-
Notifications
You must be signed in to change notification settings - Fork 2
/
Xinteg_hh.f90
471 lines (389 loc) · 20.5 KB
/
Xinteg_hh.f90
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
! ===========================================================================================================
module xx_integral_hh
use xx_kinds
use xx_public_variables
use xx_pass_integ
implicit none
private :: COUPLING_HH
public :: IFCT_HH_X12
contains
! ------------------------------
function IFCT_HH_X12(dum) result(dsig)
real(kind=double), dimension(dim(ii)), intent(in) :: dum ! vegas integration variable
real(kind=double), dimension(dim(ii)) :: var ! internal integration variable
real(kind=double) :: dsig
integer :: inlo, iq
real(kind=double), dimension(1:30) :: massin,massix,massin_1,massin_2
real(kind=double), dimension(1:20) :: C
real(kind=double) :: m1,m2,s,qf,qr,beta,del_s4,gamt,beta1,beta2
real(kind=double) :: sw,alpha,alpha_s,mu_tgb,nlo,ALPHAS
real(kind=double) :: x1m,x1p,x1,x1_jac,x2m,x2p,x2,x2_jac,t2m,t2p,t2,t2_jac,s4m,s4p,s4,s4_jac
real(kind=double) :: z4m,z4p,z4,s4s4,theta_s4,prop_s4,betas4,t2s4m,t2s4p,t2s4,t2s4_jac
real(kind=double) :: z3m,z3p,z3,s3s3,theta_s3,prop_s3,beta1s3,beta2s3,t2s3m,t2s3p,t2s3,t2s3_jac
real(kind=double) :: s3m,s3p,s3,s3_jac,betax,t2xm,t2xp,t2x,t2x_jac,s4s3m,s4s3p,s4s3,s4s3_jac
real(kind=double) :: s4xm,s4xp,s4x,s4x_jac
real(kind=double) :: s4_1m,s4_1p,s4_1_jac,s4_1
real(kind=double) :: t2_1m,t2_1p,t2_1_jac,t2_1
real(kind=double) :: s3_1m,s3_1p,s3_1_jac,s3_1
real(kind=double) :: z3_1m,z3_1p,z3_1
real(kind=double) :: beta1_1,beta2_1
real(kind=double) :: s4_2m,s4_2p,s4_2_jac,s4_2
real(kind=double) :: t2_2m,t2_2p,t2_2_jac,t2_2
real(kind=double) :: s3_2
real(kind=double) :: beta_1,beta1_2,beta2_2
real(kind=double) :: LUMI
real(kind=double) :: HH_QBB,HH_QBV,HH_QBSY,HH_QBS,HH_QBD,HH_QBH,HH_QGH,HH_QGOS,HH_GBH,HH_GBOS
if (ii>8) then ! finish early
dsig = 0.0
return
end if
var(1:dim(ii)) = dum(1:dim(ii)) * ( 1.0 - 2.0*cut ) + cut ! cut off the integration in general
iq = -1 ! no impact for the bottom density
massin(1:30) = 0.0 ! initialize the massin arrays
massix(1:30) = 0.0
massin_1(1:30) = 0.0
massin_2(1:30) = 0.0
m1 = mch ! assign the final state masses
m2 = mch
mu_tgb = mu_susy * tan_b ! for the delta mb corrections
sw = sqrt( 1.0 - mw**2/mz**2 ) ! weak parameters in the on-shell scheme
alpha = sqrt(2.0) * mw**2 * sw**2 /pi * gf
x1m = (m1+m2)**2 /sc ! x1-x2 integration, map x->log(x)
x1p = 1.0
x1 = x1m * (x1p/x1m)**var(1)
x1_jac = x1 * log(x1p/x1m)
x2m = (m1+m2)**2 /sc /x1
x2p = 1.0
x2 = x2m * (x2p/x2m)**var(2)
x2_jac = x2 * log(x2p/x2m)
s = x1 * x2 * sc ! partonic cm energy
if (iscaling==1) s = (m1+m2)**2 * (eta+1) ! overwrite integration for scaling fct
if (isca==0) then ! renormalization/factorization scale, factorization scale low
qf = scafac * (m1+m2)/4.0
qr = scafac * (m1+m2)/2.0
else if (isca==1) then
qf = scafac * sqrt(s)/4.0
qr = scafac * sqrt(s)
end if
if (qf < 30.0) qf = 30.0 ! too small scales are not good
if (qr < 30.0) qr = 30.0
if (iscaling==0) then ! nlo factor [always nlo alpha_s]
alpha_s = ALPHAS(qr,2)
nlo = 4.0 * pi * alpha_s
else if (iscaling==1) then
nlo = 1.0
end if
if (ii<=0) then ! coupling factor alpha_s not always nlo
inlo = 0
else if (ii>0) then
inlo = 1
end if
theta_s4 = 0.0 ! the os subtraction theta function
theta_s3 = 0.0
gamt = ewi * mt ! always a small width needed for arcustan
if ((s>(mt+m2)**2).and.(mt>m1)) theta_s4 = 1.0 ! intermediate top
if ((s>(mt+m1)**2).and.(mt>m2)) theta_s3 = 1.0 ! intermediate top
del_s4 = eps_sli * min(m1**2,m2**2) & ! unit is m^2
* (1.0-(m1+m2)**2/s)*(1.0-(m1-m2)**2/s) ! rescale the s4 cutoff
if (ii/=4) del_s4 = 0.0
s4p = 0.0 ! only for real corrections
select case (ii) ! all the phase spaces
case(-1,0,1,2,3) ! born_lo, born_nlo, virt
beta = sqrt(1.0-(m1+m2)**2/s) & ! t2 integration
*sqrt(1.0-(m1-m2)**2/s)
t2m = -1.0/2.0 * ( s + m2**2 - m1**2 + s*beta )
t2p = -1.0/2.0 * ( s + m2**2 - m1**2 - s*beta )
t2 = var(3) * (t2p-t2m) + t2m
t2_jac = t2p-t2m
case(4) ! real(qb)
beta = ((1.0-del_s4/s)**2-(m1+m2)**2/s) & ! t2 integration shifted
*((1.0-del_s4/s)**2-(m1-m2)**2/s)
if (beta>=0.0) then
beta = sqrt(beta)
else
print*, " IFCT_HH_X12: sqrt(beta) not defined "
beta = 0.0
end if
t2m = -1.0/2.0 * ( s - del_s4 + m2**2 - m1**2 + s*beta )
t2p = -1.0/2.0 * ( s - del_s4 + m2**2 - m1**2 - s*beta )
t2 = var(3) * (t2p-t2m) + t2m
t2_jac = t2p-t2m
s4m = del_s4 ! s4 mapped to log
s4p = s + t2 + m2**2 - m1**2 + s*m2**2/t2 ! -> only a slight improvement
! s4 = s4m * (s4p/s4m)**var(4)
! s4_jac = s4 * log(s4p/s4m)
if (s4p<s4m) then
n_faulty = n_faulty+1
dsig = 0.0
return
end if
s4 = var(4) * (s4p-s4m) + s4m
s4_jac = s4p-s4m
case(5) ! crossed(qg), no os subtraction
beta = ((1.0-del_s4/s)**2-(m1+m2)**2/s) & ! t2 integration shifted
*((1.0-del_s4/s)**2-(m1-m2)**2/s)
if (beta>=0.0) then
beta = sqrt(beta)
else
print*, " IFCT_HH_X12: sqrt(beta) not defined "
beta = 0.0
end if
t2m = -1.0/2.0 * ( s - del_s4 + m2**2 - m1**2 + s*beta )
t2p = -1.0/2.0 * ( s - del_s4 + m2**2 - m1**2 - s*beta )
t2 = var(3) * (t2p-t2m) + t2m
t2_jac = t2p-t2m
s4m = del_s4 ! s4 mapped to log
s4p = s + t2 + m2**2 - m1**2 + s*m2**2/t2 ! -> only a slight improvement
s4 = var(4) * (s4p-s4m) + s4m
s4_jac = s4p-s4m
s3_1m = 0.0 ! for the s3 integration, complete phase space
s3_1p = s + m1**2 - m2**2 - 2.0 * sqrt(s*m1**2)
s3_1 = var(5) * (s3_1p-s3_1m) + s3_1m
s3_1_jac = s3_1p-s3_1m
beta1_1 = (s-s3_1-m2**2+m1**2)**2 - 4.0*m1**2*s
if (beta1_1<0.0) then
n_faulty = n_faulty+1
dsig = 0.0
return
else
beta1_1 = sqrt( beta1_1 )
end if
s4_1m = s3_1/2.0/(s3_1+m2**2) * (s - s3_1 - m1**2 - m2**2 - beta1_1)
s4_1p = s3_1/2.0/(s3_1+m2**2) * (s - s3_1 - m1**2 - m2**2 + beta1_1)
s4_1 = var(6) * (s4_1p-s4_1m) + s4_1m
s4_1_jac = s4_1p-s4_1m
beta2_1 = (s-s4_1-m1**2+m2**2)**2 - 4.0*s*m2**2
if (beta2_1<0.0) then
n_faulty = n_faulty+1
dsig = 0.0
return
else
beta2_1 = sqrt( beta2_1 )
end if
t2_1m = -1.0/2.0 * ( s - s4_1 - m1**2 + m2**2 + beta2_1 )
t2_1p = -1.0/2.0 * ( s - s4_1 - m1**2 + m2**2 - beta2_1 )
t2_1 = var(7) * (t2_1p-t2_1m) + t2_1m
t2_1_jac = t2_1p-t2_1m
t2_1_jac = t2_1_jac * 2.0/s4_1*(s4_1+m1**2) / beta2_1 ! including the over-all jacobian
case(6) ! on-shell(qg)
if (theta_s3==0.0) then
dsig = 0.0
return
end if
s3_1m = 0.0 ! for the s3 integration, complete phase space
s3_1p = s + m1**2 - m2**2 - 2.0 * sqrt(s*m1**2)
z3_1m = atan( (s3_1m + m2**2 - mt**2)/mt/gamt )
z3_1p = atan( (s3_1p + m2**2 - mt**2)/mt/gamt )
z3_1 = var(3) * (z3_1p-z3_1m) + z3_1m
s3_1 = mt*gamt*tan(z3_1) + mt**2 - m2**2
s3_1_jac = ((s3_1+m2**2-mt**2)**2/mt/gamt+mt*gamt)*(z3_1p-z3_1m)
beta1_1 = (s-s3_1-m2**2+m1**2)**2 - 4.0*m1**2*s
if (beta1_1<0.0) then
n_faulty = n_faulty+1
dsig = 0.0
return
else
beta1_1 = sqrt( beta1_1 )
end if
s4_1m = s3_1/2.0/(s3_1+m2**2) * (s - s3_1 - m1**2 - m2**2 - beta1_1)
s4_1p = s3_1/2.0/(s3_1+m2**2) * (s - s3_1 - m1**2 - m2**2 + beta1_1)
s4_1 = var(4) * (s4_1p-s4_1m) + s4_1m
s4_1_jac = s4_1p-s4_1m
beta2_1 = (s-s4_1-m1**2+m2**2)**2 - 4.0*s*m2**2
if (beta2_1<0.0) then
n_faulty = n_faulty+1
dsig = 0.0
return
else
beta2_1 = sqrt( beta2_1 )
end if
t2_1m = -1.0/2.0 * ( s - s4_1 - m1**2 + m2**2 + beta2_1 )
t2_1p = -1.0/2.0 * ( s - s4_1 - m1**2 + m2**2 - beta2_1 )
t2_1 = var(5) * (t2_1p-t2_1m) + t2_1m
t2_1_jac = t2_1p-t2_1m
t2_1_jac = t2_1_jac * 2.0/s4_1*(s4_1+m1**2) / beta2_1 ! including the over-all jacobian
s3_2 = mt**2 - m2**2 ! go to constrained phase space
beta1_2 = (s-s3_2-m2**2+m1**2)**2 - 4.0*m1**2*s
if (beta1_2<0.0) then
n_faulty = n_faulty+1
dsig = 0.0
return
else
beta1_2 = sqrt( beta1_2 )
end if
s4_2m = s3_2/2.0/(s3_2+m2**2) * (s - s3_2 - m1**2 - m2**2 - beta1_2)
s4_2p = s3_2/2.0/(s3_2+m2**2) * (s - s3_2 - m1**2 - m2**2 + beta1_2)
s4_2 = var(4) * (s4_2p-s4_2m) + s4_2m
s4_2_jac = s4_2p-s4_2m
beta2_2 = (s-s4_2-m1**2+m2**2)**2 - 4.0*s*m2**2
if (beta2_2<0.0) then
n_faulty = n_faulty+1
dsig = 0.0
return
else
beta2_2 = sqrt( beta2_2 )
end if
t2_2m = -1.0/2.0 * ( s - s4_2 - m1**2 + m2**2 + beta2_2 )
t2_2p = -1.0/2.0 * ( s - s4_2 - m1**2 + m2**2 - beta2_2 )
t2_2 = var(5) * (t2_2p-t2_2m) + t2_2m
t2_2_jac = t2_2p-t2_2m
t2_2_jac = t2_2_jac * 2.0/s4_2*(s4_2+m1**2) / beta2_2 ! including the over-all jacobian
prop_s3 = mt**2*gamt**2 / ((s3_1+m2**2-mt**2)**2+mt**2*gamt**2) ! compensate for the wrong breit-wigner
case(7,8) ! crossed(gb) including on-shell
if ( (ii==8).and.(theta_s4==0.0) ) then
dsig = 0.0
return
end if
s4m = 0.0
s4p = s + m2**2 - m1**2 - 2.0 * sqrt(s*m2**2)
z4m = atan( (s4m + m1**2 - mt**2)/mt/gamt ) ! s4 mapped to atan
z4p = atan( (s4p + m1**2 - mt**2)/mt/gamt ) ! since s4t=s4+m1^2-mt^2
z4 = var(3) * (z4p-z4m) + z4m
s4 = mt*gamt*tan(z4) + mt**2 - m1**2
s4_jac = ((s4+m1**2-mt**2)**2/mt/gamt+mt*gamt)*(z4p-z4m)
beta = sqrt( dabs( (s-s4-m1**2+m2**2)**2 - 4.0*s*m2**2 ) ) ! absolute value because of numerics
t2m = -1.0/2.0 * ( s - s4 - m1**2 + m2**2 + beta ) ! t2 integration as usual
t2p = -1.0/2.0 * ( s - s4 - m1**2 + m2**2 - beta )
t2 = var(4) * (t2p-t2m) + t2m
t2_jac = t2p-t2m
if (theta_s4==1.0) then ! restricted phase space for theta_s4=1
s4_1 = mt**2 - m1**2
beta_1 = sqrt( (s-s4_1-m1**2+m2**2)**2 - 4.0*s*m2**2 )
t2_1m = -1.0/2.0 * ( s - s4_1 - m1**2 + m2**2 + beta_1 )
t2_1p = -1.0/2.0 * ( s - s4_1 - m1**2 + m2**2 - beta_1 )
t2_1 = var(4) * (t2_1p-t2_1m) + t2_1m
t2_1_jac = t2_1p-t2_1m
prop_s4 = mt**2*gamt**2 / ((s4+m1**2-mt**2)**2+mt**2*gamt**2) ! compensate for the wrong breit-wigner
end if
end select
massin(1) = s ! assign the mass arrays
massin(2) = t2
massin(3) = s4 ! s4 only for 2->3 processes
massin(6) = m1
massin(7) = mt
massin(8) = mz
massin(9) = mh1
massin(10) = mh2
massin(12) = qr ! renormalization scale
massin(13) = qf ! factorization scale
massin(15) = mg
massin(16) = msq(-5)
massin(17) = msq( 5)
massin(18) = msq(-6)
massin(19) = msq( 6)
massin(20) = del_s4 ! slicing parameter only fort ii=4
massin(21) = s4p ! s4^max for the log(delta) terms
massin(25) = gamt ! width of the top
massin(26) = 0.0 ! gamma/m of s channel particles in breit wigner
if ( (ii==5).or.(ii==6).or.(ii==8) ) then ! s3 subtraction phase space
massin_1(1:30) = massin(1:30)
massin_1(2) = t2_1
massin_1(3) = s4_1
massin_1(4) = s3_1
end if
if (ii==6) then ! restricted phace space for s3 subtraction
massin_2(1:30) = massin(1:30)
massin_2(2) = t2_2
massin_2(3) = s4_2
massin_2(4) = s3_2
end if
call COUPLING_HH(qr,C)
if ( (m1+m2) < mz ) C(9) = 0.0 ! switch off s-channel couplings
if ( (m1+m2) < mh1 ) C(10) = 0.0
if ( (m1+m2) < mh2 ) C(11) = 0.0
dsig = 0.0
select case (ii)
case(-1,0,1) ! born
dsig = dsig + LUMI(inlo,60,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_QBB(massin,C) * t2_jac
case(2) ! virtual
dsig = dsig + nlo * LUMI(inlo,60,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_QBV(massin,C) * t2_jac
case(3) ! virtual-susy
dsig = dsig + LUMI(inlo,60,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_QBSY(massin,C,mu_tgb,alpha_s) * t2_jac
case(4) ! real(qb)
dsig = dsig + nlo * LUMI(inlo,60,icoll,idub,iq,x1,x2,qf)/s**2 &
*( HH_QBH(massin,C) &
+HH_QBD(massin,C) ) * t2_jac * s4_jac
case(5) ! crossed(qg)
dsig = dsig + nlo * LUMI(inlo,70,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_QGH(massin,C) * t2_jac * s4_jac
if (theta_s3==0.0) &
dsig = dsig + nlo * LUMI(inlo,70,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_QGOS(massin_1,C) * t2_1_jac * s4_1_jac * s3_1_jac
case(6) ! on-shell(qg)
dsig = dsig + nlo * LUMI(inlo,70,icoll,idub,iq,x1,x2,qf)/s**2 &
*( HH_QGOS(massin_1,C) * t2_1_jac * s4_1_jac * s3_1_jac &
- HH_QGOS(massin_2,C) * t2_2_jac * s4_2_jac * s3_1_jac * prop_s3 )
case(7) ! crossed(gb)
dsig = dsig + nlo * LUMI(inlo,80,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_GBH(massin,C) * t2_jac * s4_jac
if (theta_s4==0.0) &
dsig = dsig + nlo * LUMI(inlo,80,icoll,idub,iq,x1,x2,qf)/s**2 &
* HH_GBOS(massin,C) * t2_jac * s4_jac
case(8) ! on-shell(qg)
dsig = dsig + nlo * LUMI(inlo,80,icoll,idub,iq,x1,x2,qf)/s**2 &
*( HH_GBOS(massin,C) * t2_jac * s4_jac &
- HH_GBOS(massin_1,C) * t2_1_jac * s4_jac * prop_s4 )
case default
dsig = 0.0
end select
if (iscaling==0) & ! some jacobians
dsig = dsig * x1_jac * x2_jac
if (iscaling==0) & ! what is missing from the matrix elements
dsig = dsig * 4.0/(m1+m2)**2 * (4.D0*pi*alpha)**2
if (iscaling==0) & ! result in pb
dsig = dsig * gevpb
ii_done(ii) = 1
end function IFCT_HH_X12
! ------------------------------
subroutine COUPLING_HH(qr,C)
real(kind=double), intent(in) :: qr
real(kind=double), dimension(1:20), intent(out) :: C
integer :: ic
real(kind=double) :: e,g
real(kind=double) :: t3,qq,sw2,cw2,sw,cw,c2w,sqrt2
real(kind=double) :: yb,yt
real(kind=double) :: sa,ca,sb,cb,sbma,cbma,sbpa,cbpa,c2b
real(kind=double) :: RUNM_EXT
sqrt2 = sqrt(2.0)
t3 = -0.5 ! bottom quark quantum numbers
qq = -1.0/3.0
sw = sqrt( 1.0 - mw**2/mz**2 ) ! weak mixing angle
sw2 = sw**2
cw2 = 1.0 - sw2
cw = sqrt(cw2)
c2w = cw**2-sw**2
sa = sin_a ! scalar higgs mixing angle
ca = cos_a
cb = 1.D0/dsqrt(1.D0+tan_b**2) ! beta as in tan(beta)
sb = tan_b*cb
sbma = sb*ca - cb*sa
cbma = cb*ca + sb*sa
sbpa = sb*ca + cb*sa
cbpa = cb*ca - sb*sa
c2b = cb**2-sb**2
e = 1.0 ! over-all factor
g = e/sw
if (ii<=0) then
yb = RUNM_EXT(qr,5,1)
yt = RUNM_EXT(qr,6,1)
else
yb = RUNM_EXT(qr,5,2)
yt = RUNM_EXT(qr,6,2)
end if
C(1:20) = 0.0 ! initialize arrays
C(1) = e/sw/cw * ( t3 - qq*sw2 ) ! lq
C(2) = e/sw/cw * ( - qq*sw2 ) ! rq
C(3) = e*qq ! pq
C(4) = g * yb*tan_b/mw ! hl
C(5) = g * yt/tan_b/mw ! hr
C(6) = g/sqrt2 * yb/mw * sa/cb ! h1
C(7) = -g/sqrt2 * yb/mw * ca/cb ! h2
C(8) = -e ! ssp
C(9) = -g*c2w/2.0/cw ! ssz
C(10) = -g*( mw*sbma + mz/2.0/cw*c2b*sbpa ) ! lambda1 (checked with ME)
C(11) = -g*( mw*cbpa - mz/2.0/cw*c2b*cbma ) ! lambda2 (checked with ME)
end subroutine COUPLING_HH
end module xx_integral_hh