2 SUBROUTINE SASANO(KF,X,Q2,P2,ALAM,XPGA,VXPGA)
3 C...Purpose: to evaluate the parton distributions of the anomalous
4 C...photon, inhomogeneously evolved from a scale P2 (where it vanishes)
6 C...KF=0 gives the sum over (up to) 5 flavours,
7 C...KF<0 limits to flavours up to abs(KF),
8 C...KF>0 is for flavour KF only.
9 C...ALAM is the 4-flavour Lambda, which is automatically converted
10 C...to 3- and 5-flavour equivalents as needed.
11 DIMENSION XPGA(-6:6), VXPGA(-6:6), ALAMSQ(3:5)
12 DATA PMC/1.3/, PMB/4.6/, AEM/0.007297/, AEM2PI/0.0011614/
22 C...Calculate Lambda; protect against unphysical Q2 and P2 input.
23 ALAMSQ(3)=(ALAM*(PMC/ALAM)**(2./27.))**2
25 ALAMSQ(5)=(ALAM*(ALAM/PMB)**(2./23.))**2
26 P2EFF=MAX(P2,1.2*ALAMSQ(3))
27 IF(KF.EQ.4) P2EFF=MAX(P2EFF,PMC**2)
28 IF(KF.EQ.5) P2EFF=MAX(P2EFF,PMB**2)
32 C...Find number of flavours at lower and upper scale.
34 IF(P2EFF.LT.PMC**2) NFP=3
35 IF(P2EFF.GT.PMB**2) NFP=5
37 IF(Q2EFF.LT.PMC**2) NFQ=3
38 IF(Q2EFF.GT.PMB**2) NFQ=5
40 C...Define range of flavour loop.
52 C...Loop over flavours the photon can branch into.
53 DO 110 KFL=KFLMN,KFLMX
55 C...Light flavours: calculate t range and (approximate) s range.
56 IF(KFL.LE.3.AND.(KFL.EQ.1.OR.KFL.EQ.KF)) THEN
57 TDIFF=LOG(Q2EFF/P2EFF)
58 S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
59 & LOG(P2EFF/ALAMSQ(NFQ)))
62 IF(NFQ.EQ.4) Q2DIV=PMC**2
63 SNFQ=(6./(33.-2.*NFQ))*LOG(LOG(Q2DIV/ALAMSQ(NFQ))/
64 & LOG(P2EFF/ALAMSQ(NFQ)))
65 SNFP=(6./(33.-2.*(NFQ-1)))*LOG(LOG(Q2DIV/ALAMSQ(NFQ-1))/
66 & LOG(P2EFF/ALAMSQ(NFQ-1)))
67 S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNFP-SNFQ)
69 IF(NFQ.EQ.5.AND.NFP.EQ.3) THEN
71 SNF4=(6./(33.-2.*4))*LOG(LOG(Q2DIV/ALAMSQ(4))/
72 & LOG(P2EFF/ALAMSQ(4)))
73 SNF3=(6./(33.-2.*3))*LOG(LOG(Q2DIV/ALAMSQ(3))/
74 & LOG(P2EFF/ALAMSQ(3)))
75 S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNF3-SNF4)
78 C...u and s quark do not need a separate treatment when d has been done.
79 ELSEIF(KFL.EQ.2.OR.KFL.EQ.3) THEN
81 C...Charm: as above, but only include range above c threshold.
83 IF(Q2.LE.PMC**2) GOTO 110
84 P2EFF=MAX(P2EFF,PMC**2)
85 Q2EFF=MAX(Q2EFF,P2EFF)
86 TDIFF=LOG(Q2EFF/P2EFF)
87 S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
88 & LOG(P2EFF/ALAMSQ(NFQ)))
89 IF(NFQ.EQ.5.AND.NFP.EQ.4) THEN
91 SNFQ=(6./(33.-2.*NFQ))*LOG(LOG(Q2DIV/ALAMSQ(NFQ))/
92 & LOG(P2EFF/ALAMSQ(NFQ)))
93 SNFP=(6./(33.-2.*(NFQ-1)))*LOG(LOG(Q2DIV/ALAMSQ(NFQ-1))/
94 & LOG(P2EFF/ALAMSQ(NFQ-1)))
95 S=S+(LOG(Q2DIV/P2EFF)/LOG(Q2EFF/P2EFF))*(SNFP-SNFQ)
98 C...Bottom: as above, but only include range above b threshold.
100 IF(Q2.LE.PMB**2) GOTO 110
101 P2EFF=MAX(P2EFF,PMB**2)
103 TDIFF=LOG(Q2EFF/P2EFF)
104 S=(6./(33.-2.*NFQ))*LOG(LOG(Q2EFF/ALAMSQ(NFQ))/
105 & LOG(P2EFF/ALAMSQ(NFQ)))
108 C...Evaluate flavour-dependent prefactor (charge^2 etc.).
110 IF(KFL.EQ.2.OR.KFL.EQ.4) CHSQ=4./9.
111 FAC=AEM2PI*2.*CHSQ*TDIFF
113 C...Evaluate parton distributions (normalized to unit momentum sum).
114 IF(KFL.EQ.1.OR.KFL.EQ.4.OR.KFL.EQ.5.OR.KFL.EQ.KF) THEN
115 XVAL= ((1.5+2.49*S+26.9*S**2)/(1.+32.3*S**2)*X**2 +
116 & (1.5-0.49*S+7.83*S**2)/(1.+7.68*S**2)*(1.-X)**2 +
117 & 1.5*S/(1.-3.2*S+7.*S**2)*X*(1.-X)) *
118 & X**(1./(1.+0.58*S)) * (1.-X**2)**(2.5*S/(1.+10.*S))
119 XGLU= 2.*S/(1.+4.*S+7.*S**2) *
120 & X**(-1.67*S/(1.+2.*S)) * (1.-X**2)**(1.2*S) *
121 & ((4.*X**2+7.*X+4.)*(1.-X)/3. - 2.*X*(1.+X)*XL)
122 XSEA= 0.333*S**2/(1.+4.90*S+4.69*S**2+21.4*S**3) *
123 & X**(-1.18*S/(1.+1.22*S)) * (1.-X)**(1.2*S) *
124 & ((8.-73.*X+62.*X**2)*(1.-X)/9. + (3.-8.*X**2/3.)*X*XL +
127 C...Threshold factors for c and b sea.
128 SLL=LOG(LOG(Q2EFF/ALAM**2)/LOG(P2EFF/ALAM**2))
130 IF(Q2.GT.PMC**2.AND.Q2.GT.1.001*P2EFF) THEN
131 SCH=MAX(0.,LOG(LOG(PMC**2/ALAM**2)/LOG(P2EFF/ALAM**2)))
132 XCHM=XSEA*(1.-(SCH/SLL)**3)
135 IF(Q2.GT.PMB**2.AND.Q2.GT.1.001*P2EFF) THEN
136 SBT=MAX(0.,LOG(LOG(PMB**2/ALAM**2)/LOG(P2EFF/ALAM**2)))
137 XBOT=XSEA*(1.-(SBT/SLL)**3)
141 C...Add contribution of each valence flavour.
142 XPGA(0)=XPGA(0)+FAC*XGLU
143 XPGA(1)=XPGA(1)+FAC*XSEA
144 XPGA(2)=XPGA(2)+FAC*XSEA
145 XPGA(3)=XPGA(3)+FAC*XSEA
146 XPGA(4)=XPGA(4)+FAC*XCHM
147 XPGA(5)=XPGA(5)+FAC*XBOT
148 XPGA(KFL)=XPGA(KFL)+FAC*XVAL
149 VXPGA(KFL)=VXPGA(KFL)+FAC*XVAL
153 VXPGA(-KFL)=VXPGA(KFL)