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3820ca8e 1
2C
3
4C*********************************************************************
5
6C
7
8 SUBROUTINE SASANO(KF,X,Q2,P2,ALAM,XPGA,VXPGA)
9
10C...Purpose: to evaluate the parton distributions of the anomalous
11
12C...photon, inhomogeneously evolved from a scale P2 (where it vanishes)
13
14C...to Q2.
15
16C...KF=0 gives the sum over (up to) 5 flavours,
17
18C...KF<0 limits to flavours up to abs(KF),
19
20C...KF>0 is for flavour KF only.
21
22C...ALAM is the 4-flavour Lambda, which is automatically converted
23
24C...to 3- and 5-flavour equivalents as needed.
25
26 DIMENSION XPGA(-6:6), VXPGA(-6:6), ALAMSQ(3:5)
27
28 DATA PMC/1.3/, PMB/4.6/, AEM2PI/0.0011614/
29
30C
31
32C...Reset output.
33
34 DO 100 KFL=-6,6
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36 XPGA(KFL)=0.
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38 VXPGA(KFL)=0.
39
40 100 CONTINUE
41
42 IF(Q2.LE.P2) RETURN
43
44 KFA=IABS(KF)
45
46C
47
48C...Calculate Lambda; protect against unphysical Q2 and P2 input.
49
50 ALAMSQ(3)=(ALAM*(PMC/ALAM)**(2./27.))**2
51
52 ALAMSQ(4)=ALAM**2
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54 ALAMSQ(5)=(ALAM*(ALAM/PMB)**(2./23.))**2
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56 P2EFF=MAX(P2,1.2*ALAMSQ(3))
57
58 IF(KF.EQ.4) P2EFF=MAX(P2EFF,PMC**2)
59
60 IF(KF.EQ.5) P2EFF=MAX(P2EFF,PMB**2)
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62 Q2EFF=MAX(Q2,P2EFF)
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64 XL=-LOG(X)
65
66C
67
68C...Find number of flavours at lower and upper scale.
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70 NFP=4
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72 IF(P2EFF.LT.PMC**2) NFP=3
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74 IF(P2EFF.GT.PMB**2) NFP=5
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76 NFQ=4
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78 IF(Q2EFF.LT.PMC**2) NFQ=3
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80 IF(Q2EFF.GT.PMB**2) NFQ=5
81
82C
83
84C...Define range of flavour loop.
85
86 IF(KF.EQ.0) THEN
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88 KFLMN=1
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90 KFLMX=5
91
92 ELSEIF(KF.LT.0) THEN
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94 KFLMN=1
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96 KFLMX=KFA
97
98 ELSE
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100 KFLMN=KFA
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102 KFLMX=KFA
103
104 ENDIF
105
106C
107
108C...Loop over flavours the photon can branch into.
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110 DO 110 KFL=KFLMN,KFLMX
111
112C
113
114C...Light flavours: calculate t range and (approximate) s range.
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116 IF(KFL.LE.3.AND.(KFL.EQ.1.OR.KFL.EQ.KF)) THEN
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118 TDIFF=LOG(Q2EFF/P2EFF)
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120 S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
121
122 & LOG(P2EFF/ALAMSQ(NFQ)))
123
124 IF(NFQ.GT.NFP) THEN
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126 Q2DIV=PMB**2
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128 IF(NFQ.EQ.4) Q2DIV=PMC**2
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130 SNFQ=(6./(33.-2.*NFQ))*LOG(LOG(Q2DIV/ALAMSQ(NFQ))/
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132 & LOG(P2EFF/ALAMSQ(NFQ)))
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134 SNFP=(6./(33.-2.*(NFQ-1)))*LOG(LOG(Q2DIV/ALAMSQ(NFQ-1))/
135
136 & LOG(P2EFF/ALAMSQ(NFQ-1)))
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138 S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNFP-SNFQ)
139
140 ENDIF
141
142 IF(NFQ.EQ.5.AND.NFP.EQ.3) THEN
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144 Q2DIV=PMC**2
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146 SNF4=(6./(33.-2.*4))*LOG(LOG(Q2DIV/ALAMSQ(4))/
147
148 & LOG(P2EFF/ALAMSQ(4)))
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150 SNF3=(6./(33.-2.*3))*LOG(LOG(Q2DIV/ALAMSQ(3))/
151
152 & LOG(P2EFF/ALAMSQ(3)))
153
154 S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNF3-SNF4)
155
156 ENDIF
157
158C
159
160C...u and s quark do not need a separate treatment when d has been done.
161
162 ELSEIF(KFL.EQ.2.OR.KFL.EQ.3) THEN
163
164C
165
166C...Charm: as above, but only include range above c threshold.
167
168 ELSEIF(KFL.EQ.4) THEN
169
170 IF(Q2.LE.PMC**2) GOTO 110
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172 P2EFF=MAX(P2EFF,PMC**2)
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174 Q2EFF=MAX(Q2EFF,P2EFF)
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176 TDIFF=LOG(Q2EFF/P2EFF)
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178 S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
179
180 & LOG(P2EFF/ALAMSQ(NFQ)))
181
182 IF(NFQ.EQ.5.AND.NFP.EQ.4) THEN
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184 Q2DIV=PMB**2
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186 SNFQ=(6./(33.-2.*NFQ))*LOG(LOG(Q2DIV/ALAMSQ(NFQ))/
187
188 & LOG(P2EFF/ALAMSQ(NFQ)))
189
190 SNFP=(6./(33.-2.*(NFQ-1)))*LOG(LOG(Q2DIV/ALAMSQ(NFQ-1))/
191
192 & LOG(P2EFF/ALAMSQ(NFQ-1)))
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194 S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNFP-SNFQ)
195
196 ENDIF
197
198C
199
200C...Bottom: as above, but only include range above b threshold.
201
202 ELSEIF(KFL.EQ.5) THEN
203
204 IF(Q2.LE.PMB**2) GOTO 110
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206 P2EFF=MAX(P2EFF,PMB**2)
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208 Q2EFF=MAX(Q2,P2EFF)
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210 TDIFF=LOG(Q2EFF/P2EFF)
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212 S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
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214 & LOG(P2EFF/ALAMSQ(NFQ)))
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216 ENDIF
217
218C
219
220C...Evaluate flavour-dependent prefactor (charge^2 etc.).
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222 CHSQ=1./9.
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224 IF(KFL.EQ.2.OR.KFL.EQ.4) CHSQ=4./9.
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226 FAC=AEM2PI*2.*CHSQ*TDIFF
227
228C
229
230C...Evaluate parton distributions (normalized to unit momentum sum).
231
232 IF(KFL.EQ.1.OR.KFL.EQ.4.OR.KFL.EQ.5.OR.KFL.EQ.KF) THEN
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234 XVAL= ((1.5+2.49*S+26.9*S**2)/(1.+32.3*S**2)*X**2 +
235
236 & (1.5-0.49*S+7.83*S**2)/(1.+7.68*S**2)*(1.-X)**2 +
237
238 & 1.5*S/(1.-3.2*S+7.*S**2)*X*(1.-X)) *
239
240 & X**(1./(1.+0.58*S)) * (1.-X**2)**(2.5*S/(1.+10.*S))
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242 XGLU= 2.*S/(1.+4.*S+7.*S**2) *
243
244 & X**(-1.67*S/(1.+2.*S)) * (1.-X**2)**(1.2*S) *
245
246 & ((4.*X**2+7.*X+4.)*(1.-X)/3. - 2.*X*(1.+X)*XL)
247
248 XSEA= 0.333*S**2/(1.+4.90*S+4.69*S**2+21.4*S**3) *
249
250 & X**(-1.18*S/(1.+1.22*S)) * (1.-X)**(1.2*S) *
251
252 & ((8.-73.*X+62.*X**2)*(1.-X)/9. + (3.-8.*X**2/3.)*X*XL +
253
254 & (2.*X-1.)*X*XL**2)
255
256C
257
258C...Threshold factors for c and b sea.
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260 SLL=LOG(LOG(Q2EFF/ALAM**2)/LOG(P2EFF/ALAM**2))
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262 XCHM=0.
263
264 IF(Q2.GT.PMC**2.AND.Q2.GT.1.001*P2EFF) THEN
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266 SCH=MAX(0.,LOG(LOG(PMC**2/ALAM**2)/LOG(P2EFF/ALAM**2)))
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268 XCHM=XSEA*(1.-(SCH/SLL)**3)
269
270 ENDIF
271
272 XBOT=0.
273
274 IF(Q2.GT.PMB**2.AND.Q2.GT.1.001*P2EFF) THEN
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276 SBT=MAX(0.,LOG(LOG(PMB**2/ALAM**2)/LOG(P2EFF/ALAM**2)))
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278 XBOT=XSEA*(1.-(SBT/SLL)**3)
279
280 ENDIF
281
282 ENDIF
283
284C
285
286C...Add contribution of each valence flavour.
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288 XPGA(0)=XPGA(0)+FAC*XGLU
289
290 XPGA(1)=XPGA(1)+FAC*XSEA
291
292 XPGA(2)=XPGA(2)+FAC*XSEA
293
294 XPGA(3)=XPGA(3)+FAC*XSEA
295
296 XPGA(4)=XPGA(4)+FAC*XCHM
297
298 XPGA(5)=XPGA(5)+FAC*XBOT
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300 XPGA(KFL)=XPGA(KFL)+FAC*XVAL
301
302 VXPGA(KFL)=VXPGA(KFL)+FAC*XVAL
303
304 110 CONTINUE
305
306 DO 120 KFL=1,5
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308 XPGA(-KFL)=XPGA(KFL)
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310 VXPGA(-KFL)=VXPGA(KFL)
311
312 120 CONTINUE
313
314C
315
316 RETURN
317
318 END