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pyhimult.f
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1 
2 C*********************************************************************
3 
4  SUBROUTINE pyhimult(MMUL)
5 
6 C...Initializes treatment of multiple interactions, selects kinematics
7 C...of hardest interaction if low-pT physics included in run, and
8 C...generates all non-hardest interactions.
9  common/lujets/n,k(9000,5),p(9000,5),v(9000,5)
10  SAVE /lujets/
11  common/ludat1/mstu(200),paru(200),mstj(200),parj(200)
12  SAVE /ludat1/
13  common/ludat2/kchg(500,3),pmas(500,4),parf(2000),vckm(4,4)
14  SAVE /ludat2/
15  common/pyhisubs/msel,msub(200),kfin(2,-40:40),ckin(200)
16  SAVE /pyhisubs/
17  common/pyhipars/mstp(200),parp(200),msti(200),pari(200)
18  SAVE /pyhipars/
19  common/pyhiint1/mint(400),vint(400)
20  SAVE /pyhiint1/
21  common/pyhiint2/iset(200),kfpr(200,2),coef(200,20),icol(40,4,2)
22  SAVE /pyhiint2/
23  common/pyhiint3/xsfx(2,-40:40),isig(1000,3),sigh(1000)
24  SAVE /pyhiint3/
25  common/pyhiint5/ngen(0:200,3),xsec(0:200,3)
26  SAVE /pyhiint5/
27  dimension nmul(20),sigm(20),kstr(500,2)
28  SAVE xt2,xt2fac,xc2,xts,irbin,rbin,nmul,sigm
29 
30 C...Initialization of multiple interaction treatment.
31  IF(mmul.EQ.1) THEN
32  IF(mstp(122).GE.1) WRITE(mstu(11),1000) mstp(82)
33  isub=96
34  mint(1)=96
35  vint(63)=0.
36  vint(64)=0.
37  vint(143)=1.
38  vint(144)=1.
39 
40 C...Loop over phase space points: xT2 choice in 20 bins.
41  100 sigsum=0.
42  DO 120 ixt2=1,20
43  nmul(ixt2)=mstp(83)
44  sigm(ixt2)=0.
45  DO 110 itry=1,mstp(83)
46  rsca=0.05*((21-ixt2)-rlu(0))
47  xt2=vint(149)*(1.+vint(149))/(vint(149)+rsca)-vint(149)
48  xt2=max(0.01*vint(149),xt2)
49  vint(25)=xt2
50 
51 C...Choose tau and y*. Calculate cos(theta-hat).
52  IF(rlu(0).LE.coef(isub,1)) THEN
53  taup=(2.*(1.+sqrt(1.-xt2))/xt2-1.)**rlu(0)
54  tau=xt2*(1.+taup)**2/(4.*taup)
55  ELSE
56  tau=xt2*(1.+tan(rlu(0)*atan(sqrt(1./xt2-1.)))**2)
57  ENDIF
58  vint(21)=tau
59  CALL pyhiklim(2)
60  ryst=rlu(0)
61  myst=1
62  IF(ryst.GT.coef(isub,7)) myst=2
63  IF(ryst.GT.coef(isub,7)+coef(isub,8)) myst=3
64  CALL pyhikmap(2,myst,rlu(0))
65  vint(23)=sqrt(max(0.,1.-xt2/tau))*(-1)**int(1.5+rlu(0))
66 
67 C...Calculate differential cross-section.
68  vint(71)=0.5*vint(1)*sqrt(xt2)
69  CALL pyhisigh(nchn,sigs)
70  110 sigm(ixt2)=sigm(ixt2)+sigs
71  120 sigsum=sigsum+sigm(ixt2)
72  sigsum=sigsum/(20.*mstp(83))
73 
74 C...Reject result if sigma(parton-parton) is smaller than hadronic one.
75  IF(sigsum.LT.1.1*vint(106)) THEN
76  IF(mstp(122).GE.1) WRITE(mstu(11),1100) parp(82),sigsum
77  parp(82)=0.9*parp(82)
78  vint(149)=4.*parp(82)**2/vint(2)
79  goto 100
80  ENDIF
81  IF(mstp(122).GE.1) WRITE(mstu(11),1200) parp(82), sigsum
82 
83 C...Start iteration to find k factor.
84  yke=sigsum/vint(106)
85  so=0.5
86  xi=0.
87  yi=0.
88  xk=0.5
89  iit=0
90  130 IF(iit.EQ.0) THEN
91  xk=2.*xk
92  ELSEIF(iit.EQ.1) THEN
93  xk=0.5*xk
94  ELSE
95  xk=xi+(yke-yi)*(xf-xi)/(yf-yi)
96  ENDIF
97 
98 C...Evaluate overlap integrals.
99  IF(mstp(82).EQ.2) THEN
100  sp=0.5*paru(1)*(1.-exp(-xk))
101  sop=sp/paru(1)
102  ELSE
103  IF(mstp(82).EQ.3) deltab=0.02
104  IF(mstp(82).EQ.4) deltab=min(0.01,0.05*parp(84))
105  sp=0.
106  sop=0.
107  b=-0.5*deltab
108  140 b=b+deltab
109  IF(mstp(82).EQ.3) THEN
110  ov=exp(-b**2)/paru(2)
111  ELSE
112  cq2=parp(84)**2
113  ov=((1.-parp(83))**2*exp(-min(100.,b**2))+2.*parp(83)*
114  & (1.-parp(83))*2./(1.+cq2)*exp(-min(100.,b**2*2./(1.+cq2)))+
115  & parp(83)**2/cq2*exp(-min(100.,b**2/cq2)))/paru(2)
116  ENDIF
117  pacc=1.-exp(-min(100.,paru(1)*xk*ov))
118  sp=sp+paru(2)*b*deltab*pacc
119  sop=sop+paru(2)*b*deltab*ov*pacc
120  IF(b.LT.1..OR.b*pacc.GT.1e-6) goto 140
121  ENDIF
122  yk=paru(1)*xk*so/sp
123 
124 C...Continue iteration until convergence.
125  IF(yk.LT.yke) THEN
126  xi=xk
127  yi=yk
128  IF(iit.EQ.1) iit=2
129  ELSE
130  xf=xk
131  yf=yk
132  IF(iit.EQ.0) iit=1
133  ENDIF
134  IF(abs(yk-yke).GE.1e-5*yke) goto 130
135 
136 C...Store some results for subsequent use.
137  vint(145)=sigsum
138  vint(146)=sop/so
139  vint(147)=sop/sp
140 
141 C...Initialize iteration in xT2 for hardest interaction.
142  ELSEIF(mmul.EQ.2) THEN
143  IF(mstp(82).LE.0) THEN
144  ELSEIF(mstp(82).EQ.1) THEN
145  xt2=1.
146  xt2fac=xsec(96,1)/vint(106)*vint(149)/(1.-vint(149))
147  ELSEIF(mstp(82).EQ.2) THEN
148  xt2=1.
149  xt2fac=vint(146)*xsec(96,1)/vint(106)*vint(149)*(1.+vint(149))
150  ELSE
151  xc2=4.*ckin(3)**2/vint(2)
152  IF(ckin(3).LE.ckin(5).OR.mint(82).GE.2) xc2=0.
153  ENDIF
154 
155  ELSEIF(mmul.EQ.3) THEN
156 C...Low-pT or multiple interactions (first semihard interaction):
157 C...choose xT2 according to dpT2/pT2**2*exp(-(sigma above pT2)/norm)
158 C...or (MSTP(82)>=2) dpT2/(pT2+pT0**2)**2*exp(-....).
159  isub=mint(1)
160  IF(mstp(82).LE.0) THEN
161  xt2=0.
162  ELSEIF(mstp(82).EQ.1) THEN
163  xt2=xt2fac*xt2/(xt2fac-xt2*log(rlu(0)))
164  ELSEIF(mstp(82).EQ.2) THEN
165  IF(xt2.LT.1..AND.exp(-xt2fac*xt2/(vint(149)*(xt2+
166  & vint(149)))).GT.rlu(0)) xt2=1.
167  IF(xt2.GE.1.) THEN
168  xt2=(1.+vint(149))*xt2fac/(xt2fac-(1.+vint(149))*log(1.-
169  & rlu(0)*(1.-exp(-xt2fac/(vint(149)*(1.+vint(149)))))))-
170  & vint(149)
171  ELSE
172  xt2=-xt2fac/log(exp(-xt2fac/(xt2+vint(149)))+rlu(0)*
173  & (exp(-xt2fac/vint(149))-exp(-xt2fac/(xt2+vint(149)))))-
174  & vint(149)
175  ENDIF
176  xt2=max(0.01*vint(149),xt2)
177  ELSE
178  xt2=(xc2+vint(149))*(1.+vint(149))/(1.+vint(149)-
179  & rlu(0)*(1.-xc2))-vint(149)
180  xt2=max(0.01*vint(149),xt2)
181  ENDIF
182  vint(25)=xt2
183 
184 C...Low-pT: choose xT2, tau, y* and cos(theta-hat) fixed.
185  IF(mstp(82).LE.1.AND.xt2.LT.vint(149)) THEN
186  IF(mint(82).EQ.1) ngen(0,1)=ngen(0,1)-1
187  IF(mint(82).EQ.1) ngen(isub,1)=ngen(isub,1)-1
188  isub=95
189  mint(1)=isub
190  vint(21)=0.01*vint(149)
191  vint(22)=0.
192  vint(23)=0.
193  vint(25)=0.01*vint(149)
194 
195  ELSE
196 C...Multiple interactions (first semihard interaction).
197 C...Choose tau and y*. Calculate cos(theta-hat).
198  IF(rlu(0).LE.coef(isub,1)) THEN
199  taup=(2.*(1.+sqrt(1.-xt2))/xt2-1.)**rlu(0)
200  tau=xt2*(1.+taup)**2/(4.*taup)
201  ELSE
202  tau=xt2*(1.+tan(rlu(0)*atan(sqrt(1./xt2-1.)))**2)
203  ENDIF
204  vint(21)=tau
205  CALL pyhiklim(2)
206  ryst=rlu(0)
207  myst=1
208  IF(ryst.GT.coef(isub,7)) myst=2
209  IF(ryst.GT.coef(isub,7)+coef(isub,8)) myst=3
210  CALL pyhikmap(2,myst,rlu(0))
211  vint(23)=sqrt(max(0.,1.-xt2/tau))*(-1)**int(1.5+rlu(0))
212  ENDIF
213  vint(71)=0.5*vint(1)*sqrt(vint(25))
214 
215 C...Store results of cross-section calculation.
216  ELSEIF(mmul.EQ.4) THEN
217  isub=mint(1)
218  xts=vint(25)
219  IF(iset(isub).EQ.1) xts=vint(21)
220  IF(iset(isub).EQ.2) xts=(4.*vint(48)+2.*vint(63)+2.*vint(64))/
221  & vint(2)
222  IF(iset(isub).EQ.3.OR.iset(isub).EQ.4) xts=vint(26)
223  rbin=max(0.000001,min(0.999999,xts*(1.+vint(149))/
224  & (xts+vint(149))))
225  irbin=int(1.+20.*rbin)
226  IF(isub.EQ.96) nmul(irbin)=nmul(irbin)+1
227  IF(isub.EQ.96) sigm(irbin)=sigm(irbin)+vint(153)
228 
229 C...Choose impact parameter.
230  ELSEIF(mmul.EQ.5) THEN
231  IF(mstp(82).EQ.3) THEN
232  vint(148)=rlu(0)/(paru(2)*vint(147))
233  ELSE
234  rtype=rlu(0)
235  cq2=parp(84)**2
236  IF(rtype.LT.(1.-parp(83))**2) THEN
237  b2=-log(rlu(0))
238  ELSEIF(rtype.LT.1.-parp(83)**2) THEN
239  b2=-0.5*(1.+cq2)*log(rlu(0))
240  ELSE
241  b2=-cq2*log(rlu(0))
242  ENDIF
243  vint(148)=((1.-parp(83))**2*exp(-min(100.,b2))+2.*parp(83)*
244  & (1.-parp(83))*2./(1.+cq2)*exp(-min(100.,b2*2./(1.+cq2)))+
245  & parp(83)**2/cq2*exp(-min(100.,b2/cq2)))/(paru(2)*vint(147))
246  ENDIF
247 
248 C...Multiple interactions (variable impact parameter) : reject with
249 C...probability exp(-overlap*cross-section above pT/normalization).
250  rncor=(irbin-20.*rbin)*nmul(irbin)
251  sigcor=(irbin-20.*rbin)*sigm(irbin)
252  DO 150 ibin=irbin+1,20
253  rncor=rncor+nmul(ibin)
254  150 sigcor=sigcor+sigm(ibin)
255  sigabv=(sigcor/rncor)*vint(149)*(1.-xts)/(xts+vint(149))
256  vint(150)=exp(-min(100.,vint(146)*vint(148)*sigabv/vint(106)))
257 
258 C...Generate additional multiple semihard interactions.
259  ELSEIF(mmul.EQ.6) THEN
260 
261 C...Reconstruct strings in hard scattering.
262  isub=mint(1)
263  nmax=mint(84)+4
264  IF(iset(isub).EQ.1) nmax=mint(84)+2
265  nstr=0
266  DO 170 i=mint(84)+1,nmax
267  kcs=kchg(lucomp(k(i,2)),2)*isign(1,k(i,2))
268  IF(kcs.EQ.0) goto 170
269  DO 160 j=1,4
270  IF(kcs.EQ.1.AND.(j.EQ.2.OR.j.EQ.4)) goto 160
271  IF(kcs.EQ.-1.AND.(j.EQ.1.OR.j.EQ.3)) goto 160
272  IF(j.LE.2) THEN
273  ist=mod(k(i,j+3)/mstu(5),mstu(5))
274  ELSE
275  ist=mod(k(i,j+1),mstu(5))
276  ENDIF
277  IF(ist.LT.mint(84).OR.ist.GT.i) goto 160
278  IF(kchg(lucomp(k(ist,2)),2).EQ.0) goto 160
279  nstr=nstr+1
280  IF(j.EQ.1.OR.j.EQ.4) THEN
281  kstr(nstr,1)=i
282  kstr(nstr,2)=ist
283  ELSE
284  kstr(nstr,1)=ist
285  kstr(nstr,2)=i
286  ENDIF
287  160 CONTINUE
288  170 CONTINUE
289 
290 C...Set up starting values for iteration in xT2.
291  xt2=vint(25)
292  IF(iset(isub).EQ.1) xt2=vint(21)
293  IF(iset(isub).EQ.2) xt2=(4.*vint(48)+2.*vint(63)+2.*vint(64))/
294  & vint(2)
295  IF(iset(isub).EQ.3.OR.iset(isub).EQ.4) xt2=vint(26)
296  isub=96
297  mint(1)=96
298  IF(mstp(82).LE.1) THEN
299  xt2fac=xsec(isub,1)*vint(149)/((1.-vint(149))*vint(106))
300  ELSE
301  xt2fac=vint(146)*vint(148)*xsec(isub,1)/vint(106)*
302  & vint(149)*(1.+vint(149))
303  ENDIF
304  vint(63)=0.
305  vint(64)=0.
306  vint(151)=0.
307  vint(152)=0.
308  vint(143)=1.-vint(141)
309  vint(144)=1.-vint(142)
310 
311 C...Iterate downwards in xT2.
312  180 IF(mstp(82).LE.1) THEN
313  xt2=xt2fac*xt2/(xt2fac-xt2*log(rlu(0)))
314  IF(xt2.LT.vint(149)) goto 220
315  ELSE
316  IF(xt2.LE.0.01*vint(149)) goto 220
317  xt2=xt2fac*(xt2+vint(149))/(xt2fac-(xt2+vint(149))*
318  & log(rlu(0)))-vint(149)
319  IF(xt2.LE.0.) goto 220
320  xt2=max(0.01*vint(149),xt2)
321  ENDIF
322  vint(25)=xt2
323 
324 C...Choose tau and y*. Calculate cos(theta-hat).
325  IF(rlu(0).LE.coef(isub,1)) THEN
326  taup=(2.*(1.+sqrt(1.-xt2))/xt2-1.)**rlu(0)
327  tau=xt2*(1.+taup)**2/(4.*taup)
328  ELSE
329  tau=xt2*(1.+tan(rlu(0)*atan(sqrt(1./xt2-1.)))**2)
330  ENDIF
331  vint(21)=tau
332  CALL pyhiklim(2)
333  ryst=rlu(0)
334  myst=1
335  IF(ryst.GT.coef(isub,7)) myst=2
336  IF(ryst.GT.coef(isub,7)+coef(isub,8)) myst=3
337  CALL pyhikmap(2,myst,rlu(0))
338  vint(23)=sqrt(max(0.,1.-xt2/tau))*(-1)**int(1.5+rlu(0))
339 
340 C...Check that x not used up. Accept or reject kinematical variables.
341  x1m=sqrt(tau)*exp(vint(22))
342  x2m=sqrt(tau)*exp(-vint(22))
343  IF(vint(143)-x1m.LT.0.01.OR.vint(144)-x2m.LT.0.01) goto 180
344  vint(71)=0.5*vint(1)*sqrt(xt2)
345  CALL pyhisigh(nchn,sigs)
346  IF(sigs.LT.xsec(isub,1)*rlu(0)) goto 180
347 
348 C...Reset K, P and V vectors. Select some variables.
349  DO 190 i=n+1,n+2
350  DO 190 j=1,5
351  k(i,j)=0
352  p(i,j)=0.
353  190 v(i,j)=0.
354  rflav=rlu(0)
355  pt=0.5*vint(1)*sqrt(xt2)
356  phi=paru(2)*rlu(0)
357  cth=vint(23)
358 
359 C...Add first parton to event record.
360  k(n+1,1)=3
361  k(n+1,2)=21
362  IF(rflav.GE.max(parp(85),parp(86))) k(n+1,2)=
363  & 1+int((2.+parj(2))*rlu(0))
364  p(n+1,1)=pt*cos(phi)
365  p(n+1,2)=pt*sin(phi)
366  p(n+1,3)=0.25*vint(1)*(vint(41)*(1.+cth)-vint(42)*(1.-cth))
367  p(n+1,4)=0.25*vint(1)*(vint(41)*(1.+cth)+vint(42)*(1.-cth))
368  p(n+1,5)=0.
369 
370 C...Add second parton to event record.
371  k(n+2,1)=3
372  k(n+2,2)=21
373  IF(k(n+1,2).NE.21) k(n+2,2)=-k(n+1,2)
374  p(n+2,1)=-p(n+1,1)
375  p(n+2,2)=-p(n+1,2)
376  p(n+2,3)=0.25*vint(1)*(vint(41)*(1.-cth)-vint(42)*(1.+cth))
377  p(n+2,4)=0.25*vint(1)*(vint(41)*(1.-cth)+vint(42)*(1.+cth))
378  p(n+2,5)=0.
379 
380  IF(rflav.LT.parp(85).AND.nstr.GE.1) THEN
381 C....Choose relevant string pieces to place gluons on.
382  DO 210 i=n+1,n+2
383  dmin=1e8
384  DO 200 istr=1,nstr
385  i1=kstr(istr,1)
386  i2=kstr(istr,2)
387  dist=(p(i,4)*p(i1,4)-p(i,1)*p(i1,1)-p(i,2)*p(i1,2)-
388  & p(i,3)*p(i1,3))*(p(i,4)*p(i2,4)-p(i,1)*p(i2,1)-
389  & p(i,2)*p(i2,2)-p(i,3)*p(i2,3))/max(1.,p(i1,4)*p(i2,4)-
390  & p(i1,1)*p(i2,1)-p(i1,2)*p(i2,2)-p(i1,3)*p(i2,3))
391  IF(istr.EQ.1.OR.dist.LT.dmin) THEN
392  dmin=dist
393  ist1=i1
394  ist2=i2
395  istm=istr
396  ENDIF
397  200 CONTINUE
398 
399 C....Colour flow adjustments, new string pieces.
400  IF(k(ist1,4)/mstu(5).EQ.ist2) k(ist1,4)=mstu(5)*i+
401  & mod(k(ist1,4),mstu(5))
402  IF(mod(k(ist1,5),mstu(5)).EQ.ist2) k(ist1,5)=
403  & mstu(5)*(k(ist1,5)/mstu(5))+i
404  k(i,5)=mstu(5)*ist1
405  k(i,4)=mstu(5)*ist2
406  IF(k(ist2,5)/mstu(5).EQ.ist1) k(ist2,5)=mstu(5)*i+
407  & mod(k(ist2,5),mstu(5))
408  IF(mod(k(ist2,4),mstu(5)).EQ.ist1) k(ist2,4)=
409  & mstu(5)*(k(ist2,4)/mstu(5))+i
410  kstr(istm,2)=i
411  kstr(nstr+1,1)=i
412  kstr(nstr+1,2)=ist2
413  210 nstr=nstr+1
414 
415 C...String drawing and colour flow for gluon loop.
416  ELSEIF(k(n+1,2).EQ.21) THEN
417  k(n+1,4)=mstu(5)*(n+2)
418  k(n+1,5)=mstu(5)*(n+2)
419  k(n+2,4)=mstu(5)*(n+1)
420  k(n+2,5)=mstu(5)*(n+1)
421  kstr(nstr+1,1)=n+1
422  kstr(nstr+1,2)=n+2
423  kstr(nstr+2,1)=n+2
424  kstr(nstr+2,2)=n+1
425  nstr=nstr+2
426 
427 C...String drawing and colour flow for q-qbar pair.
428  ELSE
429  k(n+1,4)=mstu(5)*(n+2)
430  k(n+2,5)=mstu(5)*(n+1)
431  kstr(nstr+1,1)=n+1
432  kstr(nstr+1,2)=n+2
433  nstr=nstr+1
434  ENDIF
435 
436 C...Update remaining energy; iterate.
437  n=n+2
438  IF(n.GT.mstu(4)-mstu(32)-10) THEN
439  CALL luerrm(11,'(PYHIMULT:) no more memory left in LUJETS')
440  IF(mstu(21).GE.1) RETURN
441  ENDIF
442  mint(31)=mint(31)+1
443  vint(151)=vint(151)+vint(41)
444  vint(152)=vint(152)+vint(42)
445  vint(143)=vint(143)-vint(41)
446  vint(144)=vint(144)-vint(42)
447  IF(mint(31).LT.240) goto 180
448  220 CONTINUE
449  ENDIF
450 
451 C...Format statements for printout.
452  1000 FORMAT(/1x,'****** PYHIMULT: initialization of multiple inter',
453  &'actions for MSTP(82) =',i2,' ******')
454  1100 FORMAT(8x,'pT0 =',f5.2,' GeV gives sigma(parton-parton) =',1p,
455  &e9.2,' mb: rejected')
456  1200 FORMAT(8x,'pT0 =',f5.2,' GeV gives sigma(parton-parton) =',1p,
457  &e9.2,' mb: accepted')
458 
459  RETURN
460  END