forked from alisw/POWHEG
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathsigsoftvirt.f
471 lines (451 loc) · 16.1 KB
/
sigsoftvirt.f
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
subroutine btildevirt(resvirt)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_br.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_em.h'
include 'pwhg_flg.h'
include 'pwhg_par.h'
include 'pwhg_pdf.h'
real * 8 resvirt(flst_nborn)
real * 8 c(-6:6),gamma(-6:6),gammap(-6:6),gammatilde(-6:6)
integer j,jb,fl1,fl2,fl,leg,legi,legj,jres,kres
real * 8 Q,I,s,etot,e,eij,virt_arr(flst_nborn),tot,kij,arglog,
1 loglog,pborn(0:3,nlegborn)
real * 8 pdfb1(-pdf_nparton:pdf_nparton),
1 pdfb2(-pdf_nparton:pdf_nparton)
logical ini
data ini/.true./
real * 8 ddilog,dotp
external ddilog,dotp
save c,gamma,gammap,gammatilde,ini
real * 8 tiny
parameter (tiny=1d-14)
real * 8 ll,llew,rescfac
real * 8 Intm_ep,Int0m_0,Int0m_ep,Intmm_0,Intmm_ep
external Intm_ep,Int0m_0,Int0m_ep,Intmm_0,Intmm_ep
real * 8 tmp,tmpew,Qem,Iem,ch_i,ch_j,ch1,ch2
logical pwhg_isfinite
real * 8 chargeofparticle
external pwhg_isfinite,chargeofparticle
integer sigma
external sigma
logical is_charged, is_coloured
external is_charged, is_coloured
c if virtual.f, will not do smartsig when this flag is active
if (flg_novirtual) then
resvirt = 0d0
return
endif
c from 2.100 of FNO2007
if(ini) then
do j=-6,6
if(j.eq.0) then
c(j)=ca
gamma(j)=(11*ca-4*tf*st_nlight)/6
gammap(j)=(67d0/9-2*pi**2/3)*ca-23d0/9*tf*st_nlight
gammatilde(j)=ca/6d0
else
c(j)=cf
gamma(j)=3d0/2*cf
gammap(j)=(13d0/2-2*pi**2/3)*cf
gammatilde(j)=cf/2
endif
enddo
ini=.false.
endif
if(.not.flg_minlo) then
c get pdfs
call pdfcall(1,kn_xb1,pdfb1)
call pdfcall(2,kn_xb2,pdfb2)
endif
tot=0
call sigvirtual(virt_arr)
c Strong Q contribution
Q = 0
c EW Q contribution
Qem = 0
do jres=1,flst_nreson
kres=flst_reslist(jres)
if(kres.ne.0) then
call boost2reson(kn_cmpborn(:,kres),nlegborn,
1 kn_cmpborn,pborn)
etot=pborn(0,kres)
else
pborn=kn_cmpborn
etot=2*kn_cmpborn(0,1)
endif
s=etot**2
if(.not.flg_minlo) then
ll = log(par_csicut**2*s/st_muren2)
if(flg_with_em) llew = log(par_csicut**2*s/em_muren2)
rescfac = 1
endif
do jb=1,flst_nborn
c Strong Q contribution
Q = 0
c EW Q contribution
Qem = 0
if(flg_minlo) then
call setlocalscales(jb,2,rescfac)
ll = log(par_csicut**2*s/st_muren2)
if(flg_with_em) llew = log(par_csicut**2*s/em_muren2)
c get pdfs
call pdfcall(1,kn_xb1,pdfb1)
call pdfcall(2,kn_xb2,pdfb2)
endif
fl1=flst_born(1,jb)
fl2=flst_born(2,jb)
c initial-state parton contribution
if(kres.eq.0) then
if(is_coloured(fl1)) then
Q=Q-log(st_mufact2/st_muren2)*(gamma(fl1)+2*c(fl1)*
1 log(par_csicut))
if(flg_drscheme) then
Q=Q-gammatilde(fl1)
endif
endif
if(is_coloured(fl2)) then
Q=Q-log(st_mufact2/st_muren2)*
1 (gamma(fl2)+2*c(fl2)*log(par_csicut))
if(flg_drscheme) then
Q=Q-gammatilde(fl2)
endif
endif
c EW photonic contribution
ch1=chargeofparticle(fl1)
ch2=chargeofparticle(fl2)
if (flg_with_em.and.ch1.ne.0) then
Qem=Qem-log(st_mufact2/em_muren2)*(
1 (1.5d0+2*log(par_csicut))*ch1**2)
endif
if (flg_with_em.and.ch2.ne.0) then
Qem=Qem-log(st_mufact2/em_muren2)*(
3 + (1.5d0+2*log(par_csicut))*ch2**2)
endif
endif
c loop on final-state massless partons
do leg=3,nlegborn
if(leg.ne.kres.and.flst_bornres(leg,jb).ne.kres) cycle
fl=flst_born(leg,jb)
if(is_coloured(fl)) then
if(kn_masses(leg).eq.0) then
if(flg_drscheme) then
Q=Q-gammatilde(fl)
endif
e=pborn(0,leg)
Q=Q+gammap(fl)
1 -log(s/st_muren2)*(gamma(fl)-2*c(fl)
3 *log(2*e/(par_csicut*etot)))
3 +2*c(fl)*(log(2*e/etot)**2-log(par_csicut)**2)
4 -2*gamma(fl)*log(2*e/etot)
else
Q = Q - c(flst_born(leg,jb))*
1 (ll-0.5*Intm_ep(pborn(0,leg)))
endif
endif
c WEW
if (flg_with_em.and.chargeofparticle(fl).ne.0) then
if(kn_masses(leg).eq.0) then
write(*,*) ' not prepared to handle this!'
call pwhg_exit(-1)
else
Qem = Qem -
1 (llew-0.5*Intm_ep(kn_cmpborn(0,leg)))
2 * chargeofparticle(fl)**2
endif
endif
enddo
Q=Q*br_born(jb)
Qem=Qem*br_born(jb)
Iem=0
I=0
do legi=1,nlegborn
if(legi.ne.kres.and.flst_bornres(legi,jb).ne.kres)
1 cycle
do legj=legi+1,nlegborn
if(legj.ne.kres.and.flst_bornres(legj,jb).ne.kres)
1 cycle
c both particles are colored
if(is_coloured(flst_born(legi,jb)).and.
1 is_coloured(flst_born(legj,jb)) ) then
c massless-massless case
if (kn_masses(legi).eq.0.and.kn_masses(legj).eq.0)
1 then
kij=dotp(pborn(0,legi),pborn(0,legj))
eij=pborn(0,legi)*pborn(0,legj)
arglog = abs(1-kij/(2*eij))
if (arglog.lt.tiny) then
loglog = 0d0
else
loglog = log(arglog)*log(kij/(2*eij))
endif
I=I+(1d0/2*ll**2
1 +ll*log(kij/(2*eij))
2 -ddilog(kij/(2*eij))
3 +1d0/2*log(kij/(2*eij))**2
4 -loglog)*
5 br_bornjk(legi,legj,jb)
endif
c massless-massive case
if (kn_masses(legi).eq.0.and.kn_masses(legj).gt.0)
1 then
I = I + (0.5*(0.5*ll**2 - pi**2/6)
1 +0.5*Int0m_0(pborn(0,legi),pborn(0,legj))*ll
2 -0.5*Int0m_ep(pborn(0,legi),pborn(0,legj)))*
3 br_bornjk(legi,legj,jb)
endif
c massive-massless case
if (kn_masses(legi).gt.0.and.kn_masses(legj).eq.0)
1 then
I = I + (0.5*(0.5*ll**2 - pi**2/6)
1 +0.5*Int0m_0(pborn(0,legj),pborn(0,legi))*ll
2 -0.5*Int0m_ep(pborn(0,legj),pborn(0,legi)))*
3 br_bornjk(legj,legi,jb)
endif
c massive-massive case
if (kn_masses(legi).gt.0.and.kn_masses(legj).gt.0)
1 then
I = I + (0.5*ll*
1 Intmm_0(pborn(0,legi),pborn(0,legj))
2 -0.5*Intmm_ep(pborn(0,legi),pborn(0,legj)))
3 *br_bornjk(legi,legj,jb)
endif
endif
ch_i=chargeofparticle(flst_born(legi,jb))
ch_j=chargeofparticle(flst_born(legj,jb))
c both particles are charged
if (flg_with_em.and.ch_i.ne.0.and.ch_j.ne.0) then
c massless-massless case
if (kn_masses(legi).eq.0.and.kn_masses(legj).eq.0)
1 then
kij=dotp(kn_cmpborn(0,legi),kn_cmpborn(0,legj))
eij=kn_cmpborn(0,legi)*kn_cmpborn(0,legj)
arglog = abs(1-kij/(2*eij))
if (arglog.lt.tiny) then
loglog = 0d0
else
loglog = log(arglog)*log(kij/(2*eij))
endif
Iem=Iem+(1d0/2*llew**2
1 +llew*log(kij/(2*eij))
2 -ddilog(kij/(2*eij))+1d0/2*log(kij/(2*eij))**2
3 -loglog)*
4 br_born(jb)*ch_i*ch_j*(-1)*
5 sigma(flst_born(legi,jb),legi)*
6 sigma(flst_born(legj,jb),legj)
endif
c massless-massive case
if (kn_masses(legi).eq.0.and.kn_masses(legj).gt.0)
1 then
Iem = Iem + (0.5*(0.5*llew**2 - pi**2/6)
1 +0.5*Int0m_0(kn_cmpborn(0,legi),kn_cmpborn(0,legj))*llew
2 -0.5*Int0m_ep(kn_cmpborn(0,legi),kn_cmpborn(0,legj)))*
3 br_born(jb)*ch_i*ch_j*(-1)*
4 sigma(flst_born(legi,jb),legi)*
5 sigma(flst_born(legj,jb),legj)
endif
c massive-massless case
if (kn_masses(legi).gt.0.and.kn_masses(legj).eq.0)
1 then
Iem = Iem + (0.5*(0.5*llew**2 - pi**2/6)
1 +0.5*Int0m_0(kn_cmpborn(0,legj),kn_cmpborn(0,legi))*llew
2 -0.5*Int0m_ep(kn_cmpborn(0,legj),kn_cmpborn(0,legi)))*
3 br_born(jb)*ch_i*ch_j*(-1)*
4 sigma(flst_born(legi,jb),legi)*
5 sigma(flst_born(legj,jb),legj)
endif
c massive-massive case
if (kn_masses(legi).gt.0.and.kn_masses(legj).gt.0)
1 then
Iem = Iem + (0.5*llew*
1 Intmm_0(kn_cmpborn(0,legi),kn_cmpborn(0,legj))
2 -0.5*Intmm_ep(kn_cmpborn(0,legi),kn_cmpborn(0,legj)))*
3 br_born(jb)*ch_i*ch_j*(-1)*
4 sigma(flst_born(legi,jb),legi)*
5 sigma(flst_born(legj,jb),legj)
endif
endif
enddo
enddo
I=I*2
c WEW
Iem=Iem*2
if(jres.eq.1) then
c first time
resvirt(jb)=( (Q+I+virt_arr(jb))*st_alpha
1 + (Qem+Iem)*em_alpha )/(2*pi)
2 *pdfb1(fl1)*pdfb2(fl2)*kn_jacborn * rescfac
else
c others
resvirt(jb)=resvirt(jb)+( (Q+I)*st_alpha
1 + (Qem+Iem)*em_alpha )/(2*pi)
2 *pdfb1(fl1)*pdfb2(fl2)*kn_jacborn * rescfac
endif
tot=tot+resvirt(jb)
enddo
enddo
if (.not.pwhg_isfinite(tot)) then
do jb=1,flst_nborn
resvirt(jb)=0d0
enddo
endif
end
c I_ep(k,m)
function Int0m_ep(k,m)
c / [ ]
c | d phi [ k.m k0 ]
c Int0m_ep = -2 | d cos th ----- log(sin th sin phi) l0^2 [ ------- - ------ ]
c | pi [ k.l m.l k.l l0 ]
c / [ ]
c the range in phi is 0<phi<pi.
implicit none
real * 8 Int0m_ep, k(0:3),m(0:3)
real * 8 kh(0:3),mh(0:3),khmh,b
integer j
real * 8 ddilog,dotp
external ddilog,dotp
do j=0,3
kh(j)=k(j)/k(0)
mh(j)=m(j)/m(0)
enddo
b=sqrt(1-dotp(mh,mh))
khmh=dotp(kh,mh)
Int0m_ep=-2*(log((1-b)/(1+b))**2/4+log(khmh/(1+b))*log(khmh/(1-b))
# +ddilog(1-khmh/(1+b))+ddilog(1-khmh/(1-b)))
end
c I_0(k,m)
c / [ ]
c | d phi [ k.m k0 ]
c I_0 = | d cos th ----- l0^2 [ ------- - ------ ]
c | pi [ k.l m.l k.l l0 ]
c / [ ]
c the range in phi is 0<phi<pi.
function Int0m_0(k,m)
implicit none
real * 8 Int0m_0, k(0:3),m(0:3)
real * 8 kh(0:3),mh(0:3)
integer j
real * 8 dotp
external ddilog,dotp
do j=0,3
kh(j)=k(j)/k(0)
mh(j)=m(j)/m(0)
enddo
Int0m_0=log( dotp(kh,mh)**2/dotp(mh,mh) )
end
function Intm_ep(p)
c / 2
c | d phi p
c Intm_ep = -2 | d cos th ----- log(sin th sin phi) l0^2 -------
c | pi (p.l)^2
c /
c the range in phi is 0<phi<pi.
implicit none
real * 8 p(0:3),Intm_ep
real * 8 beta2,beta
integer j
beta2=0
do j=1,3
beta2=beta2+(p(j)/p(0))**2
enddo
beta=sqrt(beta2)
if(beta.lt.1d-4) then
Intm_ep=2*(2+2*beta**2/3+2*beta**4/5+2*beta**6/7)
else
Intm_ep=2*log((1+beta)/(1-beta))/beta
endif
end
function Intmm_ep(p1,p2)
c /
c | d phi p1.p2
c Intmm_ep= -2 | d cos th ----- log(sin th sin phi) k0^2 ----------
c | pi p1.k p2.k
c /
c p1^2>0, p2^2>0.
c The range in phi is 0<phi<pi.
implicit none
real * 8 p1(0:3),p2(0:3), intmm_ep
real * 8 i,z,zm,zmob,zp,z1,z1ob,z2,a,b,x1,x2,bv1(3),bv2(3),
1 bb1,bb2,b1b2,b2
integer j
real * 8 ddilog,tmp
external ddilog
i(z)=-1d0/2*log((z-zm)*(zp-z)/((zp+z)*(z+zm)))**2
# -2*ddilog(2*zm/(zp-zm)*(zp-z)/(zm+z))
# -2*ddilog(-2*zp/(zp-zm)*(zm+z)/(zp-z))
do j=1,3
bv1(j)=p1(j)/p1(0)
bv2(j)=p2(j)/p2(0)
enddo
bb1=0
bb2=0
b1b2=0
do j=1,3
bb1=bb1+bv1(j)**2
bb2=bb2+bv2(j)**2
b1b2=b1b2+bv1(j)*bv2(j)
enddo
if(bb1.gt.bb2) then
tmp=bb1
bb1=bb2
bb2=tmp
endif
a=bb1+bb2-2*b1b2
x1=bb1-b1b2
x2=bb2-b1b2
b=bb1*bb2-b1b2**2
zp=sqrt(a)+sqrt(a-b)
zm=sqrt(a)-sqrt(a-b)
c zm over b (introduce to handle back-to-back case without generating 0/0)
zmob=1/zp
z1=sqrt(x1**2+b)-x1
z2=sqrt(x2**2+b)+x2
if(bb1.eq.0) then
c handle limiting case, b1=0
b2=sqrt(bb2)
Intmm_ep=(-0.5d0*log((1-b2)/(1+b2))**2
1 +2*ddilog(0d0)-2*ddilog(-2*b2/(1-b2)))
1 * (1-b1b2)/sqrt(a-b)
else
c z1 over b (same as before
z1ob=1/(sqrt(x1**2+b)+x1)
Intmm_ep=(i(z2)
1 +1d0/2*log((z1ob-zmob)*(zp-z1)/((zp+z1)*(z1ob+zmob)))**2
2 +2*ddilog(2*zmob/(zp-zm)*(zp-z1)/(zmob+z1ob))
3 +2*ddilog(-2*zp/(zp-zm)*(zm+z1)/(zp-z1)) )
4 *(1-b1b2)/sqrt(a-b)
endif
end
function Intmm_0(p1,p2)
c /
c | d phi p1.p2
c Intmm_0 = | d cos th ----- k0^2 ----------
c | pi p1.k p2.k
c /
c the range in phi is 0<phi<pi.
implicit none
real * 8 p1(0:3),p2(0:3), Intmm_0
real * 8 kh(3),gh(3),k2,g2,kg,beta,ombeta2
integer j
do j=1,3
kh(j)=p1(j)/p1(0)
gh(j)=p2(j)/p2(0)
enddo
k2=0
g2=0
kg=0
do j=1,3
k2=k2+kh(j)**2
g2=g2+gh(j)**2
kg=kg+kh(j)*gh(j)
enddo
ombeta2=(1-k2)*(1-g2)/(1-kg)**2
beta=sqrt(1-ombeta2)
c Intmm_0=log((1+beta)/(1-beta))/beta
c Equivalent:
Intmm_0=log((1+beta)**2/ombeta2)/beta
end