Newer
Older
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
c $Id: angdis.f,v 1.15 2000/01/12 16:02:33 bass Exp $
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine angdisnew(sqrts,m1,m2,iline,costh,phi)
c
c Revision : 1.1
c
c input: sqrts, m1, m2, iline : characteristics of the ingoing channel
coutput costh : cos(theta) of theta-angle
coutput phi : phi-angle
c
c {\tt angdisnew} delivers phi and cos(theta) scattering angles
c according to the angular distributions given by Mao et al.
c {\tt angdisnew} performs numerical inversion of the integral of the
c differential cross-section by means of a bisection method.
c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
implicit none
real*8 sqrts, m1, m2, costh, costhcoll, phi, ranf, pi, s
real*8 anginter
integer iline
logical symlog(38)
parameter (pi = 3.14159265358979312d0)
c symmetrize or not angular distribution (depending on iline)
c this data statements may be changed ...
data symlog /14*.true., 1*.false., 6*.true., 7*.false.,
& 7*.true., 1*.false., 2*.true./
s = sqrts*sqrts
phi = 2.0d0*pi*ranf(0)
goto (4, 4, 4, 4, 4, 4, 4, 4, 4, 9,
& 9, 4, 4, 4, 4, 4, 4, 4, 4, 9,
c ISO-FB interpolation for MB iline 26/27/28
& 4, 4,10,10,10,11,11,11, 4, 4,
& 4, 4, 4, 4, 4, 9, 9, 4) abs(iline)
c cross-sections NN (Mao et al.)
4 continue
costh = -costhcoll(s,m1,m2,symlog(abs(iline)))
return
c isotropic decay
9 continue
costh = 1.0d0-2.0d0*ranf(0)
return
c no deflection at all
10 continue
costh = 1.0d0
return
c smooth interpolation between iso and f-b:
11 continue
cbl only for intermediate masses, otherwise no deflection (zero degree scattering)
if(sqrts.gt.6d0) goto 10
costh = anginter()
return
end
function costhcoll(s,m1,m2,sym)
implicit none
real*8 costhcoll, s, m1, m2, x, dct, ct, dsigma, ranf
integer j
logical sym
x = ranf(0)
dct = 2.0d0
costhcoll = -1.0d0
c
c for jmax=12 the accuracy is better than 0.1 degree
c
do j=1,12 ! accuracy 2**-jmax
dct = 0.5d0*dct
ct = costhcoll+dct
if (dsigma(s,m1,m2,sym,ct).le.x) costhcoll=ct
enddo
c
c randomize in final interval in order to avoid discrete angles
c
costhcoll = costhcoll+ranf(0)*dct
return
end
function dsigma(s_in,m1_in,m2_in,sym,costh)
c
cc dsigma(s\_in,chosth) = int_-1^costh dsigma/dOmega(s_in,..) dOmega
cc it is normalized such that dsigma(s\_in,-1) = 0 and
cc dsigma(s\_in,1) = 1
implicit none
include 'coms.f'
real*8 dsigma
real*8 s_in, m1_in, m2_in, costh,
& msi, cmsi, gsi, mom, cmom, gom, mpi, cmpi, gpi, m
real*8 m42, mpi2, cmpi2, d_pi1, d_pi2, cm6gp,
& cpi_3, cpi_2, cpi_1, cpi_m, cpi_l, cpi_0,
& msi2, cmsi2, cmsi4, cmsi6, d_si1, d_si2, d_si3, cm2gs,
& csi_3, csi_2, csi_1, csi_m, csi_l, csi_0,
& mom2, cmom2, cmom4, cmom6, d_om1, d_om2, d_om3, s_om1,
& cm2go, com_3, com_2, com_1, com_m, com_l,
& fac1, d_mx1, d_mx2, d_mx3,
& cmx_o1, cmx_s1, cmx_om, cmx_sm, fac2, fac3,
& cmx_olc, cmx_ols, cmx_slc, cmx_sls
real*8 sig, tp_pi, tp_si, tp_om, tm_pi, tm_si, tm_om,
& bom_3, bom_2, bom_1, bom_m, bom_0, bom_l,
& bmx_o1, bmx_s1, bmx_om, bmx_sm, bmx_ol, bmx_sl
real*8 s, tmax, tp, to, twos, brak1, norm,
& t1_pi, t2_pi, t1_si, t2_si, t1_om, t2_om,
& t3_pi, t4_pi, t3_si, t4_si, t3_om, t4_om
logical firstlog, sym
common /nn/ norm
c define masses and coupling constants
data msi /0.550d0/ cmsi /1.200d0/ gsi /9.40d0/
data mom /0.783d0/ cmom /0.808d0/ gom /10.95d0/
data mpi /0.138d0/ cmpi /0.510d0/ gpi /7.27d0/
data m /0.938d0/
save firstlog
save m42, mpi2, cmpi2, d_pi1, d_pi2, cm6gp,
& cpi_3, cpi_2, cpi_1, cpi_m, cpi_l, cpi_0
save msi2, cmsi2, cmsi4, cmsi6, d_si1, d_si2, d_si3, cm2gs,
& csi_3, csi_2, csi_1, csi_m, csi_l, csi_0
save mom2, cmom2, cmom4, cmom6, d_om1, d_om2, d_om3, s_om1,
& cm2go, com_3, com_2, com_1, com_m, com_l
save fac1, d_mx1, d_mx2, d_mx3,
& cmx_o1, cmx_s1, cmx_om, cmx_sm, fac2, fac3,
& cmx_olc, cmx_ols, cmx_slc, cmx_sls
sig(tp_pi,tp_si,tp_om,tm_pi,tm_si,tm_om) =
c pion
& +((cpi_3*tp_pi + cpi_2)*tp_pi + cpi_1)*tp_pi
& + cpi_m/tm_pi + cpi_0 + cpi_l*log(tp_pi*tm_pi)
c sigma
& +((csi_3*tp_si + csi_2)*tp_si + csi_1)*tp_si
& + csi_m/tm_si + csi_0 + csi_l*log(tp_si*tm_si)
c omega
& +((bom_3*tp_om + bom_2)*tp_om + bom_1)*tp_om
& + bom_m/tm_om + bom_0 + bom_l*log(tp_om*tm_om)
c mix
& + bmx_o1*(tp_om - 1.0d0)
& + bmx_s1*(tp_si - 1.0d0)
& + bmx_om*log(tm_om)
& + bmx_sm*log(tm_si)
& + bmx_ol*log(tp_om)
& + bmx_sl*log(tp_si)
c calculate constants only once!
if(firstlog) goto 1000
if (info) write(6,*)
$ '(info) dsigma: calculating constants for ang. dist.'
c define constants for pion-Term (no s-dependence)
m42 = 4.0d0*m*m
mpi2 = mpi*mpi
cmpi2 = cmpi*cmpi
d_pi1 = cmpi2-mpi2
d_pi2 = d_pi1*d_pi1
cm6gp = 1.5d0*cmpi2**3*gpi**4*m42*m42/d_pi2
cpi_3 = -(cm6gp/3.0d0)
cpi_2 = -(cm6gp*mpi2/d_pi1)
cpi_1 = -(cm6gp*mpi2*(2.0d0*cmpi2 + mpi2)/d_pi2)
cpi_m = -(cm6gp*cmpi2*mpi2/d_pi2)
cpi_l = -(cm6gp*2.0d0*cmpi2*mpi2*(cmpi2 + mpi2)/d_pi2/d_pi1)
cpi_0 = -(cpi_3 + cpi_2 + cpi_1 + cpi_m)
c define constants for sigma-Term (no s-dependence)
msi2 = msi*msi
cmsi2 = cmsi*cmsi
cmsi4 = cmsi2*cmsi2
cmsi6 = cmsi2*cmsi4
d_si1 = m42-cmsi2
d_si2 = m42-msi2
d_si3 = cmsi2-msi2
cm2gs = 0.5d0*cmsi2*gsi**4/d_si3**2
csi_3 = -(cm2gs*d_si1**2/3.0d0)
csi_2 = -(cm2gs*cmsi2*d_si1*d_si2/d_si3)
csi_1 = -(cm2gs*cmsi4*(2.0d0*d_si1 + d_si2)*d_si2/d_si3**2)
csi_m = -(cm2gs*cmsi6*d_si2**2/msi2/d_si3**2)
csi_l = -(cm2gs*cmsi6*d_si2*(d_si1 + d_si2)*2.0d0/d_si3**3)
csi_0 = -(csi_3 + csi_2 + csi_1 + csi_m)
c define constants for omega-Term
mom2 = mom*mom
cmom2 = cmom*cmom
cmom4 = cmom2*cmom2
cmom6 = cmom2*cmom4
d_om1 = m42-cmom2
d_om2 = m42-mom2
d_om3 = cmom2-mom2
s_om1 = cmom2+mom2
cm2go = 0.5d0*cmom2*gom**4/d_om3**2
com_3 = cm2go/3.0d0
com_2 = -(cm2go*cmom2/d_om3)
com_1 = cm2go*cmom4/d_om3**2
com_m = cm2go*cmom6/(d_om3**2*mom2)
com_l = -(cm2go*cmom6*4.0d0/d_om3**3)
c define constants for mix-Term
fac1 = -((gsi*gom*cmsi2*cmom2)**2*m42)
d_mx1 = cmom2 - cmsi2
d_mx2 = cmom2 - msi2
d_mx3 = cmsi2 - mom2
cmx_o1 = fac1/(cmom2*d_mx1**2*d_mx2*d_om3)
cmx_s1 = fac1/(cmsi2*d_mx1**2*d_mx3*d_si3)
cmx_om = fac1/(d_om3**2*d_mx3**2*(mom2 - msi2))
cmx_sm = fac1/(d_si3**2*d_mx2**2*(msi2 - mom2))
fac2 = (-fac1)/(d_mx1**3*d_om3**2*d_mx2**2)
fac3 = (-fac1)/(d_mx1**3*d_mx3**2*d_si3**2)
cmx_olc =
& fac2*(3.0d0*cmom2**3 - cmom2**2*cmsi2
& - 2.0d0*cmom2**2*mom2 - 2.0d0*cmom2**2*msi2
& + cmom2*mom2*msi2 + cmsi2*mom2*msi2
& - 4.0d0*cmom2**2*m42 + 2.0d0*cmom2*cmsi2*m42
& + 3.0d0*cmom2*mom2*m42 - cmsi2*mom2*m42
& + 3.0d0*cmom2*msi2*m42 - cmsi2*msi2*m42
& - 2.0d0*mom2*msi2*m42)
cmx_ols =
& fac2*(8.0d0*cmom2**2 - 4.0d0*cmom2*cmsi2
& - 6.0d0*cmom2*mom2 + 2.0d0*cmsi2*mom2
& - 6.0d0*cmom2*msi2 + 2.0d0*cmsi2*msi2
& + 4.0d0*mom2*msi2)
cmx_slc =
& fac3*(cmom2*cmsi2**2 - 3.0d0*cmsi2**3
& + 2.0d0*cmsi2**2*mom2 + 2.0d0*cmsi2**2*msi2
& - cmom2*mom2*msi2 - cmsi2*mom2*msi2
& - 2.0d0*cmom2*cmsi2*m42 + 4.0d0*cmsi2**2*m42
& + cmom2*mom2*m42 - 3.0d0*cmsi2*mom2*m42
& + cmom2*msi2*m42 - 3.0d0*cmsi2*msi2*m42
& + 2.0d0*mom2*msi2*m42)
cmx_sls =
& fac3*(4.0d0*cmom2*cmsi2 - 8.0d0*cmsi2**2
& - 2.0d0*cmom2*mom2 + 6.0d0*cmsi2*mom2
& - 2.0d0*cmom2*msi2 + 6.0d0*cmsi2*msi2
& - 4.0d0*mom2*msi2)
firstlog = .true.
if (info) write(6,*) '(info) dsigma: calculation finished'
c s-dependence beyond this point
1000 continue
s = s_in - (m1_in+m2_in)**2 + m42
tmax = s-m42
tp = 0.5d0*(costh+1.0d0)*tmax
twos = 2.0d0*s
c define s-dependent stuff for omega-Term
brak1 = (twos-m42)**2
bom_3 = com_3*(-(2.0d0*cmom2**2) - 2.0d0*cmom2*twos - brak1)
bom_2 = com_2*(2.0d0*cmom2*mom2 + s_om1*twos + brak1)
bom_1 = com_1*(-(4.0d0*cmom2*mom2) - 2.0d0*mom2**2 -
& 2.0d0*(cmom2+2*mom2)*twos - 3.0d0*brak1)
bom_m = com_m*(-(2.0d0*mom2**2)- 2.0d0*mom2*twos - brak1)
bom_l = com_l*(s_om1*mom2 + (cmom2 + 3.0d0*mom2)*s + brak1)
bom_0 = -(bom_3 + bom_2 + bom_1 + bom_m)
c define s-dependent stuff for mix-Term
bmx_o1 = cmx_o1*(d_om1 - twos)
bmx_s1 = cmx_s1*(d_si1 - twos)
bmx_om = cmx_om*(d_om2 - twos)
bmx_sm = cmx_sm*(d_si2 - twos)
bmx_ol = cmx_olc + cmx_ols*s
bmx_sl = cmx_slc + cmx_sls*s
t1_pi = 1.0d0/(1.0d0+tmax/cmpi2)
t2_pi = 1.0d0+tmax/mpi2
t1_si = 1.0d0/(1.0d0+tmax/cmsi2)
t2_si = 1.0d0+tmax/msi2
t1_om = 1.0d0/(1.0d0+tmax/cmom2)
t2_om = 1.0d0+tmax/mom2
norm = sig(t1_pi,t1_si,t1_om,t2_pi,t2_si,t2_om)
t1_pi = 1.0d0/(1.0d0+tp/cmpi2)
t2_pi = 1.0d0+tp/mpi2
t1_si = 1.0d0/(1.0d0+tp/cmsi2)
t2_si = 1.0d0+tp/msi2
t1_om = 1.0d0/(1.0d0+tp/cmom2)
t2_om = 1.0d0+tp/mom2
if (sym) then
norm=2.0d0*norm
to = tmax-tp
t3_pi = 1.0d0/(1.0d0+to/cmpi2)
t4_pi = 1.0d0+to/mpi2
t3_si = 1.0d0/(1.0d0+to/cmsi2)
t4_si = 1.0d0+to/msi2
t3_om = 1.0d0/(1.0d0+to/cmom2)
t4_om = 1.0d0+to/mom2
dsigma = (sig(t1_pi,t1_si,t1_om,t2_pi,t2_si,t2_om)
& -sig(t3_pi,t3_si,t3_om,t4_pi,t4_si,t4_om))/norm+0.5d0
else
dsigma = sig(t1_pi,t1_si,t1_om,t2_pi,t2_si,t2_om)/norm
end if
return
end
function anginter()
implicit none
real*8 ranf, anginter, a
c*
a=8d0
c*
c the costheta distribution p(x) is proportional to exp(a*x)
c x is chosen between -1 and +1
c a=0 corresponds to isotropic distr.
c a=infinity corresponds to exactly forward distr.
c inverse transform method is used:
anginter=1d0/a*log( ranf(0)*(exp(a)-exp(-a))+exp(-a) )
if(anginter.lt.-1d0.or.anginter.gt.1d0)then
write(*,*)"#angdis# illegal costh value: ",anginter
endif
return
end