1
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
2
c FINITE PART OF THE INTEGRATE DIPOLES
3
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
5
c fi(1), regular piece at z!=1
6
c fi(2), delta piece at z=1
7
c fi(3), plus distribution at z!=1
8
c fi(4), plus distribution at z=1
9
c fi(5), mass correction to plus distribution at z!=1
10
c fi(6), mass correction to plus distribution at z=1
11
c fi(7), delta piece at z=1-4m^2/s
12
c fi(8), plus distribution at z!=1-4m^2/s
13
c fi(9), plus distribution at z=1-4m^2/s
14
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
17
SUBROUTINE finiteff(mi,mk,sik,id,id1,fi)
18
c calculates the finite terms when both emitter
19
c and spectator are in the final state
25
REAL*8 mi,mk,sik,fi(9)
28
REAL*8 ddilog,lambda_tr
29
external ddilog,lambda_tr
31
REAl*8 cf,ca,rhoi,rhok,rho,musq_i,musq_k,gsq,pi
32
REAL*8 xp,yp,vik,muk,rho1,rho2,L,yl,rs,Qik2,a,b,c,d,xm,x,mui
33
PARAMETER (cf=4d0/3d0,ca=3d0)
34
PARAMETER (pi=3.1415926535897932385d0)
41
c For the massive cases, sik is the Qik^2 from CDST and vice versa.
51
C ij~ massive and massive spectator
52
if(mi.gt.0d0 .and. mk .gt. 0d0.and.id.eq.1) then
54
vik=Sqrt(lambda_tr(1d0,musq_i,musq_k))/(1d0-musq_i-musq_k)
55
rhoi=Sqrt((1d0-vik+2d0*musq_i/(1d0-musq_i-musq_k))/
56
& (1d0+vik+2d0*musq_i/(1d0-musq_i-musq_k)))
57
rhok=Sqrt((1d0-vik+2d0*musq_k/(1d0-musq_i-musq_k))/
58
& (1d0+vik+2d0*musq_k/(1d0-musq_i-musq_k)))
59
rho=Sqrt((1d0-vik)/(1d0+vik))
60
fi(2)=(gsq*(6 + 2*L + 2*rs +
61
& 2*mk*((4*mk - 2*Sqrt(sik))/Qik2 + 1/(mk - Sqrt(sik))) -
62
& (2*Pi**2)/(3.*vik) - 4*Log(-mi**2 + (mk - Sqrt(sik))**2) +
63
& 2*Log(mi - (mi*mk)/Sqrt(sik)) -
64
& (4*mi**2*Log(mi/(-mk + Sqrt(sik))))/Qik2 + 3*Log(sik) -
65
& (-4*Log(rho**2)*Log(1 + rho**2) + Log(rhoi**2)**2 +
67
& 4*Log(rho)*(L + 2*Log(sik/Qik2)))/(2.*vik) -
68
& (2*(-2*ddilog(rho**2) + ddilog(1 - rhoi**2) +
69
& ddilog(1 - rhok**2)))/vik))/(16.*Pi**2)
71
C adding alpha dependent terms
72
if(alpha_ff.ne.1d0) then
73
a=(2*muk)/(1 - musq_i - musq_k)
74
b=(2*(1 - muk))/(1 - musq_i - musq_k)
75
c=(2*(1 - muk)*muk)/(1 - musq_i - musq_k)
76
d=(1 - musq_i - musq_k)/2.
77
xp=(-musq_i + (1 - muk)**2 +
78
& Sqrt(lambda_tr(1d0,musq_i,musq_k)))/(1-musq_i-musq_k)
79
xm=(-musq_i + (1 - muk)**2 -
80
& Sqrt(lambda_tr(1d0,musq_i,musq_k)))/(1-musq_i-musq_k)
81
yp=1 - (2*(1 - muk)*muk)/(1 - musq_i - musq_k)
82
x=yp - alpha_ff*yp + Sqrt(((4*musq_i*musq_k)/
83
& ((musq_i - (1 - muk)**2)*(1 - musq_i - musq_k)) +
84
& 1/yp - alpha_ff*yp)*(yp - alpha_ff*yp))
85
fi(2)=fi(2)+gsq*(1/(1- muk)-(2*(2-2*musq_i-muk))/
86
& (1-musq_i-musq_k)+(3*(1+alpha_ff*yp))/2. +
87
& (musq_i*(1 - alpha_ff*yp))/(2.*(musq_i +
88
& alpha_ff*(1 - musq_i - musq_k)*yp)) -
89
& 2*DLog((alpha_ff*(1 - musq_i - musq_k)*yp)/
90
& (-musq_i + (1 - muk)**2)) +
91
& ((1 + musq_i - musq_k)*
92
& DLog((musq_i + alpha_ff*(1 - musq_i - musq_k)*yp)
93
& /(1 - muk)**2))/(2.*(1 - musq_i - musq_k)) +
94
& (2*(-(DLog(b)*DLog((a*(-b + xm))/((a + b)*xm))) +
95
& DLog(b - x)*DLog(((a + x)*(-b + xm))/
96
& ((a + b)*(-x + xm))) +
97
& DLog((c + xm)/(a + xm))*DLog((-x + xm)/xm) +
98
& DLog(a*(b - xp))*DLog(xp) +
99
& (DLog((a + x)/a)*DLog(a*(a + x)*(a + xp)**2))/2. -
100
& DLog(c)*DLog(((a - c)*xp)/(a*(c + xp))) +
101
& DLog(d)*DLog(((a + x)*xm*xp)/(a*(-x + xm)*(-x + xp))) -
102
& DLog((a + x)*(b - xp))*DLog(-x + xp) +
103
& DLog(c + x)*DLog(((a-c)*(-x + xp))/((a + x)*(c + xp)))-
104
& ddilog(b/(a + b)) + ddilog(c/(-a + c)) +
105
& ddilog((b - x)/(a + b)) - ddilog((c + x)/(-a + c)) +
106
& ddilog(b/(b - xm)) - ddilog((b - x)/(b - xm)) -
107
& ddilog(xm/(a + xm)) + ddilog(xm/(c + xm)) +
108
& ddilog((-x + xm)/(a+xm)) - ddilog((-x + xm)/(c + xm))+
109
& ddilog(a/(a + xp)) - ddilog((a + x)/(a + xp)) -
110
& ddilog(xp/(-b + xp)) - ddilog(c/(c + xp)) +
111
& ddilog((c + x)/(c + xp)) +
112
& ddilog((-x + xp)/(-b + xp))))/vik)/(8.*Pi**2)
116
C ij~ massive and massless spectator
117
elseif(mi.gt.0d0.and.mk.eq.0d0.and.id.eq.1) then
119
fi(2)= (gsq*(72d0 + 6d0*L*(4d0 + L) - 11d0*Pi**2 + 24d0*rs +
120
& (24d0*musq_i*DLog(musq_i))/(-1d0 + musq_i) +
121
& 6d0*(4d0*DLog(1 - musq_i)**2 +
122
& (2d0 + 2d0*L - Log(musq_i))*DLog(musq_i) -
123
& 4d0*DLog(1d0 - musq_i)*(2d0 + L + DLog(musq_i))) -
124
& 24d0*ddilog(1d0 - musq_i)))/(192d0*Pi**2)
126
C adding alpha dependent terms
127
if(alpha_ff.ne.1d0) then
128
fi(2)=fi(2)+(gsq*(-2*DLog(alpha_ff) +
129
& (2*DLog(alpha_ff+(1-alpha_ff)*musq_i))/(1-musq_i) +
130
& (-2 + 3*alpha_ff-alpha_ff/(alpha_ff+(1-alpha_ff)*musq_i) -
131
& ((3 - musq_i)*DLog(alpha_ff+(1-alpha_ff)*musq_i))/
132
& (1 - musq_i))/2. +2*(-(DLog(alpha_ff)*DLog(musq_i))-
133
& ddilog((-1+ musq_i)/musq_i) +
134
& ddilog((alpha_ff*(-1 + musq_i))/musq_i))))/(8.*pi**2)
137
C ij~ massless quark and massive spectator
138
elseif(mi.eq.0d0 .and. mk.gt.0d0 .and. id.eq.1) then
139
if(scheme .eq. 'HV') then
141
elseif(scheme .eq. 'DR') then
144
fi(2)= (gsq*((36*L*(1 + muk) +
145
& 6*L**2*(1 + muk) - 11*Pi**2 +
146
& 24*(5 + rs) + muk*(-11*Pi**2 + 24*(2 + rs)) -
147
& 36*(1 + muk)*Log((-1 + muk)**2) - 6*(1 + muk)*
148
& (-4*Log(1 - musq_k)**2 + Log(musq_k)*(-2*L + Log(musq_k))+
149
& 4*Log(1 - musq_k)*(L + Log(musq_k))))/(1 + muk)
150
& - 24*ddilog(1 - musq_k)))/
153
C adding alpha dependent terms
154
if(alpha_ff.ne.1d0) then
155
yp=(1d0-musq_k)/(1d0+musq_k)
156
xp=yp*(1d0-alpha_ff)+
157
& Sqrt((1d0-alpha_ff)*(1d0-alpha_ff*yp**2))
158
fi(2)=fi(2)+(gsq*((-3*((1-alpha_ff)*yp+DLog(alpha_ff)))/2. +
159
& 2*(-DLog((1-xp+yp)/(1+yp))**2+DLog((1+2*xp*yp-yp**2)/
160
& ((1 + xp - yp)*(1 - xp + yp)))**2/2. +
161
& 2*(DLog((1+xp-yp)/(1-yp))*DLog((1+yp)/2.) +
162
& DLog((1+yp)/(2.*yp))*DLog((1+2*xp*yp-yp**2)/(1-yp**2))-
163
& ddilog((1-yp)/2.) +ddilog((1 + xp - yp)/2.) +
164
& ddilog((1 - yp)/(1 + yp)) -
165
& ddilog((1+2*xp*yp-yp**2)/(1+yp)**2)))
170
C ij~ massless quark and massless spectator
171
elseif(mi.eq.0d0 .and. mk.eq.0d0 .and. id.eq.1) then
172
if(scheme .eq. 'HV') then
174
elseif(scheme .eq. 'DR') then
177
fi(2)=(gsq*(6*L*(3+L)-7*pi**2+12*(5+rs)))/(96.*pi**2)
179
C adding alpha dependent terms
180
if (alpha_ff.ne.1d0) then
181
fi(2)=fi(2)+((gsq*((3*(-1 + alpha_ff - DLog(alpha_ff)))/2.
182
& - DLog(alpha_ff)**2))/(8.*pi**2))
186
C ij~ gluon and massive spectator
187
elseif(mk.gt.0d0.and. id.eq.0) then
188
if(scheme .eq. 'HV') then
190
elseif(scheme .eq. 'DR') then
194
if(id1.eq.1.and.mi.gt.0d0) then
195
fi(2)=(gsq*((2*(1 - (4*musq_i)/(-1 + muk)**2)**1.5*muk)/
196
& (1 + muk) + (8*Sqrt(1 - (4*musq_i)/(-1 + muk)**2)*
197
& (1 + mui - muk)*(-1 + mui + muk))/(3.*(-1 + muk)**2)
198
& - 2*DLog(mui) + 2*DLog((1 +
199
& Sqrt(1 - (4*musq_i)/(-1 + muk)**2))/2.)+2*DLog(1 - muk)-
200
& (2*musq_k*((8*musq_i*Sqrt(1 - (4*musq_i)/(-1 + muk)**2))/
201
& (-1 + musq_k)-DLog((1-Sqrt(1-(4*musq_i)/(-1 + muk)**2))/
202
& (1 + Sqrt(1 - (4*musq_i)/(-1 + muk)**2))) +
203
& ((-1 + 4*musq_i + musq_k)/(-1 + musq_k))**1.5*
204
& DLog((-Sqrt(1 - (4*musq_i)/(-1 + muk)**2) +
205
& Sqrt((-1 + 4*musq_i + musq_k)/(-1 + musq_k)))/
206
& (Sqrt(1 - (4*musq_i)/(-1 + muk)**2) +
207
& Sqrt((-1 + 4*musq_i + musq_k)/(-1 + musq_k))))))
208
& /(1 - musq_k)))/(24.*Pi**2)/ca
211
C adding alpha dependent terms
212
if(alpha_ff.ne.1d0) then
214
c=-1.+2*musq_i+musq_k
215
yp=1.-2*muk*(1.-muk)/(1.-2*musq_i-musq_k)
216
b=sqrt(c**2*yp**2-4.*musq_i**2)
217
d=sqrt(alpha_ff*c**2*yp**2-4.*musq_i**2)
218
fi(2)=fi(2)-gsq*((c*Sqrt(-c + 2*musq_i)*(4*(b - d)*musq_i**2
219
& + c**2*yp*(-2*alpha_ff*b-d*(-2+yp) + alpha_ff**2*b*yp)+
220
& 4*c*musq_i*(d - d*yp + b*(-1 + alpha_ff*yp))) -
221
& 2*b*d*Sqrt(-c + 2*musq_i)*
222
& (c**2 - 2*(1 + c)*musq_i + 4*musq_i**2)
223
& *DATAN((2*musq_i)/Sqrt(-4*musq_i**2 + c**2*yp**2)) +
224
& 2*b*d*Sqrt(-c + 2*musq_i)*
225
& (c**2 - 2*(1 + c)*musq_i + 4*musq_i**2)
227
& Sqrt(-4*musq_i**2 + alpha_ff**2*c**2*yp**2)) +
228
& b*d*(2*a*(c + c**2 + 2*musq_i - 4*musq_i**2)*
229
& DLog(-((-c - 2*musq_i)**2.5
230
& *(1 + c - 2*musq_i)*(-1 + yp))) -
231
& 2*a*(c + c**2 + 2*musq_i - 4*musq_i**2)*
232
& DLog((-c - 2*musq_i)**2.5
233
& *(1 + c - 2*musq_i)*(1 - alpha_ff*yp)) +
234
& 2*c*Sqrt(-c + 2*musq_i)*DLog(-2*(b + c*yp))
235
& + 3*c**2*Sqrt(-c + 2*musq_i)*DLog(-2*(b + c*yp)) -
236
& 4*c*musq_i*Sqrt(-c + 2*musq_i)*DLog(-2*(b + c*yp))
237
& - 2*c*Sqrt(-c + 2*musq_i)*Log(-2*(d + alpha_ff*c*yp)) -
238
& 3*c**2*Sqrt(-c + 2*musq_i)*DLog(-2*(d + alpha_ff*c*yp))
239
& + 4*c*musq_i*Sqrt(-c + 2*musq_i)*
240
& DLog(-2*(d + alpha_ff*c*yp)) -
241
& 2*a*c*DLog(-4*musq_i**2 - b*Sqrt(c**2 - 4*musq_i**2) +
242
& c**2*yp) - 2*a*c**2*DLog(-4*musq_i**2 -
243
& b*Sqrt(c**2 - 4*musq_i**2) + c**2*yp) -
244
& 4*a*musq_i*DLog(-4*musq_i**2 - b*Sqrt(c**2 - 4*musq_i**2)
245
& + c**2*yp) + 8*a*musq_i**2*DLog(-4*musq_i**2 -
246
& b*Sqrt(c**2 - 4*musq_i**2) + c**2*yp) +
247
& 2*a*c*DLog(-4*musq_i**2 - d*Sqrt(c**2 - 4*musq_i**2) +
248
& alpha_ff*c**2*yp) + 2*a*c**2*Log(-4*musq_i**2 -
249
& d*Sqrt(c**2 - 4*musq_i**2) + alpha_ff*c**2*yp) +
250
& 4*a*musq_i*DLog(-4*musq_i**2 - d*Sqrt(c**2 - 4*musq_i**2)
251
& + alpha_ff*c**2*yp) - 8*a*musq_i**2*DLog(-4*musq_i**2 -
252
& d*Sqrt(c**2 - 4*musq_i**2) + alpha_ff*c**2*yp)))/
253
& (3.*c*(-c+2*musq_i)**1.5*Sqrt(-4*musq_i**2 + c**2*yp**2)
254
& *Sqrt(-4*musq_i**2+alpha_ff**2*c**2*yp**2)))/
261
elseif(id1.eq.1.and. mi.eq.0d0) then
262
fi(2)=(gsq*((-1 + muk)*(-6*L*(1 + muk) - 4*(4 + muk)
263
c$$$ & + 9*(1 + muk)*rs) + 12*(-1 + muk**2)*DLog(1 - muk) +
264
c RF No scheme dependence here. All in the g -> gg.
265
& ) + 12*(-1 + musq_k)*DLog(1 - muk) +
266
& 12*musq_k*DLog((2*muk)/(1 + muk))))/
267
& (144.*(-1 + musq_k)*pi**2)/ca
268
C adding alpha dependent terms
269
if(alpha_ff.ne.1d0) then
270
fi(2)=fi(2)-(gsq*(-((-1 + alpha_ff)*(-1 + muk)**2) +
271
& DLog(alpha_ff) + musq_k*(DLog(4d0) + DLog(1/alpha_ff)
272
& + 2*DLog(muk) - 2*DLog(1 + muk) -
273
& 2*DLog(1+alpha_ff-(2*alpha_ff)/(1+muk))))/
274
& (3.*(-1+musq_k)))/(8.*pi**2)/ca
278
elseif(id1.eq.0) then
279
fi(2)=(gsq*((200 + 66*L + 9*L**2-(132*muk)/(1 + muk)-15*Pi**2
280
& - 132*DLog(1 - muk) - (24*musq_k*DLog((2*muk)/(1 +
281
& muk)))/(-1 + musq_k) +66*DLog(1 - musq_k) + 9*(4*(L -
282
& DLog(muk))*DLog(muk) - 2*(L + 2*DLog(muk))*DLog(1 -
283
& musq_k) + DLog(1 - musq_k)**2) - 36*ddilog(1 - musq_k)))
286
C adding alpha dependent terms
287
if (alpha_ff.ne.1d0) then
288
yl=1d0 + alpha_ff*(-1 + muk)**2 - musq_k -
289
& Sqrt(abs((-1+muk)**2*(alpha_ff**2*(-1+muk)**2+
290
& (1+muk)**2-2*alpha_ff*(1+musq_k))))
291
fi(2)=fi(2)-(gsq*((11*(-2+2*muk+yl)**2)/
292
& ((-1+musq_k)*(-2+yl))
293
& -44*Log(2-2*muk) - 22*Log(muk) + 24*Log(2/(1 + muk))*
294
& (Log(2/(1 + muk)) + 2*Log(1 + muk)) +
295
& (2*((-11 + 15*musq_k)*Log(2*muk) +
296
& 4*musq_k*(-Log(-8*(-1+muk)*musq_k)+
297
& Log((-2 + yl)**2+4*musq_k*(-1 + yl))) +
298
& (11 - 15*musq_k)*Log(2 - yl)))/(-1 + musq_k) +
299
& 22*Log(2 - 2*musq_k - yl) +
300
& 22*Log(yl)-12*(4*Log(1-yl/2.)*Log(-(yl/(-1+musq_k)))-
301
& Log(-(yl/(-1+musq_k)))**2 +
302
& Log((-2*(-2 + 2*musq_k + yl))/
303
& ((-1 + musq_k)*(-2 + yl)))**2 +
304
& 2*Log(-(yl/(-1+musq_k)))*(
305
& Log((-2*(-2+2*musq_k+yl))/((-1+musq_k)*(-2+yl))) -
306
& 2*Log(1 + yl/(-2 + 2*musq_k)))) + 48*ddilog(1 - muk) -
307
& 48*ddilog(1/(1 + muk)) -
308
& 48*ddilog(yl/2.) + 48*ddilog(yl/(2 - 2*musq_k))))/
313
C ij~ gluon and massless spectator
314
elseif(mk.eq.0d0.and.id.eq.0) then
315
if(scheme .eq. 'HV') then
317
elseif(scheme .eq. 'DR') then
321
if(id1.eq.1.and.mi.gt.0d0) then
322
fi(2)=(gsq*(-16*Sqrt(1-4*musq_i)+16*musq_i*Sqrt(1-4*musq_i)+
323
c$$$ & 9*rs-12*DLog(Sqrt(musq_i))+
324
c RF No scheme dependence here. All in the g -> gg.
325
& 12*DLog(Sqrt(musq_i))+
326
& 12*DLog((1 + Sqrt(1 - 4*musq_i))/2.)))/(144.*pi**2)/ca
327
C adding alpha dependent terms
328
if (alpha_ff.ne.1d0) then
329
fi(2)=fi(2)-(gsq*(Sqrt(1-4*musq_i)+
330
& Sqrt(-4*musq_i**2+alpha_ff**2*(1-2*musq_i)**2) +
331
& (2*Sqrt(-4*musq_i**2+alpha_ff**2*(1-2*musq_i)**2))/
332
& (-alpha_ff+2*(-1+alpha_ff)*musq_i) +
333
& (-1 + 2*musq_i)*(-2*DATAN((2*musq_i)/
334
& Sqrt(1 - 4*musq_i)) +
335
& 2*DATan((2*musq_i)/
336
& Sqrt(-4*musq_i**2 + alpha_ff**2*(1 - 2*musq_i)**2))+
337
& DLog(-2*(-1 + 2*musq_i + Sqrt(1 - 4*musq_i))) -
338
& DLog(-2*(alpha_ff*(-1+2*musq_i)+
339
& Sqrt(-4*musq_i**2+alpha_ff**2*(1-2*musq_i)**2))))))/
343
elseif(id1.eq.1.and. mi.eq.0d0) then
344
c$$$ fi(2)=-(gsq*(8 + 3*L - 9*rs*ca))/(144.*pi**2)/ca
345
c RF No scheme dependence here. All in the g -> gg.
346
fi(2)=-(gsq*(8 + 3*L))/(144.*pi**2)/ca
348
C adding alpha dependent terms
349
if (alpha_ff.ne.1d0) then
350
fi(2)=fi(2)-(gsq*(-1 + alpha_ff - DLog(alpha_ff)))/
355
elseif(id1.eq.0) then
356
fi(2)=(gsq*((200+6*L*(11+3*L)-21*pi**2)+36*rs))/(144.*pi**2)
358
C adding alpha dependent terms
359
if (alpha_ff.ne.1d0) then
360
fi(2)=fi(2)-(gsq*(11-11*alpha_ff+11*DLog(alpha_ff)+
361
& 6*DLog(alpha_ff)**2))/(24.*pi**2)
369
SUBROUTINE finitefi(mi,sik,sikzone,x,id1,id2,fi)
370
c calculates the finite terms when emitter is in
371
c final state and spectator is in initial state
377
REAL*8 mi,qsq,sik,x,fi(9),sikzone
384
REAl*8 cf,ca,rhoi,rhok,rho,musq_i,gsq,pi
385
REAL*8 L,L_one,rs,musq_i_one
386
PARAMETER (cf=4d0/3d0,ca=3d0)
387
PARAMETER (pi=3.1415926535897932385d0)
390
musq_i_one=mi**2/sikzone
392
L_one=DLog(mu**2/sikzone)
398
C massive quark (ij~: quark)
399
if(mi .gt. 0d0 .and. id1.eq.1) then
401
fi(2)=(gsq*((1d0+DLOG(musq_i_one/(musq_i_one+1d0)))*L_one
402
& -2d0*ddilog(-musq_i_one)-pi**2/3d0+2d0+
403
& DLOG(musq_i_one)**2/2d0+DLOG(1+musq_i_one)**2/2d0-
404
& 2d0*DLOG(musq_i_one)*DLOG(1+musq_i_one)+DLOG(musq_i_one)))
407
c adding the alpha dependent term
408
if(alpha_fi.ne.1d0) then
409
fi(2)=fi(2)+gsq/(8.*pi**2)*2.*DLog(alpha_fi)*
410
& (DLog((1d0+musq_i_one)/(musq_i_one))-1d0)
412
if(x.gt.(1d0-alpha_fi)) then
413
fi(1)=gsq/(8.*pi**2)*((1.-x)/(2.*(1-x+musq_i)**2)+2./
414
& (1-x)*DLog(((2.-x+musq_i)*musq_i_one)
415
& /((1.+musq_i_one)*(1-x+musq_i))))
416
fi(3)=gsq/(8.*pi**2)*2./(1-x)*
417
& (DLOG((1+musq_i_one)/(musq_i_one))-1d0)
421
C massless quark (ij~: quark)
422
elseif(mi.eq.0d0 .and. id1.eq.1) then
423
if(scheme .eq. 'HV') then
425
elseif(scheme .eq. 'DR') then
428
fi(2)=(gsq*(6*(7+L_one*(3+L_one))-7*pi**2+12*rs))/(96.*pi**2)
429
c adding the alpha dependent term
430
if (alpha_fi.ne.1d0) then
431
fi(2)=fi(2)+gsq/(8.*pi**2)*(-3./2.*Dlog(alpha_fi)-
434
if(x.gt.(1d0-alpha_fi)) then
435
fi(1)=gsq/(4d0*pi**2*(1-x))*DLog(2d0-x)
436
fi(3)=-(gsq*(3/(1-x)+(4*DLog(1-x))/(1-x)))/(16.*pi**2)
441
elseif(id1.eq.0) then
442
if(scheme .eq. 'HV') then
444
elseif(scheme .eq. 'DR') then
447
C 1. g-> QQ (i:massive quark )
448
if(id2.eq.1.and.mi.gt.0d0) then
449
fi(7)=-(gsq*(5*Sqrt(1-4*musq_i_one)+
450
& 4*musq_i_one*Sqrt(1-4*musq_i_one)+DLog(64d0) +
451
& 3*DLog(musq_i_one) -
452
& 6*DLog(1+Sqrt(1-4*musq_i_one))))/(72.*pi**2)/ca
453
c adding the alpha dependent term
454
if (alpha_fi.ne.1d0) then
455
fi(7)=fi(7)+(gsq*((5 - 16*musq_i_one**2 -
456
& 5*Sqrt(((1 - 4*musq_i_one)*
457
& (alpha_fi - 4*musq_i_one))/alpha_fi) -
458
& 4*musq_i_one*(4 + Sqrt(((1 - 4*musq_i_one)*
459
& (alpha_fi - 4*musq_i_one))/
460
& alpha_fi**3)))/Sqrt(1 - 4*musq_i_one)-
461
& 6*DLog(1+Sqrt(1-4*musq_i_one)) +
462
& 6*DLog(Sqrt(alpha_fi)+
463
& Sqrt(alpha_fi-4*musq_i_one))))/(72.*pi**2)/ca
465
if(x.lt.1d0-4d0*musq_i)then
466
if(x.gt.(1d0-alpha_fi)) then
467
fi(8)=(gsq*Sqrt(1+(4*musq_i)/(-1 +x))*
468
& (1 + 2*musq_i - x))/(24.*pi**2*(-1 + x)**2)/ca
473
c 2. g-> qq (i:massless quark)
474
elseif(id2.eq.1.and.mi.eq.0d0) then
475
c RF No scheme dependence here. All in the g -> gg.
476
fi(2)=-(gsq*(10 + 6*L_one))/(144.*pi**2)/ca
477
c adding the alpha dependent term
478
if(alpha_fi.ne.1d0) then
479
fi(2)=fi(2)+gsq/(8d0*pi**2)*DLog(alpha_fi)/3./ca
481
if(x.gt.(1d0-alpha_fi)) then
482
fi(3)=gsq/(24.*pi**2*(1 - x))/ca
486
C 3. g-> gg (i: gluon )
487
elseif(id2.eq.0) then
488
fi(2)=(gsq*(134 + 6*L_one*(11 + 3*L_one) -
489
& 21*pi**2 + 36*rs))/(144.*pi**2)
490
c adding the alpha dependent term
491
if (alpha_fi.ne.1d0) then
492
fi(2)=fi(2)+gsq/(8.*pi**2)*
493
& (-2d0*DLOG(alpha_fi)**2-11d0/3d0*DLOG(alpha_fi))
495
if(x.gt.(1d0-alpha_fi)) then
496
fi(1)=-(gsq*DLog(2 - x))/(2.*pi**2*(-1 + x))
497
fi(3)=(gsq*(-11/(1-x)+(12*DLog(1-x))/(-1+x)))/(24.*pi**2)
506
SUBROUTINE finiteif(mk,sik,sikzone,x,id1,id2,fi)
507
c calculates the finite terms when the emitter is
508
c in the initial state and the spectator is in the
515
REAL*8 mk,sik,sikzone,x,fi(9)
523
REAL*8 zp,musq_k,L,L_one,rs,musq_k_one
524
PARAMETER (cf=4d0/3d0,ca=3d0)
525
PARAMETER (pi=3.1415926535897932385d0)
529
musq_k_one=mk**2/sikzone
530
zp=(1d0-x)/(1d0-x+musq_k)
532
L_one=DLog(mu**2/sikzone)
538
c quark-quark splitting
539
if(id1 .eq.1.and.id2.eq.1) then
540
if(scheme .eq. 'HV') then
542
elseif(scheme .eq. 'DR') then
545
fi(2)=(gsq*(2*L_one**2-pi**2+4*rs+6*DLog(mu**2/muf**2) +
546
& 2*DLog(1 + musq_k_one)*(2*L_one + DLog(1 + musq_k_one)) +
547
& 8*ddilog(1/(1 + musq_k_one))))/(32.*pi**2)
548
fi(1)=-(gsq*(-((-1 + x**2)*(L - DLog(mu**2/muf**2)))+
549
& (-1+x**2)*DLog(1 - x) - 2*DLog(2 - x) +
550
& (-1+x)*(-1 + x +(1+x)*DLog((-1+x)/(-1-musq_k+x)))))/
551
& (8.*pi**2*(-1 + x))
552
fi(3)=(gsq*(L-DLog(mu**2/muf**2)-2*DLog(1 - x)))/
553
& (4.*pi**2*(-1 + x))
554
fi(4)=(gsq*(L_one-DLog(mu**2/muf**2)-2*DLog(1 - x)))/
555
& (4.*pi**2*(-1 + x))
557
fi(5)=gsq/(4d0*pi**2)*Dlog((2d0-x)/(2d0-x+musq_k))/(1d0-x)
558
fi(6)=gsq/(4d0*pi**2)*Dlog(1d0/(1d0+musq_k_one))/(1d0-x)
560
c adding the alpha dependent term
561
if(zp.gt.alpha_if) then
562
fi(1)=fi(1)-(gsq*(-((1+x)*DLog(zp/alpha_if)) +
563
& (2*DLog(((1+alpha_if-x)*zp)/(alpha_if*(1-x+zp))))/
564
& (1 - x)))/(8.*pi**2)
567
c quark-gluon splitting (i:quark, ij~: gluon)
568
elseif(id1.eq.1.and.id2.eq.0 ) then
569
fi(1)=(cf*gsq*(x**2 - L*(2 + (-2 + x)*x) +
570
& (2 + (-2 + x)*x)*DLog(mu**2/muf**2) +
571
& (2 + (-2 + x)*x)*DLog(1 - x) +
572
& (2 + (-2 + x)*x)*DLog((-1 + x)/(-1 - musq_k + x))))/
574
c adding the alpha dependent term
575
if(zp.gt.alpha_if) then
576
if(musq_k.gt.0d0) then
578
& (cf*gsq*((2*musq_k*DLog((1 - zp)/(1 - alpha_if)))/x
579
& + ((1 + (1 - x)**2)*DLog(zp/alpha_if))/x))/
581
elseif(musq_k.eq.0d0) then
582
fi(1)=fi(1)-(cf*gsq*(2-2*x+x**2)*
583
& DLog(zp/alpha_if))/(8.*pi**2*x)/ca
587
c gluon-quark splitting (i:gluon, ij~: quark)
588
elseif(id1.eq.0.and.id2.eq.1) then
589
fi(1)=(gsq*(-L + 2*(1 + L)*x - 2*(1 + L)*x**2 +
590
& (1 + 2*(-1 + x)*x)*DLog(mu**2/muf**2) +
591
& (1 + 2*(-1 + x)*x)*DLog(1 - x) +
592
& (1 + 2*(-1 + x)*x)*DLog((-1 + x)/(-1 - musq_k + x))))
594
c adding the alpha dependent term
595
if(zp.gt.alpha_if) then
596
fi(1)=fi(1)-(gsq*((1-x)**2+x**2)*
597
& DLog(zp/alpha_if))/(16.*pi**2)/cf
600
c gluon-gluon splitting (i:gluon, ij~:gluon)
601
elseif(id1.eq.0.and.id2.eq.0) then
602
if(scheme .eq. 'HV') then
604
elseif(scheme .eq. 'DR') then
607
if(musq_k.gt.0d0) then
608
fi(2)=(gsq*(6*L_one**2 - 3*pi**2 + 12*rs
609
& + (22 - 4*Nf/ca)*DLog(mu**2/muf**2) +
610
& 6*DLog(1 + musq_k_one)*(2*L_one + Log(1 + musq_k_one))
611
& + 24*ddilog(1/(1 + musq_k_one))))/(96.*pi**2)
612
fi(1)=(gsq*(L - 3*L*x + 3*L*x**2 - 2*L*x**3 + L*x**4 -
613
& (-1 + x)*(-1 + x*(2 + (-1 + x)*x))*DLog(mu**2/muf**2) -
614
& (-1 + x)*(-1 + x*(2 + (-1 + x)*x))*DLog(1 - x)
615
& + x*DLog(2 - x) - musq_k*DLog(musq_k/(1 + musq_k - x))
616
& + musq_k*x*DLog(musq_k/(1 + musq_k - x)) -
617
& (-1 + x)*(-1 + x*(2 + (-1 + x)*x))*Log((-1 + x)/
618
& (-1 - musq_k + x))))/(4.*pi**2*(-1 + x)*x)
619
fi(4)=(gsq*(L_one - DLog(mu**2/muf**2) - 2*DLog(1 - x)))/
620
& (4.*pi**2*(-1 + x))
621
fi(3)=(gsq*(L - DLog(mu**2/muf**2) - 2*DLog(1 - x)))/
622
& (4.*pi**2*(-1 + x))
623
fi(5)=gsq/(4d0*pi**2)*DLog((2d0-x)/(2d0-x+musq_k))/(1d0-x)
624
fi(6)=gsq/(4d0*pi**2)*Dlog((1d0)/(1d0+musq_k_one))/(1d0-x)
625
c adding the alpha dependent term
626
if(zp.gt.alpha_if) then
627
fi(1)=fi(1)+(gsq*((-2*musq_k*DLog((1-zp)/(1-alpha_if)))/x
628
& -2*(-1+(1 - x)/x + (1 - x)*x)*DLog(zp/alpha_if) +
629
& (2*DLog((alpha_if*(1-x+zp))/((1+alpha_if-x)*zp)))/
630
& (1 - x)))/(8.*pi**2)
632
elseif(musq_k.eq.0d0) then
633
fi(2)=(gsq*((6*L_one**2 + pi**2) + 12*rs
634
& + (22 - 4*Nf/ca)*DLog(mu**2/muf**2)))/(96.*pi**2)
635
fi(1)=(gsq*((-1 + x*(2 + (-1 + x)*x))*
636
& (L-DLog(mu**2/muf**2)-DLog(1-x))-
637
& x*Dlog(2-x)/(1-x)))/(4.*pi**2*x)
638
fi(4)=(gsq*(L_one-DLog(mu**2/muf**2)-2*DLog(1-x)))/
639
& (4.*pi**2*(-1 + x))
640
fi(3)=(gsq*(L-DLog(mu**2/muf**2)-2*DLog(1-x)))/
641
& (4.*pi**2*(-1 + x))
642
c adding the alpha dependent term
643
if(zp.gt.alpha_if) then
644
fi(1)=fi(1)+(gsq*((1 - 3*x + 3*x**2
645
& - 2*x**3 + x**4)*DLog(zp/alpha_if) -
646
& x*DLog((alpha_if*(1 - x + zp))/
647
& ((1 + alpha_if - x)*zp))))/(4.*pi**2*(-1 + x)*x)
655
SUBROUTINE finiteii(sik,sikzone,x,id1,id2,fi)
656
c calculates the finite terms when both emitter
657
c and spectator are in the initial state.
663
REAL*8 sik,sikzone,x,fi(9)
672
PARAMETER (cf=4d0/3d0,ca=3d0)
673
PARAMETER (pi=3.1415926535897932385d0)
677
L_one=dlog(mu**2/sikzone)
683
c quark-quark splitting (i:quark, ij~: quark)
684
if(id1 .eq.1.and.id2.eq.1) then
685
if(scheme .eq. 'HV') then
687
elseif(scheme .eq. 'DR') then
690
fi(2)=(gsq*(2*L_one**2-pi**2+4*rs+6*DLog(mu**2/muf**2)))/
692
fi(1)=-(gsq*(-1 + x + (-1 - x)*(L -dLog(mu**2/muf**2))
693
& + 2*(1 + x)*dLog(1 - x)))/(8.*pi**2)
694
fi(4)=-(gsq*((2*(L_one - dLog(mu**2/muf**2)))/(1 - x)
695
& + (4*dLog(1 - x))/(-1 + x)))/(8.*pi**2)
696
fi(3)=-(gsq*((2*(L - dLog(mu**2/muf**2)))/(1 - x)
697
& + (4*dLog(1 - x))/(-1 + x)))/(8.*pi**2)
698
c adding the alpha dependent term
699
if((1d0-x).gt.alpha_ii) then
700
fi(1)=fi(1)+(gsq*(1+x**2)*DLog(alpha_ii/(1-x)))/
705
c quark-gluon splitting (i:quark, ij~:gluon)
706
elseif(id1.eq.1.and.id2.eq.0) then
707
fi(1)=(cf*gsq*(x**2 - L*(2 + (-2 + x)*x)
708
& +(2 + (-2 + x)*x)*dLog(mu**2/muf**2) +
709
& 2*(2 + (-2 + x)*x)*DLog(1 - x)))/(8.*pi**2*x)/ca
710
c adding the alpha dependent term
711
if((1d0-x).gt.alpha_ii) then
712
fi(1)=fi(1)+(cf*gsq*(1+(1-x)**2)*DLog(alpha_ii/(1-x)))/
717
c gluon-quark splitting (i:gluon, ij~:quark)
718
elseif(id1.eq.0.and.id2.eq.1) then
719
fi(1)=(gsq*(-L + 2*(1 + L)*x - 2*(1 + L)*x**2
720
& + (1 + 2*(-1 + x)*x)*DLog(mu**2/muf**2) +
721
& (2 + 4*(-1 + x)*x)*DLog(1 - x)))/(16.*pi**2)/cf
722
c adding the alpha dependent term
723
if((1d0-x).gt.alpha_ii) then
724
fi(1)=fi(1)+(gsq*((1-x)**2+x**2)*DLog(alpha_ii/(1-x)))/
728
c gluon-gluon splitting (i:gluon, ij~:gluon)
729
elseif(id1.eq.0.and.id2.eq.0) then
730
if(scheme .eq. 'HV') then
732
elseif(scheme .eq. 'DR') then
735
fi(2)=(gsq*(6*L_one**2 - 3*pi**2 + 12*rs + (22 -
736
& 4*Nf/ca)*DLog(mu**2/muf**2)))/(96.*pi**2)
737
fi(1)=(gsq*(-1 + x*(2 + (-1 + x)*x))*
738
& (L-DLog(mu**2/muf**2)-2*DLog(1-x)))/(4.*pi**2*x)
739
fi(4)=-(gsq*((2*(L_one-DLog(mu**2/muf**2)))/(1 - x)
740
& + (4*DLog(1 - x))/(-1 + x)))/(8.*pi**2)
741
fi(3)=-(gsq*((2*(L-DLog(mu**2/muf**2)))/(1 - x)
742
& + (4*DLog(1 - x))/(-1 + x)))/(8.*pi**2)
743
c adding the alpha dependent term
744
if((1d0-x).gt.alpha_ii) then
745
fi(1)=fi(1)+(gsq*(-1+(1-x)*x)**2*DLog(alpha_ii/(1-x)))/
753
* dilog64.F,v 1.1.1.1 1996/04/01 15:02:05 mclareni
755
* Revision 1.1.1.1 1996/04/01 15:02:05 mclareni
761
* imp64.inc,v 1.1.1.1 1996/04/01 15:02:59 mclareni Exp
763
* Revision 1.1.1.1 1996/04/01 15:02:59 mclareni
769
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
771
PARAMETER (Z1 = 1, HF = Z1/2)
772
PARAMETER (PI = 3.14159 26535 89793 24D0)
773
PARAMETER (PI3 = PI**2/3, PI6 = PI**2/6, PI12 = PI**2/12)
774
DATA C( 0) / 0.42996 69356 08136 97D0/
775
DATA C( 1) / 0.40975 98753 30771 05D0/
776
DATA C( 2) /-0.01858 84366 50145 92D0/
777
DATA C( 3) / 0.00145 75108 40622 68D0/
778
DATA C( 4) /-0.00014 30418 44423 40D0/
779
DATA C( 5) / 0.00001 58841 55418 80D0/
780
DATA C( 6) /-0.00000 19078 49593 87D0/
781
DATA C( 7) / 0.00000 02419 51808 54D0/
782
DATA C( 8) /-0.00000 00319 33412 74D0/
783
DATA C( 9) / 0.00000 00043 45450 63D0/
784
DATA C(10) /-0.00000 00006 05784 80D0/
785
DATA C(11) / 0.00000 00000 86120 98D0/
786
DATA C(12) /-0.00000 00000 12443 32D0/
787
DATA C(13) / 0.00000 00000 01822 56D0/
788
DATA C(14) /-0.00000 00000 00270 07D0/
789
DATA C(15) / 0.00000 00000 00040 42D0/
790
DATA C(16) /-0.00000 00000 00006 10D0/
791
DATA C(17) / 0.00000 00000 00000 93D0/
792
DATA C(18) /-0.00000 00000 00000 14D0/
793
DATA C(19) /+0.00000 00000 00000 02D0/
796
ELSEIF(X .EQ. -1) THEN
803
A=-PI3+HF*(LOG(-T)**2-LOG(1+1/T)**2)
804
ELSEIF(T .LT. -1) THEN
808
A=-PI6+A*(A+LOG(1+1/T))
809
ELSE IF(T .LE. -HF) THEN
813
A=-PI6+A*(-HF*A+LOG(1+T))
814
ELSE IF(T .LT. 0) THEN
818
ELSE IF(T .LE. 1) THEN
added
removed
Template/LO/SubProcesses/finiteterms.f
