HERWIG/src/sasano.f

   1
   2 C
   3
   4 C*********************************************************************
   5
   6 C
   7
   8       SUBROUTINE SASANO(KF,X,Q2,P2,ALAM,XPGA,VXPGA)
   9
  10 C...Purpose: to evaluate the parton distributions of the anomalous
  11
  12 C...photon, inhomogeneously evolved from a scale P2 (where it vanishes)
  13
  14 C...to Q2.
  15
  16 C...KF=0 gives the sum over (up to) 5 flavours,
  17
  18 C...KF<0 limits to flavours up to abs(KF),
  19
  20 C...KF>0 is for flavour KF only.
  21
  22 C...ALAM is the 4-flavour Lambda, which is automatically converted
  23
  24 C...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
  30 C
  31
  32 C...Reset output.
  33
  34       DO 100 KFL=-6,6
  35
  36       XPGA(KFL)=0.
  37
  38       VXPGA(KFL)=0.
  39
  40   100 CONTINUE
  41
  42       IF(Q2.LE.P2) RETURN
  43
  44       KFA=IABS(KF)
  45
  46 C
  47
  48 C...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
  53
  54       ALAMSQ(5)=(ALAM*(ALAM/PMB)**(2./23.))**2
  55
  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)
  61
  62       Q2EFF=MAX(Q2,P2EFF)
  63
  64       XL=-LOG(X)
  65
  66 C
  67
  68 C...Find number of flavours at lower and upper scale.
  69
  70       NFP=4
  71
  72       IF(P2EFF.LT.PMC**2) NFP=3
  73
  74       IF(P2EFF.GT.PMB**2) NFP=5
  75
  76       NFQ=4
  77
  78       IF(Q2EFF.LT.PMC**2) NFQ=3
  79
  80       IF(Q2EFF.GT.PMB**2) NFQ=5
  81
  82 C
  83
  84 C...Define range of flavour loop.
  85
  86       IF(KF.EQ.0) THEN
  87
  88         KFLMN=1
  89
  90         KFLMX=5
  91
  92       ELSEIF(KF.LT.0) THEN
  93
  94         KFLMN=1
  95
  96         KFLMX=KFA
  97
  98       ELSE
  99
 100         KFLMN=KFA
 101
 102         KFLMX=KFA
 103
 104       ENDIF
 105
 106 C
 107
 108 C...Loop over flavours the photon can branch into.
 109
 110       DO 110 KFL=KFLMN,KFLMX
 111
 112 C
 113
 114 C...Light flavours: calculate t range and (approximate) s range.
 115
 116       IF(KFL.LE.3.AND.(KFL.EQ.1.OR.KFL.EQ.KF)) THEN
 117
 118         TDIFF=LOG(Q2EFF/P2EFF)
 119
 120         S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
 121
 122      &  LOG(P2EFF/ALAMSQ(NFQ)))
 123
 124         IF(NFQ.GT.NFP) THEN
 125
 126           Q2DIV=PMB**2
 127
 128           IF(NFQ.EQ.4) Q2DIV=PMC**2
 129
 130           SNFQ=(6./(33.-2.*NFQ))*LOG(LOG(Q2DIV/ALAMSQ(NFQ))/
 131
 132      &    LOG(P2EFF/ALAMSQ(NFQ)))
 133
 134           SNFP=(6./(33.-2.*(NFQ-1)))*LOG(LOG(Q2DIV/ALAMSQ(NFQ-1))/
 135
 136      &    LOG(P2EFF/ALAMSQ(NFQ-1)))
 137
 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
 143
 144           Q2DIV=PMC**2
 145
 146           SNF4=(6./(33.-2.*4))*LOG(LOG(Q2DIV/ALAMSQ(4))/
 147
 148      &    LOG(P2EFF/ALAMSQ(4)))
 149
 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
 158 C
 159
 160 C...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
 164 C
 165
 166 C...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
 171
 172         P2EFF=MAX(P2EFF,PMC**2)
 173
 174         Q2EFF=MAX(Q2EFF,P2EFF)
 175
 176         TDIFF=LOG(Q2EFF/P2EFF)
 177
 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
 183
 184           Q2DIV=PMB**2
 185
 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)))
 193
 194           S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNFP-SNFQ)
 195
 196         ENDIF
 197
 198 C
 199
 200 C...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
 205
 206         P2EFF=MAX(P2EFF,PMB**2)
 207
 208         Q2EFF=MAX(Q2,P2EFF)
 209
 210         TDIFF=LOG(Q2EFF/P2EFF)
 211
 212         S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
 213
 214      &  LOG(P2EFF/ALAMSQ(NFQ)))
 215
 216       ENDIF
 217
 218 C
 219
 220 C...Evaluate flavour-dependent prefactor (charge^2 etc.).
 221
 222       CHSQ=1./9.
 223
 224       IF(KFL.EQ.2.OR.KFL.EQ.4) CHSQ=4./9.
 225
 226       FAC=AEM2PI*2.*CHSQ*TDIFF
 227
 228 C
 229
 230 C...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
 233
 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))
 241
 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
 256 C
 257
 258 C...Threshold factors for c and b sea.
 259
 260         SLL=LOG(LOG(Q2EFF/ALAM**2)/LOG(P2EFF/ALAM**2))
 261
 262         XCHM=0.
 263
 264         IF(Q2.GT.PMC**2.AND.Q2.GT.1.001*P2EFF) THEN
 265
 266           SCH=MAX(0.,LOG(LOG(PMC**2/ALAM**2)/LOG(P2EFF/ALAM**2)))
 267
 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
 275
 276           SBT=MAX(0.,LOG(LOG(PMB**2/ALAM**2)/LOG(P2EFF/ALAM**2)))
 277
 278           XBOT=XSEA*(1.-(SBT/SLL)**3)
 279
 280         ENDIF
 281
 282       ENDIF
 283
 284 C
 285
 286 C...Add contribution of each valence flavour.
 287
 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
 299
 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
 307
 308       XPGA(-KFL)=XPGA(KFL)
 309
 310       VXPGA(-KFL)=VXPGA(KFL)
 311
 312   120 CONTINUE
 313
 314 C
 315
 316       RETURN
 317
 318       END