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da0e9ce3 1//--------------------------------------------------------------------------
2//
3// Environment:
4// This software is part of the EvtGen package developed jointly
5// for the BaBar and CLEO collaborations. If you use all or part
6// of it, please give an appropriate acknowledgement.
7//
8// Copyright Information: See EvtGen/COPYRIGHT
9// Copyright (C) 2000 Caltech, UCSB
10//
11// Module:
12// Description: Form factors for b->sll according to Ali, Ball et al.
13// hep-ph/9910221v2
14//
15// Modification history:
16//
17// Ryd January 5, 2000 Module created
18//
19// jjhollar October 7 2005 Add Ball & Zwicky '05 LCSR
20// ofte August 2006 Add some more pi l l FF models
21//------------------------------------------------------------------------
22#include "EvtGenBase/EvtPatches.hh"
23
24#include "EvtGenBase/EvtPatches.hh"
25#include "EvtGenBase/EvtPDL.hh"
26#include "EvtGenModels/EvtbTosllBallFF.hh"
27#include <math.h>
28
29EvtbTosllBallFF::EvtbTosllBallFF(int ffmodel)
30{
31 _theFFModel = ffmodel;
32}
33
34
35void EvtbTosllBallFF::getScalarFF(EvtId parent, EvtId daught,
36 double t, double /*mass*/,
37 double& fp,double& f0,double& ft){
38
39 int model = _theFFModel;
40
41 double m=EvtPDL::getMeanMass(parent);
42 double md=EvtPDL::getMeanMass(daught);
43
44 double shat=t/(m*m);
45 double shat2=shat*shat;
46 double shat3=shat2*shat;
47
48 if (daught == EvtPDL::getId(std::string("K+")) ||
49 daught == EvtPDL::getId(std::string("K-")) ||
50 daught == EvtPDL::getId(std::string("K_S0")) ||
51 daught == EvtPDL::getId(std::string("K0")) ||
52 daught == EvtPDL::getId(std::string("anti-K0")) ||
53 daught == EvtPDL::getId(std::string("K_L0"))
54 )
55 {
56 // B --> K form factors
57 if (model == 1) {
58 //this is Ali-Ball '01 (or really Ali-Ball'99 minimum allowed)
59 fp = 0.278*exp(1.568*shat+0.470*shat2+0.885*shat3);
60 f0 = 0.278*exp(0.740*shat+0.080*shat2+0.425*shat3);
61 ft = 0.300*exp(1.600*shat+0.501*shat2+0.796*shat3);
62 }
63 if (model == 2) {
64 //this is Ali-Ball '99 (central values)
65 fp = 0.319*exp(1.465*shat+0.372*shat2+0.782*shat3);
66 f0 = 0.319*exp(0.633*shat-0.095*shat2+0.591*shat3);
67 ft = 0.355*exp(1.478*shat+0.373*shat2+0.700*shat3);
68 }
69 if (model == 3) {
70 //QCD sum rules (Colangelo et al)
71 fp = 0.25/(1.-t/(5.0*5.0));
72 f0 = 0.25/(1.-t/(7.0*7.0));
73 ft = - 0.14/((1.0 - t/(5.0*5.0))*(1.0 - t/(7.0*7.0)));
74 }
75 if (model == 4) {
76 // Quark model (Melikhov et al - hep-ph/9711362)
77 fp = 0.36/(1. - 0.048*t + 0.00063*t*t);
78 double fm = -0.30/(1. - 0.050*t + 0.00061*t*t);
79 f0 = fp + fm*(t/(m*m - md*md));
80 ft = -(m+md)*0.06/(1 -0.049*t + 0.00064*t*t);
81 }
82 if (model == 5) {
83 fp = 0.341/(1. - 1.41*shat + 0.406*shat*shat);
84 f0 = 0.341/(1. - 0.41*shat -0.361*shat*shat);
85 ft = 0.374/(1. - 1.42*shat + 0.434*shat*shat);
86 }
87 if (model == 6) {
88 // Ball-Zwicky LCSR '05 "set 2" (mb = 4.8)
89 fp = (0.1616 / (1. - (t/29.30))) +
90 (0.1730 / (1. - (t/29.30)) / (1. - (t/29.30)));
91 f0 = (0.3302 / (1. - (t/37.46/37.46)));
92 ft = (0.1614 / (1. - (t/29.30))) +
93 (0.1981 / (1. - (t/29.30)) / (1. - (t/29.30)));
94 }
95 if (model == 7){
96 // Ball-Zwicky LCSR '05 "set 4" (mb = 4.6)
97 fp = (0.1903 / (1. - (t/29.30))) +
98 (0.1478 / (1. - (t/29.30)) / (1. - (t/29.30)));
99 f0 = (0.3338 / (1. - (t/38.98/38.98)));
100 ft = (0.1851 / (1. - (t/29.30))) +
101 (0.1905 / (1. - (t/29.30)) / (1. - (t/29.30)));
102 }
103 }
104 else if (daught == EvtPDL::getId(std::string("pi+")) ||
105 daught == EvtPDL::getId(std::string("pi-")) ||
106 daught == EvtPDL::getId(std::string("pi0"))
107 )
108 {
109 if(model == 1){
110 // B --> pi form factors from Ball-Zwicky'01 (tabulated in hep-ph/0306251)
111 fp = 0.261/(1. - 2.03*shat + 1.293*shat*shat);
112 f0 = 0.261/(1. - 0.27*shat -0.752*shat*shat);
113 ft = 0.296/(1. - 1.28*shat + 0.193*shat*shat);
114 }
115
116 // The following two (2) and (3) should preferably be replaced with
117 // something better. ft not provided by the papers, and the ft formula
118 // (from Colangelo'96 (hep-ph/9510403v2) equation (5.1)) seem to be no good.
119 // if (model == 2) {
120 // // LatticeQCD: Okamoto'04
121 // // ... with f_T from eq. (5.1) of Colangelo'95
122 // fp = 0.23/((1.-shat)*(1.-0.63*shat));
123 // f0 = 0.23/((1.-shat)/1.18);
124 // ft = ( -(m+md)/(2*m) )/ (fp - (m*m-md*md) * ((f0-fp)/t) );
125 // }
126 // if (model == 3) {
127 // // LatticeQCD: Shigemitsu'04
128 // // ... with f_T from eq. (5.1) of Colangelo'95
129 // fp = 0.42*(1.0-0.41)/((1.-shat)*(1.-0.63*shat));
130 // f0 = 0.42*(1.0-0.41)/((1.-shat)/1.18);
131 // ft = ( -(m+md)/(2*m) )/ (fp - (m*m-md*md) * ((f0-fp)/t) );
132 // }
133
134 if (model == 4) {
135 // Quark model - B -> pi set 1 (Melikhov-Nikitin'96)
136 fp = 0.29/pow((1.-t/(6.48*6.48)),2.54);
137 double fm = -0.26/pow((1.-t/(6.34*6.34)),2.49);
138 f0 = fp + fm*(t/(m*m - md*md));
139 ft = -(m+md)*0.05/pow((1.-t/(6.47*6.47)),2.50);
140 }
141 if (model == 5) {
142 // Melikhov-Stech '00. (hep-ph/0001113)
143 // relativistic dispersion approach based on constituent quark picture
144 fp = 0.29/((1.-shat)*(1.-0.48*shat));
145 f0 = 0.29/(1.-0.76*shat +0.28*shat*shat);
146 ft = 0.28/((1.-shat)*(1.-0.48*shat));
147 }
148 if(model == 6){
149 // Ball-Zwicky LCSR '05 "set 2" (mb = 4.8)
150 fp = (0.744 / (1. - (t/(5.32*5.32)))) + (-0.486 / (1. - (t/40.73)));
151 f0 = (0.258 / (1. - (t/33.81)));
152 ft = (1.387 / (1. - (t/(5.32*5.32)))) + (-1.134 / (1. - (t/32.22)));
153 }
154 if(model == 7){
155 // Ball-Zwicky LCSR '05 "set 4" (mb = 4.6)
156 fp = (0.944 / (1. - (t/(5.32*5.32)))) + (-0.669 / (1. - (t/34.27)));
157 f0 = (0.270 / (1. - (t/33.63)));
158 ft = (0.152 / (1. - (t/(5.32*5.32)))) +
159 (0.122 / (1. - (t/28.40)) / (1. - (t/28.40)));
160 }
161 }
162 else if (daught == EvtPDL::getId(std::string("eta")) ||
163 daught == EvtPDL::getId(std::string("eta'"))
164 )
165 {
166 if(model == 1){
167 // B --> eta form factors
168 fp = 0.261/(1. - 2.03*shat + 1.293*shat*shat);
169 f0 = 0.261/(1. - 0.27*shat -0.752*shat*shat);
170 ft = 0.296/(1. - 1.28*shat + 0.193*shat*shat);
171 }
172 if(model == 6){
173 // Ball-Zwicky LCSR '05 "set 2" (mb = 4.8)
174 fp = (0.1220 / (1. - (t/28.40))) +
175 (0.1553 / (1. - (t/28.40)) / (1. - (t/28.40)));
176 f0 = (0.2734 / (1. - (t/31.03/31.03)));
177 ft = (0.1108 / (1. - (t/28.40))) +
178 (0.1752 / (1. - (t/28.40)) / (1. - (t/28.40)));
179 }
180 if(model == 7){
181 // Ball-Zwicky LCSR '05 "set 2" (mb = 4.8)
182 fp = (0.1380 / (1. - (t/28.40))) +
183 (0.1462 / (1. - (t/28.40)) / (1. - (t/28.40)));
184 f0 = (0.2799 / (1. - (t/30.46/30.46)));
185 ft = (0.1160 / (1. - (t/28.40))) +
186 (0.1841 / (1. - (t/28.40)) / (1. - (t/28.40)));
187 }
188 }
189
190 // cout << "shat "<<shat<<"\t"<<"fp "<<fp<<"\t"<<"f0 "<<f0<<"\t"
191 // <<"ft "<<ft<<endl;
192
193}
194
195
196void EvtbTosllBallFF::getVectorFF(EvtId parent, EvtId daught,
197 double t, double /*mass*/,
198 double& a1,double& a2,double& a0, double& v,
199 double& t1, double& t2, double& t3 ){
200
201 int model = _theFFModel;
202
203 double m=EvtPDL::getMeanMass(parent);
204 double md=EvtPDL::getMeanMass(daught);
205
206 double shat=t/(m*m);
207 double shat2=shat*shat;
208
209 if (
210 daught == EvtPDL::getId(std::string("K*+")) ||
211 daught == EvtPDL::getId(std::string("K*-")) ||
212 daught == EvtPDL::getId(std::string("K*0")) ||
213 daught == EvtPDL::getId(std::string("anti-K*0"))
214 )
215 {
216 if (model == 1) {
217 //this is Ali-Ball '01
218 a1 = 0.294*exp(0.656*shat+0.456*shat2);
219 a2 = 0.246*exp(1.237*shat+0.822*shat2);
220 a0 = 0.412*exp(1.543*shat+0.954*shat2);
221 v = 0.399*exp(1.537*shat+1.123*shat2);
222
223 t1 = 0.334*exp(1.575*shat+1.140*shat2);
224 t2 = 0.334*exp(0.562*shat+0.481*shat2);
225 t3 = 0.234*exp(1.230*shat+1.089*shat2);
226 }
227 if (model == 2) {
228 //this is Ali-Ball '99
229 a1=0.337*exp(0.602*shat+0.258*shat2);
230 a2=0.282*exp(1.172*shat+0.567*shat2);
231 a0=0.471*exp(1.505*shat+0.710*shat2);
232 v=0.457*exp(1.482*shat+1.015*shat2);
233
234 t1=0.379*exp(1.519*shat+1.030*shat2);
235 t2=0.379*exp(0.517*shat+0.426*shat2);
236 t3=0.260*exp(1.129*shat+1.128*shat2);
237 }
238 if (model == 3) {
239 //QCD sum rules (Colangelo et al)
240 // JJH - Changed in accordance with erratum (Phys. Rev. D 57, 3186 (1998))
241 a1 = 0.37*(1 - 0.023*t);
242 a2 = 0.40*(1 + 0.034*t);
243 a0 = 0.3/(1.- t/(4.8*4.8));
244 v = 0.47/(1.- t/(5.0*5.0));
245
246 t1 = 0.19/(1.-t/(5.3*5.3));
247 t2 = 0.19*(1. - 0.02*t);
248 t3 = 0.3*(1. + 0.01*t);
249 }
250
251 if (model == 4) {
252 // Quark model (Melikhov et al)
253 a1 = 1.6/(1 - 0.0288*t + 0.00028*t*t); a1 = a1/(m+md);
254 a2 = (m+md)*0.036/(1. - 0.053*t + 0.00082*t*t);
255 double aminus = 0.041/(1. - 0.055*t + 0.00088*t*t);
256 double f = 1.60/(1. - 0.0288*t + 0.00028*t*t);
257 double aplus = -0.036/(1. - 0.053*t + 0.00082*t*t);
258 a0 = (t*aminus + f + (m*m-md*md)*aplus)/(2.0*md);
259 v = (m+md)*0.048/(1. - 0.057*t + 0.00085*t*t);
260
261 t1 = 0.28/(1. - 0.058*t + 0.0009*t*t);
262 double gplus = -0.28/(1. - 0.058*t + 0.0009*t*t);
263 double gminus = 0.24/(1. - 0.059*t + 0.00096*t*t);
264 t2 = -gplus - (t*gminus)/(m*m-md*md);
265 double h = 0.0037/(1. - 0.075*t + 0.0016*t*t);
266 t3 = (m+md)*(m+md)*((gminus/(m*m-md*md) - h/2.));
267
268 }
269 if (model == 5) {
270 a1 = 0.337/(1. - 0.60*shat - 0.023*shat*shat);
271 a2 = 0.283/(1. - 1.18*shat + 0.281*shat*shat);
272 a0 = 0.470/(1. - 1.55*shat + 0.680*shat*shat);
273 v = 0.458/(1. - 1.55*shat + 0.575*shat*shat);
274 t1 = 0.379/(1. - 1.59*shat + 0.615*shat*shat);
275 t2 = 0.379/(1. - 0.49*shat - 0.241*shat*shat);
276 t3 = 0.261/(1. - 1.20*shat + 0.098*shat*shat);
277 }
278 if (model == 6) {
279 // Ball-Zwicky LCSR '05 (mb = 4.8)
280 a1 = 0.290 / (1. - (t/40.38));
281 a2 = (-0.084 / (1. - (t/52.00))) +
282 (0.342 / (1. - (t/52.00))/(1. - (t/52.00)));
283 a0 = (1.364 / (1. - (t/(5.28*5.28)))) +
284 (-0.990 / (1. - (t/36.78)));
285 v = (0.923 / (1. - (t/(5.32*5.32)))) +
286 (-0.511 / (1. - (t/49.40)));
287 t1 = (0.823 / (1. - (t/(5.32*5.32)))) +
288 (-0.491 / (1 - (t/46.31)));
289 t2 = 0.333 / (1. - (t/41.41));
290 t3 = (-0.036 / (1. - (t/48.10))) +
291 (0.368 / (1. - (t/48.10)) / (1. - (t/48.10)));
292 }
293 }
294 else if (daught == EvtPDL::getId(std::string("rho+")) ||
295 daught == EvtPDL::getId(std::string("rho-")) ||
296 daught == EvtPDL::getId(std::string("rho0"))
297 )
298 {
299 if(model == 1){
300 // B --> rho form factors
301 a1 = 0.261/(1. - 0.29*shat - 0.415*shat*shat);
302 a2 = 0.223/(1. - 0.93*shat - 0.092*shat*shat);
303 a0 = 0.372/(1. - 1.40*shat + 0.437*shat*shat);
304 v = 0.338/(1. - 1.37*shat + 0.315*shat*shat);
305 t1 = 0.285/(1. - 1.41*shat + 0.361*shat*shat);
306 t2 = 0.285/(1. - 0.28*shat - 0.500*shat*shat);
307 t3 = 0.202/(1. - 1.06*shat - 0.076*shat*shat);
308 }
309 if(model == 6){
310 // Ball-Zwicky LCSR '05 (mb = 4.8)
311 a1 = 0.240 / (1. - (t/37.51));
312 a2 = (0.009 / (1. - (t/40.82))) +
313 (0.212 / (1. - (t/40.82)) / (1. - (t/40.82)));
314 a0 = (1.527 / (1. - (t/(5.28*5.28)))) +
315 (-1.220 / (1. - (t/33.36)));
316 v = (1.045 / (1. - (t/(5.32*5.32)))) +
317 (-0.721 / (1. - (t/38.34)));
318 t1 = (0.897 / (1. - (t/(5.32*5.32)))) +
319 (-0.629 / (1 - (t/38.04)));
320 t2 = 0.267 / (1. - (t/38.59));
321 t3 = (0.022 / (1. - (t/40.88))) +
322 (0.246 / (1. - (t/40.88)) / (1. - (t/40.88)));
323 }
324 }
325 else if (daught == EvtPDL::getId(std::string("omega"))
326 )
327 {
328 if(model == 1){
329 // B --> rho form factors
330 a1 = 0.261/(1. - 0.29*shat - 0.415*shat*shat);
331 a2 = 0.223/(1. - 0.93*shat - 0.092*shat*shat);
332 a0 = 0.372/(1. - 1.40*shat + 0.437*shat*shat);
333 v = 0.338/(1. - 1.37*shat + 0.315*shat*shat);
334 t1 = 0.285/(1. - 1.41*shat + 0.361*shat*shat);
335 t2 = 0.285/(1. - 0.28*shat - 0.500*shat*shat);
336 t3 = 0.202/(1. - 1.06*shat - 0.076*shat*shat);
337 }
338 if(model == 6){
339 // Ball-Zwicky LCSR '05 (mb = 4.8)
340 a1 = -0.217 / (1. - (t/37.01));
341 a2 = (0.006 / (1. - (t/41.24))) +
342 (0.192 / (1. - (t/41.24)) / (1. - (t/41.24)));
343 a0 = (1.321 / (1. - (t/(5.28*5.28)))) +
344 (-1.040 / (1. - (t/34.47)));
345 v = (1.006 / (1. - (t/(5.32*5.32)))) +
346 (-0.713 / (1. - (t/37.45)));
347 t1 = (0.865 / (1. - (t/(5.32*5.32)))) +
348 (-0.622 / (1 - (t/37.19)));
349 t2 = 0.242 / (1. - (t/37.95));
350 t3 = (0.023 / (1. - (t/40.87))) +
351 (0.220 / (1. - (t/40.87)) / (1. - (t/40.87)));
352 }
353 }
354 else if (daught == EvtPDL::getId(std::string("phi"))
355 )
356 {
357 if(model == 6){
358 // Ball-Zwicky LCSR '05 (mb = 4.8)
359 a1 = 0.308 / (1. - (t/36.54));
360 a2 = (-0.054 / (1. - (t/48.94))) +
361 (0.288 / (1. - (t/48.94)) / (1. - (t/48.94)));
362 a0 = (3.310 / (1. - (t/(5.28*5.28)))) +
363 (-2.835 / (1. - (t/31.57)));
364 v = (1.484 / (1. - (t/(5.32*5.32)))) +
365 (-1.049 / (1. - (t/39.52)));
366 t1 = (1.303 / (1. - (t/(5.32*5.32)))) +
367 (-0.954 / (1 - (t/38.28)));
368 t2 = 0.349 / (1. - (t/37.21));
369 t3 = (0.027 / (1. - (t/45.56))) +
370 (0.321 / (1. - (t/45.56)) / (1. - (t/45.56)));
371 }
372 }
373
374}
375
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