this flag may pro- *
947 * duce an ENORMOUS AMOUNT of output! *
948 * *
949 * *
950 * *
951 * 2.5 Features *
952 * *
953 * *
954 * If NPTYPE = 1, NGROUP = 1 and NSET = 1, the user has the possi- *
955 * bility to use his/her own private set of structure functions *
956 * (i.e. CDHS effective structure functions could be inseted here, *
957 * or the user could implement a new set of structure functions for *
958 * testing purposes). To insert the private set the DUMMY subroutine *
959 * *
960 * SUBROUTINE STRPRIV(X,SCALE,UPV,DNV,USEA,DSEA,STR,CHM,BOT,TOP,GL) *
961 * *
962 * should be activated by the user. All variables have to be defined *
963 * as DOUBLE PRECISION. The variables have the same meaning as des- *
964 * cribed for the subroutine STRUCTM in Section 2.2 (for explanations *
965 * see there). *
966 * *
967 * *
968 ******************************* - 15 - ********************************
9691***********************************************************************
970 * *
971 * For the calculation of the strong coupling constant alpha(s) *
972 * (see Section 3) with the user's private set of structure functions *
973 * the user should provide a value for the variables QCDL4 and QCDL5 *
974 * via the subroutine PDFSET at the initialization phase. In fact, *
975 * because only the parameter QCDL5 is used in the alpha(s) calcul- *
976 * ation, only this definition is mandatory. *
977 * *
978 * *
979 * *
980 * 2.6 PION Structure Functions *
981 * *
982 * *
983 * All the available sets of structure functions of the PION have *
984 * been added to the package as well: *
985 * *
986 * *
987 * - the old Owens (OW-P) sets 1 and 2 [21], *
988 * - the newer sets 1 to 3 of Aurenche et al. (ABFKW-P) [22], *
989 * - the very new Sutton, Martin, Roberts and Stirling (SMRS-P) *
990 * sets 1 to 3 [23] and *
991 * - the very new Gl"uck, Reya and Vogt (GRV-P) [24] sets of LO *
992 * and NLL calculations. *
993 * *
994 * The calling sequence to the pion set of structure functions is *
995 * kept identical to those described in Section 2.2 for the nucleon *
996 * structure fuctions. It can be either *
997 * *
998 * CALL STRUCTM(X,SCALE,UPV,DNV,USEA,DSEA,STR,CHM,BOT,TOP,GL) *
999 * *
1000 * or *
1001 * *
1002 * CALL PFTOPDG(X,SCALE,DXPDF) *
1003 * *
1004 * or the old version of the main steering routine *
1005 * *
1006 * CALL STRUCTF(X,SCALE,UPV,DNV,SEA,STR,CHM,BOT,TOP,GL) *
1007 * *
1008 * where, as before, the INPUTs are to be provided by the user in *
1009 * DOUBLE PRECISION. The OUTPUT has the same definitions as before *
1010 * (see Section 2.2). In case of the pion structure functions it is *
1011 * also returned X * parton distribution function with *
1012 * UPV = DNV, SEA = STR (USEA = DSEA = STR) and TOP = 0 *
1013 * (DXPDF(1) = DXPDF(2), DXPDF(3) = DXPDF(-1) = DXPDF(-2) and *
1014 * DXPDF(6) = 0). *
1015 * *
1016 * A list of available sets of PION structure functions in the *
1017 * package is given in Table 2. *
1018 * *
1019 * *
1020 * *
1021 * *
1022 * *
1023 * *
1024 * *
1025 * *
1026 * *
1027 * *
1028 ******************************* - 16 - ********************************
10291***********************************************************************
1030 * *
1031 * 2.7 PHOTON Structure Functions *
1032 * *
1033 * *
1034 * In the previous version, all the available sets of structure *
1035 * functions of the PHOTON have been added to the package as well, *
1036 * *
1037 * - the old Duke and Owens (DO-G) LO and NLL sets [25], *
1038 * - the old Drees and Grassie (DG-G) sets 1 to 4 [26], *
1039 * - the new Abramowicz, Charchula and Levy (LAC-G) [27] *
1040 * sets 1 to 3, *
1041 * - the new Gordon and Storrow (GS-G) [28] sets, the LO sets 1 *
1042 * and 2 and the NLL set, *
1043 * - the new Gl"uck, Reya and Vogt (GRV-G) [29] sets, the LO, NLL *
1044 * and the leading term of the NLL calculations, and *
1045 * - the new Aurenche et al. (ACFGP-G) [30] NLL sets 1 and 2, *
1046 * without and with massive charm. *
1047 * *
1048 * The calling sequence to the photon set of structure functions *
1049 * is also kept identical to those described in Section 2.2 for the *
1050 * nucleon structure fuctions. It can be either *
1051 * *
1052 * CALL STRUCTM(X,SCALE,UPV,DNV,USEA,DSEA,STR,CHM,BOT,TOP,GL) *
1053 * *
1054 * or *
1055 * *
1056 * CALL PFTOPDG(X,SCALE,DXPDF) *
1057 * *
1058 * or the old version of the main steering routine *
1059 * *
1060 * CALL STRUCTF(X,SCALE,UPV,DNV,SEA,STR,CHM,BOT,TOP,GL) *
1061 * *
1062 * where, as before, the INPUTs are to be provided by the user in *
1063 * DOUBLE PRECISION. The OUTPUT has the same definitions as before *
1064 * (see Section 2.2). In case of the photon structure functions it *
1065 * is also returned X * parton distribution function (note that the *
1066 * alpha(QED) has to be taken care of by the user !) with UPV = USEA, *
1067 * DNV = DSEA and TOP = 0 (DXPDF(1) = 2 * DXPDF(-1), DXPDF(2) = *
1068 * 2 * DXPDF(-2), as a result of the definitions - see Section 2.3 -, *
1069 * and DXPDF(6) = 0), while all the other quarks are set identical to *
1070 * their antiquark densities. *
1071 * *
1072 * A list of available sets of PHOTON structure functions in the *
1073 * package is given in Table 3. *
1074 * *
1075 * *
1076 * *
1077 * *
1078 * *
1079 * *
1080 * *
1081 * *
1082 * *
1083 * *
1084 * *
1085 * *
1086 * *
1087 * *
1088 ******************************* - 17 - ********************************
10891***********************************************************************
1090 * *
1091 * 2.8 How to find PDFLIB *
1092 * *
1093 * *
1094 * At CERN the PDFLIB library and corresponding documentation are *
1095 * available on all systems in the standard areas. *
1096 * *
1097 * System Library Documentation *
1098 * *
1099 * CERNVM PDFLIB TXTLIB Q PDFLIB DOC Q *
1100 * VXCERN CERN:[PRO.LIB]PDFLIB.OLB CERN:[PRO.DOC]PDFLIB.PS *
1101 * Unix /cern/pro/lib/libpdflib.a /cern/pro/doc/pdf.ps *
1102 * systems *
1103 * *
1104 * The package may be accessed via the CERNLIB command: *
1105 * *
1106 * CERNLIB PDFLIB *
1107 * *
1108 * *
1109 * Whenever you use this program, please give reference to the *
1110 * following papers: *
1111 * *
1112 * H. Plothow-Besch, 'PDFLIB: a library of all available parton *
1113 * density functions of the nucleon, the pion and the photon *
1114 * and the corresponding alpha(s) calculations', *
1115 * Comp. Phys. Comm. 75 (1993) 396-416. *
1116 * *
1117 * and/or *
1118 * *
1119 * H. Plothow-Besch, 'PDFLIB: Structure Functions and *
1120 * alpha_s Calculations', User's Manual - Version 1.00, *
1121 * W5051 PDFLIB, 1991.03.21, CERN-PPE. *
1122 * *
1123 * and/or *
1124 * *
1125 * H. Plothow-Besch, 'PDFLIB: Nucleon, Pion and Photon Parton *
1126 * Density Functions and alpha_s Calculations', *
1127 * User's Manual - Version 6.06, W5051 PDFLIB, 1995.03.15, *
1128 * CERN-PPE. *
1129 * *
1130 * *
1131 * *
1132 * 3. alpha(s) Calculation *
1133 * *
1134 * *
1135 * Within the same package a program is provided to calculate the *
1136 * strong coupling constant alpha(s) to second order as a function *
1137 * of Lambda(QCD) of five flavours and the desired number of fla- *
1138 * vours (NFL) for the selected set of structure functions, which *
1139 * fixes Lambda(QCD). The formula on which the calculations are *
1140 * based upon can be found in Ref. [33]. The same three parameters, *
1141 * NPTYPE, NGROUP and NSET, which select a structure function set, *
1142 * is used to steer the calculation of the alpha(s) value at a given *
1143 * scale from the Lambda(QCD) defined in the selected PDF set. *
1144 * *
1145 * The value of alpha(s) is matched at the thresholds q = m_q. *
1146 * When invoked with NFL < 0, it chooses NFL as the number of fla- *
1147 * *
1148 ******************************* - 18 - ********************************
11491***********************************************************************
1150 * *
1151 * vours for which the masses are less then q. For the quark masses *
1152 * where thresholds are changed the following values have been used: *
1153 * m_charm = 1.5 GeV/c**2, m_bottom = 4.75 GeV/c**2 and *
1154 * m_top = 100 GeV/c**2. *
1155 * *
1156 * The alpha(s) value can be obtained via a call to: *
1157 * *
1158 * FUNCTION ALPHAS2(SCALE) *
1159 * *
1160 * The user has to provide the following INPUT: *
1161 * *
1162 * SCALE = QCD scale in GeV *
1163 * *
1164 * The function ALPHAS2 returns the following OUTPUT: *
1165 * *
1166 * ALPHAS2 = alpha strong to second order, *
1167 * *
1168 * if LO not equal to one. For those structure functions, for which *
1169 * the evolution is done to leading order only, alpha(s) to first *
1170 * order is returned. *
1171 * *
1172 * The same subroutine *
1173 * *
1174 * SUBROUTINE PDFSET(PARM,VALUE) *
1175 * *
1176 * as described in Section 2.1 should be used to change the default *
1177 * values of the variables NPTYPE, NGROUP, NSET, NFL, LO, TMAS, *
1178 * QCDL4, QCDL5, XMIN, XMAX, Q2MIN and Q2MAX. *
1179 * *
1180 * The internal COMMON block *
1181 * *
1182 * COMMON/W50512/ QCDL4,QCDL5 *
1183 * *
1184 * where *
1185 * *
1186 * QCDL4 = QCD scale, Lambda_4(QCD), in GeV for four flavours *
1187 * QCDL5 = QCD scale, Lambda_5(QCD), in GeV for five flavours *
1188 * corresponding to QCDL4 *
1189 * *
1190 * provides the actual value of Lambda_4(QCD) and Lambda_5(QCD) used *
1191 * in the alpha(s) calculation for four and five flavours, respectiv- *
1192 * ly, for each set of structure functions. *
1193 * *
1194 * *
1195 * *
1196 * 4. Conclusions *
1197 * *
1198 * *
1199 * In the Long Write-up as an example, the NUCLEON structure *
1200 * function distributions at the scale Q**2 = m_W**2 for u and d va- *
1201 * lence quarks as well as for the sea and gluon contributions are *
1202 * shown in Figs. 1 to 4 respectively, as a function of the parton X. *
1203 * The average X values for CERN and FNAL as well as for LHC and SSC *
1204 * energies at that scale are indicated. Please, note the logarithmic *
1205 * scale for the gluon distribution. The d/u ratio of the valence *
1206 * quarks is shown in Fig. 5. It can be seen from all these figures *
1207 * *
1208 ******************************* - 19 - ********************************
12091***********************************************************************
1210 * *
1211 * these figures that there is a large spread in shape for the dif- *
1212 * ferent sets in all contributions leading to different results in *
1213 * the cross section calculations. It should be pointed out that the *
1214 * spread from the different parametrisations in the SAME renormali- *
1215 * sation scheme is MUCH LARGER than the spread from parametrisations *
1216 * in different renormalisation schemes. This is true for ALL parton *
1217 * densities, and in particular at small X values ! *
1218 * *
1219 * A comparison to recent data is shown in Fig. 6, where the ratio *
1220 * F_2(n)/F_2(p) at Q**2 = m_W**2 is displayed. This ratio mainly re- *
1221 * flects the d/u ratio of valence quarks which is the dominant un- *
1222 * certainty of the W and Z boson cross section ratio in pp or pp_bar *
1223 * reactions at lower energies. In fact, the older sets of structure *
1224 * functions, namely the set of Owens and Reya [2] and the set of *
1225 * Baier et al. [3] have only been implemented for completeness. *
1226 * These sets should not be used for cross section calculations of *
1227 * any hard processes at high energies anymore. From Fig. 6 we con- *
1228 * clude that also the other older sets of structure functions, *
1229 * namely the two sets of Duke and Owens [5] and the two sets of *
1230 * Eichten et al. [6] should be used with some care, because they do *
1231 * not fit the recent low energy deep-inelastic lepton-nucleon data *
1232 * from NMC and BCDMS [34]. This is not surprising because these data *
1233 * were not available when the sets have been made. The new set of *
1234 * DO 1.1 superseeds the old DO sets 1 and 2 but still gives very *
1235 * limited results in the low X region, even though data are avai- *
1236 * lable there. (Please note that the last data point at the lowest *
1237 * X value shown in Fig. 6 is out of range in Q**2 for all sets of *
1238 * structure functions and that the point before last is very much at *
1239 * the limit of the allowed range). *
1240 * *
1241 * In Fig. 7 the F_2(p) distribution of the recent data from Ref. *
1242 * [35] at Q**2 = 5 GeV**2, together with the very recent data at *
1243 * Q**2 = 15 GeV**2 from the H1 and the ZEUS experiments [36] at the *
1244 * the ep-collider HERA is shown as a function of X. Overlayed on the *
1245 * same Figure are a few theoretical predictions of more recent par- *
1246 * ton parametrisations [12,13,14,15,16,20] at Q**2 = 15 GeV**2. *
1247 * Please note that most of these parametrisations are NOT real pre- *
1248 * dictions because the data are fully or partially used in the fits. *
1249 * Apart from Ref. [13] set B2, from Ref. [14] set HO, from Ref. [16] *
1250 * set D-' and (H) and from Ref. [20] the new set 2pM, most of these *
1251 * more recent parametrisations fail to describe well enough the low *
1252 * X behaviour of the present data. *
1253 * *
1254 * From Figs. 6 and 7 we conclude that the recent sets of parton *
1255 * densities, nameley the GRV set HO [14], but also the old MT set *
1256 * B2 [13] - both sets are real predictions -, and the updated MRS *
1257 * set (H) [16], could be preferred for all theoretical predictions *
1258 * involving structure functions, because they fit the present data *
1259 * best which, at the moment, still suffer from large uncertainties. *
1260 * *
1261 * As an example, the u_bar, strange and gluon densities for the *
1262 * different sets of structure functions of the PHOTON are shown in *
1263 * Figs. 7, 8 and 9 of the Long Write-up, respectively, as a function *
1264 * of X at the scale Q**2 = 100 (GeV/c)**2. In Fig. 10 a comparison *
1265 * of F_2(gamma)/alpha(QED) as a function of X at Q**2 = 100 (GeV/c)**2
1266 * for the different photon structure function sets is made. The *
1267 * *
1268 ******************************* - 20 - ********************************
12691***********************************************************************
1270 * *
1271 * charm quark density has been taken into account. The theoretical *
1272 * predictions are compared with experimental data from the JADE *
1273 * experiment [37] at the same Q**2 value. Because of the large *
1274 * experimental uncertainties no distinction between the *
1275 * different parton density sets can be made yet. *
1276 * *
1277 * Coming new sets of structure functions could and should be *
1278 * easily implemented in this package. Authors of new sets are kindly *
1279 * requested to provide us with the relevant information. *
1280 * *
1281 * Please return any problems, questions, suggestions for im- *
1282 * provements to the author of the package *
1283 * (e-mail address: PLOTHOW@CERNVM.CERN.CH). *
1284 * *
1285 * Requests for the Long Write-up of the User's Manual can be ad- *
1286 * dressed either to the author or to the CERN Program Library Office.*
1287 * *
1288 * *
1289 * *
1290 * *
1291 * *
1292 * *
1293 * 5. Acknowledgements *
1294 * *
1295 * *
1296 * The author of the package would like to thank *
1297 * M.A. Marquina/CERN-CN for help and support making this package *
1298 * available to the Physics community as part of the CERN Program *
1299 * Library. In addition we give many thanks to G. Folger/CERN-CN and *
1300 * I. McLaren/CERN-CN for thoroughly testing out the package on the *
1301 * different system areas. *
1302 * *
1303 * We also would like to thank J.M. Marraffino/FNAL for the help- *
1304 * ful comments and the correction set which he supplied. *
1305 * *
1306 * And finally we acknowledge K. Charchula/DESY who provided the *
1307 * source code of some of the photon structure functions which had *
1308 * previously been implemented in the package. *
1309 * *
1310 * *
1311 * *
1312 * *
1313 * *
1314 * *
1315 * *
1316 * *
1317 * *
1318 * *
1319 * *
1320 * *
1321 * *
1322 * *
1323 * *
1324 * *
1325 * *
1326 * *
1327 * *
1328 ******************************* - 21 - ********************************
13291***********************************************************************
1330 * *
1331 * Appendix A *
1332 * *
1333 * *
1334 * As an example how to use the package, the FORTRAN code to ob- *
1335 * tain Fig. 1 of the Long Write-up which shows the parton density *
1336 * function distributions for the up valence quark as a function of *
1337 * the parton X for all sets of structure functions is given below: *
1338 * *
1339 * PROGRAM PDFUPV *
1340 * C define the maximum number of PDF sets, the name and the cross reference
1341 * PARAMETER (NPTYMX = 3, NGRMAX = 8, NSETMX = 41) *
1342 * COMMON /W505120/ NPGSMX(NPTYMX,NGRMAX),NSETFL(NPTYMX,NGRMAX,NSETMX)
1343 * CHARACTER*8 SFNAME(NPTYMX,NGRMAX,NSETMX) *
1344 * COMMON /W505110/ SFNAME *
1345 * COMMON /W505122/ MODECR(NPTYMX,NGRMAX,NSETMX) *
1346 * C define HBOOK settings *
1347 * PARAMETER (NHBMEM = 500000) *
1348 * COMMON /PAWC/ HMEM(NHBMEM) *
1349 * PARAMETER (NB=900, ID=100) *
1350 * C define DOUBLE PRECISION variables for calling sequence to STRUCTM
1351 * DOUBLE PRECISION DX,DSCALE,DUPV,DDNV,DUSEA,DDSEA,DSTR,DCHM,DBOT,DTOP,DGL
1352 * DOUBLE PRECISION ALF,ALPHAS2 *
1353 * REAL X, SCALE, UPV, DNV, USEA, DSEA, STR, CHM, BOT, TOP, GL *
1354 * COMMON/W50516/ FIRST *
1355 * LOGICAL FIRST *
1356 * CHARACTER*20 PARM(20) *
1357 * DOUBLE PRECISION VAL(20) *
1358 * DATA SCALE/80.140/ *
1359 * DATA X00/0.002/,DX0/0.001/,XLOW/0.0015/,XUP/0.9015/ *
1360 * C *
1361 * CALL HLIMIT(NHBMEM) *
1362 * DSCALE=SCALE *
1363 * C first call to PDFSET to initialize COMMON/W505120/ *
1364 * PARM(1) = 'Init0' *
1365 * VAL(1) = 0.D0 *
1366 * CALL PDFSET(PARM,VAL) *
1367 * C loop over all existing sets of Nucleon structure functions (SF) *
1368 * NPTYPE = 1 *
1369 * NHB = 0 *
1370 * DO 20 IGR = 1,NGRMAX *
1371 * IF(NPGSMX(NPTYPE,IGR).EQ.0) GOTO 20 *
1372 * DO ISET = 1,NPGSMX(NPTYPE,IGR) *
1373 * C book histograms for each set of SF separately *
1374 * NHB = NHB + 1 *
1375 * CALL HBOOK1(ID+NHB,'U Valence quark ',NB,XLOW,XUP,0.) *
1376 * C force label printing for each set of SF (not only the 1st) *
1377 * FIRST = .TRUE. *
1378 * C define and set parameters *
1379 * PARM(1) = 'Nptype' *
1380 * VAL(1) = NPTYPE *
1381 * PARM(2) = 'Ngroup' *
1382 * VAL(2) = IGR *
1383 * PARM(3) = 'Nset' *
1384 * VAL(3) = ISET *
1385 * CALL PDFSET(PARM,VAL) *
1386 * *
1387 * *
1388 ******************************* - 22 - ********************************
13891***********************************************************************
1390 * *
1391 * Example of Fig. 1, cont'd *
1392 * *
1393 * C loop over all X bins *
1394 * DO 10 I=1,NB *
1395 * X = X00 + (I-1)*DX0 *
1396 * DX = X *
1397 * IF(X.LT.XLOW .OR. X.GT.XUP) GOTO 10 *
1398 * CALL STRUCTM(DX,DSCALE,DUPV,DDNV,DUSEA,DDSEA,DSTR,DCHM,DBOT,DGL)
1399 * UPV=DUPV *
1400 * IF(X.GT.0.499 .AND. X.LE.0.500) WRITE(6,1000) X,SCALE,UPV *
1401 * 1000 FORMAT(/,' X= ',F6.4,' Q= ',F6.3,' UPV= ',8.4) *
1402 * CALL HF1(ID+NHB,X,UPV) *
1403 * 10 CONTINUE *
1404 * C get alpha(s) for selected set of SF at Q = SCALE *
1405 * ALF = ALPHAS2(DSCALE) *
1406 * WRITE(6,4000) NPTYPE,IGR,ISET,SFNAME(NPTYPE,IGR,ISET), *
1407 * + MODECR(NPTYPE,IGR,ISET),NSF *
1408 * WRITE(6,4001) DSCALE,ALF *
1409 * 4000 FORMAT(/,' Nptype = ',I1,' Ngroup = ',I1,' Nset = ',I2, *
1410 * + ' Name = "'A8,'" CrMode = ',I3,' HBId = ',I3) *
1411 * 4001 FORMAT(1H ,' SCALE = ',F8.4,' alpha(s) = ',F6 *
1412 * C get error summary for each set of SF *
1413 * CALL PDFSTA *
1414 * ENDDO *
1415 * 20 CONTINUE *
1416 * STOP *
1417 * *
1418 * *
1419 * *
1420 * *
1421 * *
1422 * *
1423 * *
1424 * *
1425 * *
1426 * *
1427 * *
1428 * *
1429 * *
1430 * *
1431 * *
1432 * *
1433 * *
1434 * *
1435 * *
1436 * *
1437 * *
1438 * *
1439 * *
1440 * *
1441 * *
1442 * *
1443 * *
1444 * *
1445 * *
1446 * *
1447 * *
1448 ******************************* - 23 - ********************************
14491***********************************************************************
1450 * *
1451 * This code will produce the following output: *
1452 * *
1453 * *
1454 * 1. HBOOK Output : *
1455 * *
1456 * one histogram for each set of structure functions. The histo- *
1457 * gram output has then been accessed, and each histogram has been *
1458 * superimposed on one single frame using the PAW package [38] to *
1459 * obtain Fig. 1 of the Long Write-up. *
1460 * *
1461 * *
1462 * 2. Print Output (Example is given for NPTYPE = 1, *
1463 * NGROUP = 3, NSET = 41 only : *
1464 * *
1465 * ___________________________________________________________________ *
1466 *| |*
1467 *| 1***** PDFLIB Version: 6.06 Released on 950315 at 17.05 in |*
1468 *| the CERN Program Library W5051 ***** |*
1469 *| ***** Library compiled on 950315 at 2337 ***** |*
1470 *| |*
1471 *| Nucleon PDFs: Ngroup = 3, Nset = 41, for MRS Set (G) (L255-MSb)|*
1472 *| ------------------------------------------------------------------|*
1473 *| Structure Functions |*
1474 *| ------------------- |*
1475 *| |*
1476 *| X= 0.5000 Q= 80.140 UPV= 0.1176 |*
1477 *| |*
1478 *| Nptype = 1 Ngroup = 3 Nset = 41 Name = "MRS-G " CrMode = -1 HBId = 60
1479 *| Scale = 80.1400 alpha(s) = 0.1154 |*
1480 *| |*
1481 *| PDFLIB : Summary from PDFSTA |*
1482 *| Nptype = 1 Ngroup = 3 Nset = 41 Name = "MRS-G " CrMode = -1|*
1483 *| Nfl = -5 LO = 2 Tmas = 180.00 GeV/c**2 |*
1484 *| QCDL4 = 0.2550 GeV, QCDL5 = 0.1708 GeV |*
1485 *| Xmin = 0.10E-04, Xmax = 0.99999E+00, Q2min = 5.000 (GeV/c)**2,
1486 *| Q2max = 0.27E+10 (GeV/c)**2 |*
1487 *| |*
1488 *| PDFSTA: NO errors occured |*
1489 *|___________________________________________________________________|*
1490 * *
1491 * *
1492 * Apart from the two top lines the print output shown above is *
1493 * repeated for each set of structure functions. *
1494 * *
1495 * *
1496 * *
1497 * *
1498 * *
1499 * *
1500 * *
1501 * *
1502 * *
1503 * *
1504 * *
1505 * *
1506 * *
1507 * *
1508 ******************************* - 24 - ********************************
15091***********************************************************************
1510 * *
1511 * Appendix B *
1512 * *
1513 * *
1514 * A list of subroutines, functions, COMMON blocks and parameters *
1515 * of RELEVANCE to the user which are used in PDFLIB is given below: *
1516 * *
1517 * *
1518 * List of relevant subprograms and COMMON blocks in PDFLIB: *
1519 * *
1520 * _________________________________________________________________ *
1521 * | | *
1522 * | (S = Subroutine, F = Function, C = COMMON, P = Parameter) | *
1523 * | | *
1524 * | ------------------------------------------------------------- | *
1525 * | | *
1526 * | S PDFSET : to set all parameters for PDFLIB | *
1527 * | S STRUCTF : to access PDFLIB with output in PDFLIB format | *
1528 * | S STRUCTM : to access PDFLIB with output in PDFLIB format | *
1529 * | (with u_bar not equal to d_bar) | *
1530 * | S PFTOPDG : to access PDFLIB with output in PDG format | *
1531 * | S PDFSTA : to print summary of parameters and error statistics
1532 * | F ALPHAS2 : to calculate alpha(s) to second order QCD | *
1533 * | | *
1534 * | C W50510 : IFLPRT - to set print flag | *
1535 * | C W50511 : NPTYPE,NGROUP,NSET,MODE,NFL,LO,TMAS | *
1536 * | - to select a structure function set, to | *
1537 * | define number of flavours, flag for leading | *
1538 * | order and value for the mass of the top quark | *
1539 * | C W50512 : QCDL4,QCDL5 - contains Lambda_4(QCD) and | *
1540 * | Lambda_5(QCD) (in GeV) | *
1541 * | C W50513 : XMIN,XMAX,Q2MIN,Q2MAX - contains minimum and | *
1542 * | maximum values of X and Q**2 | *
1543 * | C W50516 : FIRST - to force printing name of structure | *
1544 * | function set in case of multiple choices | *
1545 * | C W50519 : NEWVER - flags NEW/OLD version of PDFLIB format| *
1546 * | C W505110 : SFNAME - contains NAME (CHARACTER*8 array with | *
1547 * | dimension SFNAME(NPTYMX,NGRMAX,NSETMX)) for | *
1548 * | each set of PDFs | *
1549 * | C W505120 : NPGSMX(NPTYMX,NGRMAX),NSETFL(NPTYMX,NGRMAX,NSETMX)*
1550 * | - contains maximum number of stucture functions| *
1551 * | per particle type and author group, and FLAG | *
1552 * | for retracted PDF set (NSETFL(I,J,K) = 0), | *
1553 * | C W505121 : NPTYCR(MODEMX),NGROCR(MODEMX),NSETCR(MODEMX) | *
1554 * | - cross reference to the NPTYPE, NGROUP and | *
1555 * | NSET value (NEW format) for a given MODE | *
1556 * | value (OLD format) | *
1557 * | C W505122 : MODECR(NPTYMX,NGRMAX,NSETMX) - cross reference | *
1558 * | to the MODE value (OLD format) for a given | *
1559 * | NPTYPE, NGROUP and NSET value (NEW format) | *
1560 * | P W5051P2 : MODEMX - maximum number of structure function | *
1561 * | sets in the OLD PDFLIB format | *
1562 * | : NPTYMX,NGRMAX,NSETMX - maximum number of | *
1563 * | structure function sets in the NEW PDFLIB | *
1564 * | format for particle type, author group number | *
1565 * | and number of sets within an author group | *
1566 * | P W5051P7 : L6 - to define logical print unit number | *
1567 * |_______________________________________________________________| *
1568 ******************************* - 25 - ********************************
15691***********************************************************************
1570 * *
1571 * Appendix C *
1572 * *
1573 * *
1574 * A complete list of subroutines, functions, COMMON blocks and *
1575 * parameters which are used in PDFLIB is given below: *
1576 * *
1577 * *
1578 * Complete list of subprograms and COMMON blocks in PDFLIB: *
1579 * (in alphabetical order) *
1580 * *
1581 * _________________________________________________________________ *
1582 * | | *
1583 * | (S = Subroutine, F = Function, C = COMMON, P = Parameter) | *
1584 * | | *
1585 * | ------------------------------------------------------------- | *
1586 * | | *
1587 * | S ABFKW1 : ABFKW SF set 1 in the pion (NP=2,NG=6,NS=1) | *
1588 * | S ABFKW2 : ABFKW SF set 2 in the pion (NP=2,NG=6,NS=2) | *
1589 * | S ABFKW3 : ABFKW SF set 3 in the pion (NP=2,NG=6,NS=3) | *
1590 * | S ACFGP1 : ACFGP SF set 1 in the photon (NP=3,NG=6,NS=1) | *
1591 * | S ACFGP2 : ACFGP SF set 1 in the photon (mc) (NP=3,NG=6,NS=2)*
1592 * | F AFCPLU : to get PD with massive charm for ACFGP | *
1593 * | F AFGETFV : to interpolate PDs in grid for ACFGP | *
1594 * | F AFPOLIN : to interpolate PDs in grid for ACFGP | *
1595 * | F AFRATIN : to interpolate PDs in grid for ACFGP | *
1596 * | F ALPHAS2 : to calculate alpha(s) to second order QCD | *
1597 * | F AUGETFV : to interpolate logarithmically PDs in grid | *
1598 * | S AURGAM : to get the PDs in the photon for ACFGP-G | *
1599 * | S AURPI1 : to get the PDs in the pion for ABFKW-P set 1 | *
1600 * | S AURPI2 : to get the PDs in the pion for ABFKW-P set 2 | *
1601 * | S AURPI3 : to get the PDs in the pion for ABFKW-P set 3 | *
1602 * | S AURPR : to get the PDs in the nucleon for ABFOW | *
1603 * | F BBETA : DOUBLE PRECISION beta function using DGAMMA | *
1604 * | F BETA : SINGLE PRECISION beta function using GAMMA | *
1605 * | S BXF3 : BEP SF set for up and down valence quarks | *
1606 * | S BXGLUE : BEP SF set for gluons | *
1607 * | S BXQBAR : BEP SF set for antiquarks | *
1608 * | F CTQ1PD : CTEQ SF sets 1M, 1MS, 1ML, 1D and 1L | *
1609 * | F CTQ1PF : Description of CTEQ sets 1M, 1MS, 1ML, 1D, 1L | *
1610 * | F CTQ2OPD : CTEQ SF sets 2M, 2MS, 2ML, 2D and 2L | *
1611 * | F CTQ2OPF : Description of CTEQ sets 2M, 2MS, 2ML, 2D, 2L | *
1612 * | S CTQ2OPS : CTEQ SF sets 2M, 2MS, 2ML, 2D and 2L | *
1613 * | F CTQ2PPD : CTEQ SF sets 2pM, 2pMS, 2pML, 2pD and 2pL | *
1614 * | F CTQ2PPF : Description of CTEQ sets 2pM, 2pMS, 2pML, 2pD, 2pL*
1615 * | S CTQ2PPS : CTEQ SF sets 2pM, 2pMS, 2pML, 2pD and 2pL | *
1616 * | F DBFINT : to interpolate linearly PDs in grid (double precision)
1617 * | S DFLM1 : interface to DFLM 160 (NP=1,NG=2,NS=7) | *
1618 * | S DFLM2 : interface to DFLM 260 (NP=1,NG=2,NS=8) | *
1619 * | S DFLM3 : interface to DFLM 360 (NP=1,NG=2,NS=9) | *
1620 * | S DFLM4 : interface to DFLM soft valence quarks (NP=1,NG=2,NS=1)
1621 * | S DFLM5 : interface to DFLM hard valence quarks (NP=1,NG=2,NS=2)
1622 * | S DFLM6 : interface to DFLM soft gluons (NP=1,NG=2,NS=3) | *
1623 * | S DFLM7 : interface to DFLM hard gluons (NP=1,NG=2,NS=4) | *
1624 * | S DFLM8 : interface to DFLM LO average fit (NP=1,NG=2,NS=5) *
1625 * | S DFLM9 : interface to DFLM NLL average fit (NP=1,NG=2,NS=6)*
1626 * | S DGPHO1 : DG SF set 1 in the photon (NP=3,NG=2,NS=1) | *
1627 * |_______________________________________________________________| *
1628 ******************************* - 26 - ********************************
16291***********************************************************************
1630 * _________________________________________________________________ *
1631 * | Complete list of subprograms, cont'd | *
1632 * | | *
1633 * | S DGPHO2 : DG SF set 2 in the photon (NP=3,NG=2,NS=2) | *
1634 * | S DGPHO3 : DG SF set 3 in the photon (NP=3,NG=2,NS=3) | *
1635 * | S DGPHO4 : DG SF set 4 in the photon (NP=3,NG=2,NS=4) | *
1636 * | S DOPHO1 : DO SF set 1 in the photon (NP=3,NG=1,NS=1) | *
1637 * | S DOPHO2 : DO SF set 2 in the photon (NP=3,NG=1,NS=2) | *
1638 * | S FXAVER : DFLM SF set of LO central average fit | *
1639 * | S FXG160 : DFLM SF set of NLL with QCDL4 = 160 | *
1640 * | S FXG260 : DFLM SF set of NLL with QCDL4 = 260 | *
1641 * | S FXG360 : DFLM SF set of NLL with QCDL4 = 360 | *
1642 * | S FXGHAR : DFLM SF set of LO hard gluon | *
1643 * | S FXGSOF : DFLM SF set of LO soft gluon | *
1644 * | S FXNLLA : DFLM SF set of NLL central average fit | *
1645 * | S FXVHAR : DFLM SF set of LO hard valence | *
1646 * | S FXVSOF : DFLM SF set of LO soft valence | *
1647 * | F GAMFUN : to calculate GAMMA funct. in either SP or DP prec.*
1648 * | F GAMMADO : to calculate GAMMA funct. in SP (Hastings) | *
1649 * | F GHRDV : GHR SF set for down quarks | *
1650 * | F GHRGL : GHR SF set for gluons | *
1651 * | F GHRUV : GHR SF set for up quarks | *
1652 * | F GHRXI : GHR SF set for antiquarks | *
1653 * | F GHRXS : GHR SF set for strange quarks | *
1654 * | F GRVFGP : GRV SF set for gluons in the pion | *
1655 * | F GRVFQBP : GRV SF set for s, c and b quarks in the pion | *
1656 * | F GRVFV : GRV SF set for up + down valence quarks | *
1657 * | F GRVFVP : GRV SF set for valence quarks in the pion | *
1658 * | F GRVFW : GRV SF set for antiquarks and gluons | *
1659 * | F GRVFWS : GRV SF set for strange, charm and bottom quarks| *
1660 * | S GRVGAH0 : GRV SF set lead. terms of NLL in the photon (NP=3,NG=5,NS=1
1661 * | S GRVGAHO : GRV SF set of NLL in the photon (NP=3,NG=5,NS=2) *
1662 * | S GRVGALO : GRV SF set of LO in the photon (NP=3,NG=5,NS=3)| *
1663 * | F GRVGF : GRV SF set for u and d quarks and gluons in the photon
1664 * | F GRVGFS : GRV SF set for s, c and b quarks in the photon | *
1665 * | S GRVHO : GRV SF set of NLL (NP=1,NG=5,NS=3) | *
1666 * | S GRVLO : GRV SF set of LO (NP=1,NG=5,NS=4) | *
1667 * | S GRVPIHO : GRV SF set of NLL in the pion (NP=2,NG=5,NS=1) | *
1668 * | S GRVPILO : GRV SF set of LO in the pion (NP=2,NG=5,NS=2) | *
1669 * | S GSXCOR : to get X coordinates for SFGSHO + LO sets 1, 2 | *
1670 * | S HMRS1EB : Description of HMRS sets E, B (1.90-retracted) | *
1671 * | S HMRS2EB : Description of HMRS sets E, B (3.90) | *
1672 * | S HMRS3EB : Description of HMRS sets E, B (4.90) | *
1673 * | S HMRSGEB : Description of HMRS sets E, E+, E- and B | *
1674 * | S KMRSEB : Description of KMRS sets E and B | *
1675 * | S KMRSGEB : Description of KMRS B0 with L=135,160,200,235 | *
1676 * | S MRSDSHP : Description of MRS sets D0', S0', D-', (H) | *
1677 * | S MRSEB : Description of MRS sets E and B | *
1678 * | S MRSEBP : Description of MRS sets E' and B' | *
1679 * | S NEWDO1 : DO SF set 1.1 (NP=1,NG=1,NS=10) | *
1680 * | S PDFSET : to set all parameters for PDFLIB | *
1681 * | S PDFSTA : to print summary of param. and error statistics| *
1682 * | S PDFVERS : to get date and time of PDFLIB Library release | *
1683 * | F PDXMT : Description of MT sets 1 to 11 | *
1684 * | S PDZXMT : MT SF sets 1 to 11 | *
1685 * | S PFTOPDG : to access PDFLIB with output in PDG format | *
1686 * | S PHLAC1 : interface to LAC-G set 1 in the photon | *
1687 * |_______________________________________________________________| *
1688 ******************************* - 27 - ********************************
16891***********************************************************************
1690 * _________________________________________________________________ *
1691 * | Complete list of subprograms, cont'd | *
1692 * | | *
1693 * | S PHLAC2 : interface to LAC-G set 2 in the photon | *
1694 * | S PHLAC3 : interface to LAC-G set 3 in the photon | *
1695 * | S RXDV : OR SF set for down valence quarks | *
1696 * | S RXGLUE : OR SF set for gluons | *
1697 * | S RXQBAR : OR SF set for antiquarks | *
1698 * | S RXUD : OR SF set for the sum of up + down quarks | *
1699 * | S SEADIS : BEBC SF set for antiquarks | *
1700 * | S SFABFOW : ABFOW SF set (NP=1,NG=6,NS=1) | *
1701 * | S SFBMA : BM SF set A (NP=1,NG=7,NS=1) | *
1702 * | S SFBMB : BM SF set B (NP=1,NG=7,NS=2) | *
1703 * | S SFCTQ11 : CTEQ SF set 1L (LO) (NP=1,NG=4,NS=12) | *
1704 * | S SFCTQ12 : CTEQ SF set 1M (NP=1,NG=4,NS=13) | *
1705 * | S SFCTQ13 : CTEQ SF set 1MS (NP=1,NG=4,NS=14) | *
1706 * | S SFCTQ14 : CTEQ SF set 1ML (NP=1,NG=4,NS=15) | *
1707 * | S SFCTQ15 : CTEQ SF set 1D (NP=1,NG=4,NS=16) | *
1708 * | S SFCTQ21 : CTEQ SF set 2L (LO) (NP=1,NG=4,NS=17) | *
1709 * | S SFCTQ22 : CTEQ SF set 2M (NP=1,NG=4,NS=18) | *
1710 * | S SFCTQ23 : CTEQ SF set 2MS (NP=1,NG=4,NS=19) | *
1711 * | S SFCTQ24 : CTEQ SF set 2MF (NP=1,NG=4,NS=20) | *
1712 * | S SFCTQ25 : CTEQ SF set 2ML (NP=1,NG=4,NS=21) | *
1713 * | S SFCTQ26 : CTEQ SF set 2D (NP=1,NG=4,NS=22) | *
1714 * | S SFDISD0 : MRS SF set D0' (DIS) (NP=1,NG=3,NS=33) | *
1715 * | S SFDISDM : MRS SF set D-' (DIS) (NP=1,NG=3,NS=34) | *
1716 * | S SFDISH : MRS SF set (H) (NP=1,NG=3,NS=36) | *
1717 * | S SFDISS0 : MRS SF set S0' (DIS) (NP=1,NG=3,NS=32) | *
1718 * | S SFEHLQ1 : EHLQ SF set 1 (NP=1,NG=1,NS=8) | *
1719 * | S SFEHLQ2 : EHLQ SF set 2 (NP=1,NG=1,NS=9) | *
1720 * | S SFGRVH : old GRV SF set of NLL (NP=1,NG=5,NS=1) | *
1721 * | S SFGRVL : old GRV SF set of LO (NP=1,NG=5,NS=2) | *
1722 * | S SFGSHO : GS SF set of NLL in the photon (NP=3,NG=4,NS=1)| *
1723 * | S SFGSLO1 : GS SF set 1 of LO in the photon (NP=3,NG=4,NS=2) *
1724 * | S SFGSLO2 : GS SF set 2 of LO in the photon (NP=3,NG=4,NS=3) *
1725 * | S SFKBMR2 : KMRS SF set B- with R2 shadowing (NP=1,NG=3,NS=19)*
1726 * | S SFKBMR5 : KMRS SF set B- with R5 shadowing (NP=1,NG=3,NS=20)*
1727 * | S SFLACG1 : LAC SF set 1 in the photon (NP=3,NG=3,NS=1) | *
1728 * | S SFLACG2 : LAC SF set 2 in the photon (NP=3,NG=3,NS=2) | *
1729 * | S SFLACG3 : LAC SF set 3 in the photon (NP=3,NG=3,NS=3) | *
1730 * | S SFMRSD0 : MRS SF set D0 (NP=1,NG=3,NS=27) | *
1731 * | S SFMRSDM : MRS SF set D- (NP=1,NG=3,NS=28) | *
1732 * | S SFMRSS0 : MRS SF set S0 (NP=1,NG=3,NS=26) | *
1733 * | S SFMSBB0 : MRS SF set B0' (NP=1,NG=3,NS= | *
1734 * | S SFMSBD0 : MRS SF set D0' (NP=1,NG=3.NS=30) | *
1735 * | S SFMSBDM : MRS SF set D-' (NP=1,NG=3,NS=31) | *
1736 * | S SFMSBH : MRS SF set (H) (NP=1,NG=3,NS=35) | *
1737 * | S SFMSBS0 : MRS SF set S0' (NP=1,NG=3,NS=29) | *
1738 * | S SFMT10 : interface to MT set 6 (MS_bar) | *
1739 * | S SFMT11 : interface to MT set LO | *
1740 * | S SFMTU1 : interface to MT set S1 (DIS) | *
1741 * | S SFMTU2 : interface to MT set B1 (DIS) | *
1742 * | S SFMTU3 : interface to MT set B2 (DIS) | *
1743 * | S SFMTU4 : interface to MT set E1 (DIS) | *
1744 * | S SFMTU5 : interface to MT set 6 (u_bar + d_bar)/2 (DIS) | *
1745 * | S SFMTU6 : interface to MT set S1 (MS_bar) | *
1746 * | S SFMTU7 : interface to MT set B1 (MS_bar) | *
1747 * |_______________________________________________________________| *
1748 ******************************* - 28 - ********************************
17491***********************************************************************
1750 * _________________________________________________________________ *
1751 * | Complete list of subprograms, cont'd | *
1752 * | | *
1753 * | S SFMTU8 : interface to MT set B2 (MS_bar) | *
1754 * | S SFMTU9 : interface to MT set E1 (MS_bar) | *
1755 * | S SMRSP31 : SMRS SF set 1 in the pion (NP=2,NG=3,NS=1) | *
1756 * | S SMRSP32 : SMRS SF set 2 in the pion (NP=2,NG=3,NS=2) | *
1757 * | S SMRSP33 : SMRS SF set 3 in the pion (NP=2,NG=3,NS=3) | *
1758 * | S SMRSPI : Description of SMRS sets 1, 2, 3 in the pion | *
1759 * | S SRCTQ21 : CTEQ SF set 2pL (LO) (NP=1,NG=4,NS=23) | *
1760 * | S SRCTQ22 : CTEQ SF set 2pM (NP=1,NG=4,NS=24) | *
1761 * | S SRCTQ23 : CTEQ SF set 2pMS (NP=1,NG=4,NS=25) | *
1762 * | S SRCTQ24 : CTEQ SF set 2pMF (NP=1,NG=4,NS=26) | *
1763 * | S SRCTQ25 : CTEQ SF set 2pML (NP=1,NG=4,NS=27) | *
1764 * | S SRCTQ26 : CTEQ SF set 2pD (NP=1,NG=4,NS=28) | *
1765 * | S STRBEBC : BEBC SF set (NP=1,NG=1,NS=2) | *
1766 * | S STRBEP : BEP SF set (NP=1,NG=1,NS=4) | *
1767 * | S STRCBP : MRS SF set B' (NP=1,NG=3,NS=7) | *
1768 * | S STRCEP : MRS SF set E' (NP=1,NG=3,NS=6) | *
1769 * | S STRDO1 : DO SF set 1 (NP=1,NG=1,NS=6) | *
1770 * | S STRDO2 : DO SF set 2 (NP=1,NG=1,NS=7) | *
1771 * | S STRGHR : GHR SF set (NP=1,NG=1,NS=5) | *
1772 * | S STRH1B : HMRS SF set B (NP=1,NG=3,NS=9 - retracted) | *
1773 * | S STRH1E : HMRS SF set E (NP=1,NG=3,NS=8 - retracted) | *
1774 * | S STRH2B : HMRS SF set B (NP=1,NG=3,NS=11) | *
1775 * | S STRH2E : HMRS SF set E (NP=1,NG=3,NS=10) | *
1776 * | S STRH3B : HMRS SF set B (NP=1,NG=3,NS=15) | *
1777 * | S STRH3B1 : HMRS SF set B - L=100 (NP=1,NG=3,NS=16) | *
1778 * | S STRH3B3 : HMRS SF set B - L=300 (NP=1,NG=3,NS=17) | *
1779 * | S STRH3E : HMRS SF set E (NP=1,NG=3,NS=14) | *
1780 * | S STRH3EM : HMRS SF set E- (NP=1,NG=3,NS=13) | *
1781 * | S STRH3EP : HMRS SF set E+ (NP=1,NG=3,NS=12) | *
1782 * | S STRKB0 : KMRS SF set B0 (NP=1,NG=3,NS=21), updated version *
1783 * | S STRKB02 : KMRS SF set B0 - L=135 (NP=1,NG=3,NS=22) | *
1784 * | S STRKB03 : KMRS SF set B0 - L=160 (NP=1,NG=3,NS=23) | *
1785 * | S STRKB04 : KMRS SF set B0 - L=200 (NP=1,NG=3,NS=24) | *
1786 * | S STRKB05 : KMRS SF set B0 - L=235 (NP=1,NG=3,NS=25) | *
1787 * | S STRKB0O : KMRS SF set B0 (old version) | *
1788 * | S STRKBM : KMRS SF set B- (NP=1,NG=3,NS=18) | *
1789 * | S STRMRS1 : MRS SF set 1 (NP=1,NG=3,NS=1) | *
1790 * | S STRMRS2 : MRS SF set 2 (NP=1,NG=3,NS=2) | *
1791 * | S STRMRS3 : MRS SF set 3 (NP=1,NG=3,NS=3) | *
1792 * | S STROWP1 : OW SF set 1 in the pion (NP=2,NG=1,NS=1) | *
1793 * | S STROWP2 : OW SF set 2 in the pion (NP=2,NG=1,NS=2) | *
1794 * | S STRPRIV : Dummy subroutine for a new set of SF | *
1795 * | S STRUCB : MRS SF set B (NP=1,NG=3,NS=4) | *
1796 * | S STRUCE : MRS SF set E (NP=1,NG=3,NS=5) | *
1797 * | S STRUCOR : OR SF set (NP=1,NG=1,NS=3) | *
1798 * | S STRUCTF : to access PDFLIB with output in PDFLIB format | *
1799 * | S STRUCTM : to access PDFLIB with output in PDFLIB format | *
1800 * | TESTGAM : main program to test PDFLIB for photons | *
1801 * | TESTGAMO : main program to test PDFLIB for photons (OLD) | *
1802 * | TESTPDF : main program to test PDFLIB in PDFLIB format | *
1803 * | TESTPDFO : main program to test PDFLIB in PDFLIB format (OLD)*
1804 * | TESTPDG : main program to test PDFLIB in PDG format | *
1805 * | TESTPDGO : main program to test PDFLIB in PDG format (OLD)| *
1806 * | TMAINUPV : main program to show how to use the package | *
1807 * |_______________________________________________________________| *
1808 ******************************* - 29 - ********************************
18091***********************************************************************
1810 * _________________________________________________________________ *
1811 * | Complete list of subprograms, cont'd | *
1812 * | | *
1813 * | TMAINUPVO: main program to show how to use the package (OLD) *
1814 * | F V3 : BEBC SF set to calculate X * VALDIS | *
1815 * | S VALDIS : BEBC SF set for up + down valence quarks | *
1816 * | S VLAMBD : Entry in PDZXMT to get Lambda value for MT sets| *
1817 * | S WATE32 : defines 32 point Gaussian quadrature routine | *
1818 * | | *
1819 * | | *
1820 * | | *
1821 * | | *
1822 * | | *
1823 * | | *
1824 * | | *
1825 * | | *
1826 * | | *
1827 * | | *
1828 * | | *
1829 * | | *
1830 * | | *
1831 * | | *
1832 * | | *
1833 * | | *
1834 * | | *
1835 * | | *
1836 * | | *
1837 * | | *
1838 * | | *
1839 * | | *
1840 * | | *
1841 * | | *
1842 * | | *
1843 * | | *
1844 * | | *
1845 * | | *
1846 * | | *
1847 * | | *
1848 * | | *
1849 * | | *
1850 * | | *
1851 * | | *
1852 * | | *
1853 * | | *
1854 * | | *
1855 * | | *
1856 * | | *
1857 * | | *
1858 * | | *
1859 * | | *
1860 * | | *
1861 * | | *
1862 * | | *
1863 * | | *
1864 * | | *
1865 * | | *
1866 * | | *
1867 * |_______________________________________________________________| *
1868 ******************************* - 30 - ********************************
18691***********************************************************************
1870 * _________________________________________________________________ *
1871 * | Complete list of subprograms, cont'd | *
1872 * | | *
1873 * | C W50510 : IFLPRT - to set print flag | *
1874 * | C W50511 : NPTYPE,NGROUP,NSET,MODE,NFL,LO,TMAS - | *
1875 * | to select structure function set, to define | *
1876 * | number of flavours, flag for leading order | *
1877 * | and value for the mass of the top quark | *
1878 * | C W50512 : QCDL4,QCDL5 - contains Lambda_4(QCD) and | *
1879 * | Lambda_5(QCD) (in GeV) | *
1880 * | C W50513 : XMIN,XMAX.Q2MIN,Q2MAX - contains minimum | *
1881 * | and maximum values of X and Q**2 | *
1882 * | C W50514 : WXMIN,WXMAX,WQ2MIN,WQ2MAX,WTXMIN,WTXMAX,WQ2MIN,| *
1883 * | WQ2MAX - error counting for fractional and | *
1884 * | total number of X and Q**2 | *
1885 * | C W50514W : PDFWGT - to transmit user filled event weight | *
1886 * | C W50515 : IFLSET,IFLSTA - to transmit flag for call to | *
1887 * | subroutine PDFSET or PDFSTA | *
1888 * | C W50516 : FIRST - to force printing name of structure | *
1889 * | function set in case of multiple choices | *
1890 * | C W50517 : N6 - contains logical print unit number | *
1891 * | C W50518 : save of COMMONs W50510, W50511, W50512, W50513 | *
1892 * | C W50519 : NEWVER - to flag NEW or OLD version of PDFLIB | *
1893 * | format | *
1894 * | C W505110 : SFNAME - contains NAME (CHARACTER*8 array with | *
1895 * | dimension SFNAME(NPTYMX,NGRMAX,NSETMX)) for | *
1896 * | each set of PDFs | *
1897 * | C W505120 : NPGSMX(NPTYMX,NGRMAX),NSETFL(NPTYMX,NGRMAX,NSETMX)*
1898 * | - to provide the actual maximum number of stuc-| *
1899 * | ture function sets per particle type and author| *
1900 * | group, NSETFL(I,J,K) = 0 for retracted PDF set | *
1901 * | C W505121 : NPTYCR(MODEMX),NGROCR(MODEMX),NSETCR(MODEMX) | *
1902 * | - to provide the cross reference to the | *
1903 * | NPTYPE, NGROUP and NSET value (NEW format) for | *
1904 * | a given MODE value (OLD format) | *
1905 * | C W505122 : MODECR(NPTYMX,NGRMAX,NSETMX) - to provide the | *
1906 * | cross reference to the MODE value (OLD format) | *
1907 * | for a given NPTYPE, NGROUP and NSET value | *
1908 * | (NEW format) | *
1909 * | P W5051P0 : LFLPRT - to define print level (D=0) | *
1910 * | P W5051P1 : LPTYPE,LGROUP,LNSET,IFL,LORD,TM - to define | *
1911 * | the defaults for a PDF set given by the | *
1912 * | particle type, author group and number of set | *
1913 * | within an author group, defaults for number of | *
1914 * | flavours, leading order flag and mass of the | *
1915 * | top quark (D=1, 5, 3, 5, 2, 100.D0) | *
1916 * | P W5051P2 : MODEMX - maximum number of structure function | *
1917 * | sets in the OLD PDFLIB format | *
1918 * | : NPTYMX,NGRMAX,NSETMX - maximum number of | *
1919 * | structure function sets in the NEW PDFLIB | *
1920 * | format for particle type, author group number | *
1921 * | and number of sets within an author group | *
1922 * | P W5051P2 : MODEMX - to define maximum number of SF sets | *
1923 * | in PDFLIB (OLD format) (D=281) | *
1924 * | P W5051P7 : L6 - to define logical print unit number (D=6) | *
1925 * | P W5051P7 : L6 - to define logical print unit number | *
1926 * | W50511C : Comments only - complete list of available SFs | *
1927 * |_______________________________________________________________| *
1928 ******************************* - 31 - ********************************
19291***********************************************************************
1930 * *
1931 * References *
1932 * *
1933 * *
1934 * [1] A.J.Buras and K.J.F. Gaemers : Nucl. Phys. B132 (1978) 249; *
1935 * BEBC WA 59 Collaboration, K. Varnell et al., Z. Phys. C36 (1987) 1.
1936 * *
1937 * [2] J.F.Owens and E. Reya : Phys. Rev. D17 (1978) 3003. *
1938 * *
1939 * [3] R. Baier, J. Engels and B. Petersson : Z. Phys. C2 (1979) 265. *
1940 * *
1941 * [4] Gl"uck, E. Hoffman and E. Reya : Z. Phys. C13 (1982) 119. *
1942 * *
1943 * [5] D.W. Duke and J.F.Owens : Phys. Rev. D30 (1984) 49. *
1944 * *
1945 * [6] E. Eichten, I Hinchliffe, K. Lane and C. Quigg : *
1946 * Rev. Mod. Phys. 56 (1984) 579 and Rev. Mod. Phys. 58 (1985) 1065.
1947 * *
1948 * [7] M. Diemoz, F. Ferroni, E. Longo and G. Martinelli : *
1949 * Z. Phys. C39 (1988) 21. *
1950 * *
1951 * [8] J.F.Owens : Phys. Lett. 266B (1991) 126. *
1952 * *
1953 * [9] A.D. Martin, R.G. Roberts and W.J. Stirling : Phys.Rev. D37 (1988) 1161;
1954 * Phys. Lett. 206B (1988) 327 and Mod. Phys. Lett. A4 (1989) 1135.
1955 * *
1956 * [10] P.N. Harriman, A.D. Martin, R.G. Roberts and W.J. Stirling : *
1957 * Phys. Rev. D42 (1990) 798 and Phys. Lett. 243B (1990) 421. *
1958 * *
1959 * [11] J. Kwiecinski, A.D. Martin, R.G. Roberts and W.J. Stirling : *
1960 * Phys. Rev. D42 (1990) 3645; *
1961 * A.D. Martin, R.G. Roberts and W.J. Stirling : *
1962 * Phys. Rev. D43 (1991) 3648. *
1963 * *
1964 * [12] A.D. Martin, R.G. Roberts and W.J. Stirling : *
1965 * Phys. Rev. D47 (1993) 867. *
1966 * *
1967 * [13] J. Morfin and W.K. Tung : Z. Phys. C52 (1991) 13. *
1968 * *
1969 * [14] M. Gl"uck, E. Reya and A. Vogt : Z. Phys. C48 (1990) 471; *
1970 * Z. Phys. C53 (1992) 127 and Phys. Lett. 306B (1993) 391. *
1971 * *
1972 * [15] P. Aurenche et al. : Phys. Rev. D39 (1989) 3275. *
1973 * *
1974 * [16] A.D. Martin, R.G. Roberts and W.J. Stirling : *
1975 * Phys. Lett. 306B (1993) 145 and Phys. Lett. 309B (1993) 492. *
1976 * *
1977 * [17] A.D. Martin, R.G. Roberts and W.J. Stirling : *
1978 * RAL Preprint, RAL-92-078 (1992) and RAL Preprint, RAL-93-077 (199
1979 * *
1980 * [18] CTEQ collaboration, J. Botts et al. : Phys. Lett. 304B (1993) 159.
1981 * *
1982 * [19] E.L. Berger and R. Meng : Phys. Lett. 304B (1993) 318; *
1983 * CERN-TH 6739/92; ANL-HEP-CP-92-108 and *
1984 * E.L. Berger, R. Meng and J. Qiu : ANL-HEP-CP-92-79. *
1985 * *
1986 * *
1987 * *
1988 ******************************* - 32 - ********************************
19891***********************************************************************
1990 * *
1991 * [20] CTEQ collaboration, J. Botts et al. : *
1992 * to be published *
1993 * *
1994 * *
1995 * [21] J.F.Owens : Phys. Rev. D30 (1984) 943. *
1996 * *
1997 * [22] P. Aurenche et al. : Phys. Lett. 233B (1989) 517. *
1998 * *
1999 * [23] P.J. Sutton, A.D. Martin, R.G. Roberts and W.J. Stirling : *
2000 * Phys. Rev. D45 (1992) 2349. *
2001 * *
2002 * [24] M. Gl"uck, E. Reya and A. Vogt : Z. Phys. C53 (1992) 651. *
2003 * *
2004 * [25] D.W. Duke and J.F.Owens : Phys. Rev. D26 (1982) 1600. *
2005 * *
2006 * [26] M. Drees and K. Grassie : Z. Phys. C28 (1985) 451. *
2007 * *
2008 * [27] H. Abramowicz, K. Charchula and A. Levy : *
2009 * Phys. Lett. 269B (1991) 458. *
2010 * *
2011 * [28] L.E. Gordon and J.K. Storrow : Z. Phys. C56 (1992) 307. *
2012 * *
2013 * [29] M. Gl"uck, E. Reya and A. Vogt : Phys. Rev. D46 (1992) 1973 *
2014 * and Phys. Rev. D45 (1992) 3986. *
2015 * *
2016 * [30] P. Aurenche et al. : Z. Phys. C56 (1992) 589. *
2017 * *
2018 * [31] G. Altarelli, R.K. Ellis and G. Martinelli : *
2019 * Nucl. Phys. B143 (1978) 521 and B157 (1979) 461. *
2020 * *
2021 * [32] H. Plothow-Besch, 'PDFLIB: a library of all available parton *
2022 * density functions of the nucleon, the pion and the photon *
2023 * and the corresponding alpha(s) calculations', *
2024 * Comp. Phys. Comm. 75 (1993) 396-416; *
2025 * H. Plothow-Besch, 'PDFLIB: Structure Functions and alpha(s) *
2026 * Calculations', User's Manual - Version 1.00, W5051 PDFLIB, *
2027 * 1991.03.21, CERN-PPE. *
2028 * *
2029 * [33] Review of Particle Properties, June 1992, *
2030 * Phys. Rev. D45 (1992), Part. II, p. III.54. *
2031 * *
2032 * [34] BCDMS Collaboration, A.C. Benvenuti et al. : Phys. Lett. 223B (1989) 485
2033 * Phys. Lett. 237B (1990) 592 and Phys. Lett. 237B (1990) 599; *
2034 * EMC Collaboration, M. Arneodo et al. : Nucl. Phys. B333 (1990) 1;
2035 * NMC Collaboration, D. Allasia et al. : Phys. Lett. 249B (1990) 366;
2036 * P. Amaudruz et al. : Nucl. Phys. B371 (1992) 3.
2037 * *
2038 * [35] NMC Collaboration, P. Amaudruz et al. : Phys. Lett. 295B (1992) 159.
2039 * *
2040 * [36] H1 Collaboration, I. Abt et al. : DESY preprint 93-117 (1993); *
2041 * ZEUS Collaboration, M. Derrick et al. : DESY preprint 93-110 (1993).
2042 * *
2043 * [37] JADE Collaboration, W. Bartel et al. : Z. Phys. C24 (1984) 231.*
2044 * *
2045 * *
2046 * *
2047 * *
2048 ******************************* - 33 - ********************************
20491***********************************************************************
2050 * *
2051 * [38] PAW, CERN Program Library Entry Q121, Long Write-up; *
2052 * R. Brun, O. Couet, C. Vandoni and P Zanarini; *
2053 * see also to References therein. *
2054 * *
2055 * *
2056 * *
2057 * *
2058 * *
2059 * *
2060 * *
2061 * *
2062 * *
2063 * *
2064 * List of Tables *
2065 * *
2066 * *
2067 * 1 List of available sets of NUCLEON structure functions in *
2068 * PDFLIB version 6.06 ...................................... 35 *
2069 * *
2070 * *
2071 * 2 List of available sets of PION structure functions in PDFLIB *
2072 * version 6.06 ............................................. 37 *
2073 * *
2074 * *
2075 * 3 List of available sets of PHOTON structure functions in PDFLIB *
2076 * version 6.06 ............................................. 38 *
2077 * *
2078 * *
2079 * *
2080 * *
2081 * *
2082 * *
2083 * *
2084 * *
2085 * *
2086 * *
2087 * *
2088 * *
2089 * *
2090 * *
2091 * *
2092 * *
2093 * *
2094 * *
2095 * *
2096 * *
2097 * *
2098 * *
2099 * *
2100 * *
2101 * *
2102 * *
2103 * *
2104 * *
2105 * *
2106 * *
2107 * *
2108 ******************************* - 34 - ********************************
21091***********************************************************************
2110 * *
2111 * Table 1 *
2112 * *
2113 * Available sets of NUCLEON structure functions in PDFLIB *
2114 * *
2115 * ------------------------------------------------------------------- *
2116 * *
2117 * Nptype *
2118 * Ngroup Q**2 Name of Set Scheme Reference *
2119 * Nset min *
2120 * QCDL4 *
2121 * ------------------------------------------------------------------- *
2122 * 0 200 0.3 ->GRV HO MS_bar NLL Default *
2123 * ------------------------------------------------------------------- *
2124 * ------------------------------------------------------------------- *
2125 * 1 1 1 PRIVATE to user *
2126 * 1 1 2 45 0.5 BEBC LO [Nucl.Phys. B132 (1978) 249]
2127 * 1 1 3 500 1.8 OR LO [Phys.Rev. D17 (1978) 3003]
2128 * 1 1 4 470 5 BEP LO [Z. Phys. C2 (1979) 265]
2129 * 1 1 5 400 4 GHR LO [Z. Phys. C13 (1982) 119]
2130 * 1 1 6 200 4 DO Set 1 LO [Phys.Rev. D30 (1984) 49]
2131 * 1 1 7 400 4 DO Set 2 LO *
2132 * 1 1 8 200 5 EHLQ Set 1 LO [Rev.Mod.Phys. 56 (1984) 579;
2133 * 1 1 9 290 5 EHLQ Set 2 LO Rev.Mod.Phys. 58 (1985) 1065]
2134 * 1 1 10 177 4 DO Set 1.1 LO [Phys.Lett.266B (1991) 3275]
2135 * ------------------------------------------------------------------- *
2136 * 1 2 1 200 10 DFLM soft valence LO [Z. Phys. C39 (1988) 21
2137 * 1 2 2 200 10 DFLM hard valence LO *
2138 * 1 2 3 200 10 DFLM soft gluon LO *
2139 * 1 2 4 200 10 DFLM hard gluon LO *
2140 * 1 2 5 200 10 DFLM central av. LO *
2141 * 1 2 6 300 10 DFLM central av. DIS NLL *
2142 * 1 2 7 160 10 DFLM 160 DIS NLL [unpublished] *
2143 * 1 2 8 260 10 ->DFLM 260 DIS NLL *
2144 * 1 2 9 360 10 DFLM 360 DIS NLL *
2145 * ------------------------------------------------------------------- *
2146 * 1 3 1 107 5 MRS 1 MS_bar NLL [Phys.Rev. D37 (1988) 1181]
2147 * 1 3 2 250 5 MRS 2 MS_bar NLL *
2148 * 1 3 3 178 5 MRS 3 MS_bar NLL *
2149 * 1 3 4 91 5 MRS E MS_bar NLL [Phys.Lett. 206B (1988) 327]
2150 * 1 3 5 228 5 MRS B MS_bar NLL *
2151 * 1 3 6 91 5 MRS E' MS_bar NLL [Mod.Phys. Lett.A4 (1989) 1135
2152 * 1 3 7 228 5 MRS B' MS_bar NLL *
2153 * 1 3 8 100 5 HMRS E (1.90) MS_bar NLL [retracted] *
2154 * 1 3 9 190 5 HMRS B (1.90) MS_bar NLL *
2155 * 1 3 10 100 5 HMRS E (3.90) MS_bar NLL *
2156 * 1 3 11 190 5 HMRS B (3.90) MS_bar NLL *
2157 * 1 3 12 100 5 HMRS E+(4.90) MS_bar NLL [Phys.Lett. 243B (1990) 421]
2158 * 1 3 13 100 5 HMRS E-(4.90) MS_bar NLL *
2159 * 1 3 14 100 5 HMRS E (4.90) MS_bar NLL [Phys.Rev. D4 (1990) 798]
2160 * 1 3 15 190 5 HMRS B (4.90) MS_bar NLL *
2161 * 1 3 16 100 5 HMRS B (8.90) MS_bar NLL [unpublished] *
2162 * 1 3 17 300 5 HMRS B (8.90) MS_bar NLL *
2163 * 1 3 18 190 5 KMRS B-(7.90) MS_bar NLL [Phys.Rev. D42 (1990) 3645]
2164 * 1 3 19 190 5 KMRS B-R2 Shadow (7.90) MS_bar NLL *
2165 * 1 3 20 190 5 KMRS B-R5 Shadow (7.90) MS_bar NLL *
2166 * 1 3 21 190 5 KMRS B0-190 (7.90) MS_bar NLL (as updated 4.92) *
2167 * *
2168 ******************************* - 35 - ********************************
21691***********************************************************************
2170 * *
2171 * Table 1 (cont'd) *
2172 * *
2173 * ------------------------------------------------------------------- *
2174 * *
2175 * Nptype *
2176 * Ngroup Q**2 Name of Set Scheme Reference *
2177 * Nset min *
2178 * QCDL4 *
2179 * ------------------------------------------------------------------- *
2180 * 1 3 22 135 5 MRS B0-135 (10.90) MS_bar NLL [Phys.Rev. D43 (1991) 3648]
2181 * 1 3 23 160 5 MRS B0-160 (10.90) MS_bar NLL *
2182 * 1 3 24 200 5 MRS B0-200 (10.90) MS_bar NLL *
2183 * 1 3 25 235 5 MRS B0-235 (10.90) MS_bar NLL *
2184 * 1 3 26 215 5 MRS S0 (4.92) MS_bar NLL [retracted] *
2185 * 1 3 27 215 5 MRS D0 (4.92) MS_bar NLL *
2186 * 1 3 28 215 5 MRS D- (4.92) MS_bar NLL *
2187 * 1 3 29 230 5 MRS S0' (11.92) MS_bar NLL [Phys.Lett. 306B (1993)145
2188 * 1 3 30 230 5 MRS D0' (11.92) MS_bar NLL *
2189 * 1 3 31 230 5 MRS D-' (11.92) MS_bar NLL *
2190 * 1 3 32 230 5 MRS S0' (2.93) DIS NLL [RAL-92-078 (1992)]
2191 * 1 3 33 230 5 MRS D0' (2.93) DIS NLL *
2192 * 1 3 34 230 5 MRS D-' (2.93) DIS NLL *
2193 * 1 3 35 230 5 MRS (H) (11.93) MS_bar NLL *
2194 * 1 3 36 230 5 MRS (H) (11.93) DIS NLL *
2195 * 1 3 37 230 5 MRS (A) (5.94 MS_bar NLL [RAL-94-055 (1994)]
2196 * 1 3 38 230 5 MRS (A) Fit (5.94) MS_bar NLL *
2197 * 1 3 39 230 5 MRS (Ap) (2.95 MS_bar NLL [RAL-94-104 (1994)]
2198 * 1 3 40 231 5 MRS (Ap) Fit(2.95) MS_bar NLL *
2199 * 1 3 41 255 5 ->MRS (G) (2.95 MS_bar NLL [RAL-95-021 (1995)]
2200 * 1 3 42 255 5 MRS (G) Fit (2.95) MS_bar NLL *
2201 * ------------------------------------------------------------------- *
2202 * 1 4 1 212 4 MT S1 DIS NLL [Z. Phys. C52 (1991) 13]
2203 * 1 4 2 194 4 MT B1 DIS NLL *
2204 * 1 4 3 191 4 MT B2 DIS NLL *
2205 * 1 4 4 155 4 MT E1 DIS NLL *
2206 * 1 4 5 237 4 MT 6 (1/2s) DIS NLL *
2207 * 1 4 6 212 4 MT S1 MS_bar NLL *
2208 * 1 4 7 194 4 MT B1 MS_bar NLL *
2209 * 1 4 8 191 4 MT B2 MS_bar NLL *
2210 * 1 4 9 155 4 MT E1 MS_bar NLL *
2211 * 1 4 10 237 4 MT 6 (1/2s) MS_bar NLL *
2212 * 1 4 11 144 4 MT LO LO *
2213 * 1 4 12 168 4 CTEQ 1L LO [retracted] *
2214 * 1 4 13 231 4 CTEQ 1M MS_bar NLL *
2215 * 1 4 14 231 4 CTEQ 1MS MS_bar NLL *
2216 * 1 4 15 322 4 CTEQ 1ML MS_bar NLL *
2217 * 1 4 16 247 4 CTEQ 1D DIS NLL *
2218 * 1 4 17 190 4 CTEQ 2L LO [retracted] *
2219 * 1 4 18 213 4 CTEQ 2M MS_bar NLL *
2220 * 1 4 19 208 4 CTEQ 2MS MS_bar NLL *
2221 * 1 4 20 208 4 CTEQ 2MF MS_bar NLL *
2222 * 1 4 21 322 4 CTEQ 2ML MS_bar NLL *
2223 * 1 4 22 235 4 CTEQ 2D DIS NLL *
2224 * 1 4 23 190 4 CTEQ 2pL LO [to be published]*
2225 * 1 4 24 213 4 CTEQ 2pM MS_bar NLL *
2226 * ------------------------------------------------------------------- *
2227 * *
2228 ******************************* - 36 - ********************************
22291***********************************************************************
2230 * *
2231 * Table 1 (cont'd) *
2232 * *
2233 * ------------------------------------------------------------------- *
2234 * *
2235 * Nptype *
2236 * Ngroup Q**2 Name of Set Scheme Reference *
2237 * Nset min *
2238 * QCDL4 *
2239 * ------------------------------------------------------------------- *
2240 * 1 4 25 208 4 CTEQ 2pMS MS_bar NLL *
2241 * 1 4 26 208 4 CTEQ 2pMF MS_bar NLL *
2242 * 1 4 27 322 4 CTEQ 2pML MS_bar NLL *
2243 * 1 4 28 235 4 CTEQ 2pD DIS NLL *
2244 * 1 4 29 177 4 CTEQ 3L LO [MSU-HEP/41024] *
2245 * 1 4 30 239 4 ->CTEQ 3M MS_bar NLL *
2246 * 1 4 31 247 4 CTEQ 3D DIS NLL *
2247 * ------------------------------------------------------------------- *
2248 * 1 5 1 160 0.2 old GRV HO MS_bar NLL [retracted] *
2249 * 1 5 2 220 0.2 old GRV LO LO *
2250 * 1 5 3 200 0.3 GRV HO MS_bar NLL [Z. Phys. C53 (1992) 127]
2251 * 1 5 4 200 0.25 GRV LO LO *
2252 * 1 5 5 200 0.4 GRV 94 LO LO [DO-TH 94/24 (1994)]
2253 * 1 5 6 200 0.4 ->GRV 94 HO MS_bar NLL *
2254 * 1 5 7 200 0.4 GRV 94 HO DIS NLL *
2255 * ------------------------------------------------------------------- *
2256 * 1 6 1 230 2 ABFOW MS_bar NLL [Phys.Rev D39 (1989) 3275]
2257 * ------------------------------------------------------------------- *
2258 * 1 7 1 254 5 BM A MS_bar NLL [Phys.Lett. 304B (1993)318
2259 * 1 7 2 254 5 BM B MS_bar NLL *
2260 * ------------------------------------------------------------------- *
2261 * *
2262 * *
2263 * Table 2 *
2264 * *
2265 * Available sets of PION structure functions in PDFLIB *
2266 * *
2267 * ------------------------------------------------------------------- *
2268 * *
2269 * Nptype *
2270 * Ngroup Q**2 Name of Set Scheme Reference *
2271 * Nset min *
2272 * QCDL4 *
2273 * ------------------------------------------------------------------- *
2274 * 2 1 1 200 4 OW-P Set 1 LO [Phys.Rev. D30 (1984) 943]
2275 * 2 1 2 400 4 OW-P Set 2 LO *
2276 * ------------------------------------------------------------------- *
2277 * 2 3 1 190 5 SMRS-P 1 MS_bar NLL [Phys.Rev. D45 (1992) 2349]
2278 * 2 3 2 190 5 ->SMRS-P 2 MS_bar NLL *
2279 * 2 3 3 190 5 SMRS-P 3 MS_bar NLL *
2280 * ------------------------------------------------------------------- *
2281 * 2 5 1 200 0.3 ->GRV-P HO MS_bar NLL [Z.Phys. C53 (1992) 651]
2282 * 2 5 2 200 0.25 GRV-P LO LO *
2283 * ------------------------------------------------------------------- *
2284 * 2 6 1 231 2 ->ABFKW-P 1 MS_bar NLL [Phys.Lett.233B (189) 517]
2285 * 2 6 2 181 2 ABFKW-P 2 MS_bar NLL *
2286 * 2 6 3 281 2 ABFKW-P 3 MS_bar NLL *
2287 * ------------------------------------------------------------------- *
2288 ******************************* - 37 - ********************************
22891***********************************************************************
2290 * *
2291 * Table 3 *
2292 * *
2293 * Available sets of PHOTON structure functions in PDFLIB *
2294 * *
2295 * ------------------------------------------------------------------- *
2296 * *
2297 * Nptype *
2298 * Ngroup Q**2 Name of Set Scheme Reference *
2299 * Nset min *
2300 * QCDL4 *
2301 * ------------------------------------------------------------------- *
2302 * 3 1 1 380 10 DO-G LO LO [Phys.Rev. D26 (1982) 1600]
2303 * 3 1 2 440 10 ->DO-G HO MS_bar NLL *
2304 * ------------------------------------------------------------------- *
2305 * 3 2 1 400 1 ->DG-G Set 1 LO [Z. Phys. C28 (1985) 451]
2306 * 3 2 2 400 1 DG-G Set 2 LO *
2307 * 3 2 3 400 20 DG-G Set 3 LO *
2308 * 3 2 4 400 200 DG-G Set 4 LO *
2309 * ------------------------------------------------------------------- *
2310 * 3 3 1 200 5 LAC-G 1 LO [Phys.Lett.269B (1991) 458]
2311 * 3 3 2 200 5 ->LAC-G 2 LO *
2312 * 3 3 3 200 5 LAC-G 3 LO *
2313 * ------------------------------------------------------------------- *
2314 * 3 4 1 200 5.3 ->GS-G HO MS_bar NLL [Z.Phys. C56 (1992) 307]
2315 * 3 4 2 200 5.3 GS-G LO set 1 LO *
2316 * 3 4 3 200 5.3 GS-G LO set 2 LO *
2317 * ------------------------------------------------------------------- *
2318 * 3 5 1 200 0.3 GRV-G LHO DIS*) NLL [Phys.Rev. D46 (1992) 1973;
2319 * 3 5 2 200 0.3 ->GRV-G HO DIS*) NLL Phys.Rev. D45 (1992) 3986]
2320 * 3 5 3 200 0.25 GRV-G LO LO *
2321 * ------------------------------------------------------------------- *
2322 * 3 6 1 200 2 ACFGP-G HO MS_bar NLL [Z.Phys. C56 (1992) 589]
2323 * 3 6 2 200 2 ->ACFGP-G HO-mc MS_bar NLL *
2324 * 3 6 3 200 2 ->AFG-G HO MS_bar NLL *
2325 * ------------------------------------------------------------------- *
2326 * 3 8 1 400 4 WHIT-G 1 LO [KEK preprint 93-160]*
2327 * 3 8 2 400 4 ->WHIT-G 2 LO *
2328 * 3 8 3 400 4 WHIT-G 3 LO *
2329 * 3 8 4 400 4 WHIT-G 4 LO *
2330 * 3 8 5 400 4 WHIT-G 5 LO *
2331 * 3 8 6 400 4 WHIT-G 6 LO *
2332 * ------------------------------------------------------------------- *
2333 * *
2334 * *
2335 * *
2336 * *) not standard, please consult references. *
2337 * *
2338 * *
2339 * *
2340 * *
2341 * *
2342 * *
2343 * *
2344 * *
2345 * *
2346 * *
2347 * *
2348 ******************************* - 38 - ********************************
23491***********************************************************************
2350 * *
2351 * *
2352 * *
2353 * *
2354 * *
2355 * *
2356 * *
2357 * *
2358 * *
2359 * *
2360 * *
2361 * *
2362 * *
2363 * *
2364 * *
2365 * *
2366 * *
2367 * *
2368 * *
2369 * *
2370 * *
2371 * *
2372 * *
2373 * *
2374 * *
2375 * *
2376 * *
2377 * *
2378 * *
2379 * *
2380 * *
2381 * *
2382 * *
2383 * *
2384 * *
2385 * *
2386 * *
2387 * *
2388 * *
2389 * *
2390 * *
2391 * *
2392 * *
2393 * *
2394 * *
2395 * *
2396 * *
2397 * *
2398 * *
2399 * *
2400 * *
2401 * *
2402 * *
2403 * *
2404 * *
2405 * *
2406 * *
2407 * *
2408 ******************************* - 39 - ********************************