1 *----------------------------------------------------------------------
5 * First version created: 20-AUG-1997 Author : Igor Lokhtin
6 * Last revision : 23-SEP-2004
8 *======================================================================
10 * Description : Event generator for simulation of parton rescattering
11 * and energy loss in quark-gluon plasma created in heavy
12 * ion AA collisons at LHC
13 * (implemented as modification of standard pythia jet event)
15 * Method : I.P.Lokhtin, A.M.Snigirev, Eur.Phys.J. C16 (2000) 527-536;
16 * I.P.Lokhtin, A.M.Snigirev, e-print hep-ph/0406038.
19 *======================================================================
21 SUBROUTINE PYQUEN(A,ifb,bfix)
22 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
24 INTEGER PYK,PYCHGE,PYCOMP
26 external pyp,pyr,pyk,pyjoin,pyshow
28 common /pyjets/ n,npad,k(4000,5),p(4000,5),v(4000,5)
29 common /pydat1/ mstu(200),paru(200),mstj(200),parj(200)
30 common /pysubs/ msel,mselpd,msub(500),kfin(2,-40:40),ckin(200)
31 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
32 common /plglur/ glur(1000,4),kglu(1000,6),nrg,nrgm
33 common /plquar/ pqua(1000,5),kqua(1000,5),nrq
34 common /parimp/ b1,psib1,rb1,rb2
37 save /pyjets/, /pydat1/, /pysubs/, /plglur/, /plquar/
38 dimension ijoik(2),ijoin(1000),nis(500),nss(500),nas(500),nus(500)
40 * set initial event paramters
42 RA=1.15d0*AW**0.333333d0 ! nucleus radius in fm
44 nf=0 ! number of active flavours in QGP
45 TC=0.2d0 ! crutical temperature
46 tau0=0.1d0 ! proper time of QGP formation
47 mvisc=0 ! flag of QGP viscosity (off here)
51 * avoid stopping run if pythia does not conserve energy due to collisional loss
54 * generate impact parameter of A-A collision with jet production
57 write(6,*) 'Impact parameter less than zero!'
61 write(6,*) 'Impact parameter larger than two nuclear radius!'
66 call bipsear(fmax1,xmin1)
77 * calculate initial QGP temperature as function of centrality
79 sb=RA*RA*(pi-2.d0*dasin(0.5d0*b1/RA))-b1*dsqrt(abs(RA*RA-
81 rtaa0=9.d0*AW*AW/(8.d0*sb0)
82 br=max(1.d-10,b1*b1/(4.d0*RA*RA))
83 call simpa(0.d0,20.d0,0.001d0,0.001d0,1.d-08,ftaa,xx,rest,
85 rtaa=rtaa0*(1.d0-br*(1.d0+(1.d0-0.25d0*br)*dlog(1.d0/br)+
87 T00=((rtaa*sb0)/(rtaa0*sb))**0.25d0
88 T0=T00*(AW/207.d0)**0.166667d0
90 * generate single event with partonic energy loss
92 if(b1.le.1.85d0*RA) then
97 * reset all in-vacuum radiated guark 4-momenta and codes to zero
106 * generate final state shower in vacuum if it was excluded before
107 nrgm=nrg ! fix number of in-medium emitted gluons
114 if(mstj(41).ne.0) goto 5
119 ip1=i ! first hard parton (line ip1)
120 kfh1=k(i,1) ! status code of first hard parton
121 qmax1=p(i,4) ! energy of first hard parton
124 ip2=i ! second hard parton (line ip2)
125 kfh2=k(i,1) ! status code of second hard parton
126 qmax2=p(i,4) ! energy of second hard parton
131 call pyshow(ip1,0,qmax1) ! vacuum showering for first hard parton
134 call pyshow(ip2,0,qmax2) ! vacuum showering for second hard parton
138 * find two leading partons after showering
140 if(k(i,3).eq.ip1) ip001=i ! first daughter of first hard parton
141 if(k(i,3).eq.ip2) ip002=i ! first daughter of second hard parton
146 if (k(i,1).eq.14) goto 3
147 if(i.ge.ip002.and.ip002.gt.0) then
149 if(ptl02.gt.ptle2.and.k(i,2).eq.k(ip2,2)) then
150 ip02=i ! leading parton in second shower (line ip02)
151 ptle2=ptl02 ! pt of the leading parton
153 elseif(ip001.gt.0) then
155 if(ptl01.gt.ptle1.and.k(i,2).eq.k(ip1,2)) then
156 ip01=i ! leading parton in first shower (line ip01)
157 ptle1=ptl01 ! pt of the leading parton
163 * replace two hard partons by two leading partons in original event record
179 * add final showering gluons to the list of in-medium emitted gluons,
180 * fill the list of emitted quarks by final showering quark pairs,
181 * and remove showering gluons and quarks from the event record
183 if(k(i,1).eq.14.or.i.eq.ip01.or.i.eq.ip02) goto 12
184 if(k(i,2).ne.21) then ! filling 'plquar' arrays for quarks
193 if(i.ge.ip002.and.ip002.gt.0) then
201 if(ish.ge.ishm.or.nur.le.2) goto 6 ! adding gluons in 'plglur' arrays
203 kglu(nur,j)=kglu(nur-1,j)
206 glur(nur,j)=glur(nur-1,j)
210 6 kglu(nur,1)=2 ! status code
211 kglu(nur,2)=k(i,2) ! particle identificator
212 kglu(nur,3)=k(ish,3) ! parent line number
213 kglu(nur,4)=0 ! special colour info
214 kglu(nur,5)=0 ! special colour info
215 kglu(nur,6)=ish ! associated parton number
216 glur(nur,1)=p(i,4) ! energy
217 glur(nur,2)=pyp(i,10) ! pt
218 glur(nur,3)=pyp(i,15) ! phi
219 glur(nur,4)=pyp(i,19) ! eta
221 do j=1,5 ! remove partons from event list
231 * stop generate event if there are no additional gluons
234 * define number of stirngs (ns) and number of entries in strings before
235 * in-medium radiation (nis(ns))
250 nis(ns+1)=nis(ns+1)+1
251 elseif(ks.eq.1.and.nis(ns+1).gt.0) then
252 nis(ns+1)=nis(ns+1)+1
253 nes=nes+nis(ns+1) ! nes - total number if entries
256 elseif(ks.ne.2.and.ksp.ne.2.and.ns.gt.0) then
257 i1=i1+1 ! last i1 lines not included in strings
260 i0=n-nes-i1 ! first i0 lines not included in strings
265 * move fragmented particles in bottom of event list
269 if(ks.ne.2.and.ksp.ne.2) then
285 if(ku.gt.i) kglu(ip,6)=ku-1
293 * define number of additional entries in strings, nas(ns)
296 if(kas.le.nss(1)) then
300 if(kas.le.nss(j).and.kas.gt.nss(j-1))
311 * add emitted gluons in event list
323 do i=nss(ia+1)-1,nss(ia),-1
338 if(i.le.nus(in).and.i.gt.nus(in-1))
350 p(ia,1)=ptg*dcos(phig)
351 p(ia,2)=ptg*dsin(phig)
352 p(ia,3)=dsqrt(abs(eg*eg-ptg*ptg))
353 if(etag.lt.0.d0) p(ia,3)=-1.*p(ia,3)
358 * rearrange partons to form strings in event list
370 ijoin(j)=nss(i-1)+nus(i-1)+j
373 call pyjoin(njoin,ijoin)
376 * add in-vacuum emitted quark pairs
386 4 ktest=k(n-1,2)+kqua(in,2)
387 if(ktest.eq.0.or.in.eq.nrq) goto 8
397 kqua(in,j)=kqua(i+1,j)
398 pqua(in,j)=pqua(i+1,j)
418 ********************************* PLINIT ***************************
419 SUBROUTINE PLINIT(ET)
420 * set nucleus thikness and plasma parameters
421 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
422 IMPLICIT INTEGER(I-N)
423 INTEGER PYK,PYCHGE,PYCOMP
425 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
426 common /plpar2/ pln0,taupl,tauh,sigpl,sigh,sigplh,sigqqh,rg,rgn
427 common /plevol/ taup(5000),temp(5000),denp(5000),enep(5000)
433 * set number degrees of freedom in QGP
435 rg=(16.d0+10.5d0*nf)/hgd
436 rgn=(16.d0+9.d0*nf)/hgd
438 * set 'fiction' sigma for parton rescattering in QGP
440 sigpl=2.25d0*2.25d0*sigqq*(16.d0+4.d0*nf)/(16.d0+9.d0*nf)
442 * set intial plasma temperature, density and energy density in perfect
443 * (if mvisc=0) or viscous (mvisc=1,2) QGP with PLVISC subroitine
445 if(mvisc.eq.2.and.T0.gt.0.6d0) hst=0.25d0
448 pln0=(16.d0+9.d0*nf)*1.2d0*(T01**3)/pi2
449 ened0=pi2*(16.d0+10.5d0*nf)*(T01**4)/30.d0
451 tau=tau0 ! proper time
453 den=pln0 ! number density
454 ened=ened0 ! energy density
456 * create array of parameters to configurate QGP time evolution
458 taup(i)=tau ! proper time
459 temp(i)=T/5.06d0 ! temperature
460 denp(i)=den ! number density
461 enep(i)=ened/5.06d0 ! energy density
462 ened1=0.5d0*hh*(1.3333d0*plvisc(T)/(tau*tau)-1.3333d0
464 T1=(30.d0*ened1/((16.d0+10.5d0*nf)*pi2))**0.25d0
466 ened=hh*(1.3333d0*plvisc(T1)/(tau1*tau1)-1.3333d0
469 T=(30.d0*ened/((16.d0+10.5d0*nf)*pi2))**0.25d0
470 den=(16.d0+9.d0*nf)*1.2d0*(T**3)/pi2
472 if(TPR.gt.TC1.and.T.le.TC1) taupl=tau-0.5d0*hh ! QGP lifetime taupl
474 tauh=taupl*rg ! mixed phase lifetime
478 ******************************** END PLINIT **************************
480 ******************************* PLEVNT ******************************
481 SUBROUTINE PLEVNT(ET)
482 * generate hard parton production vertex and passing with rescattering,
483 * collisional and radiative energy loss of each parton through plasma
484 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
485 IMPLICIT INTEGER(I-N)
486 INTEGER PYK,PYCHGE,PYCOMP
487 external plthik, pln, plt, pls, pygauss, gluang
489 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
490 common /plpar2/ pln0,taupl,tauh,sigpl,sigh,sigplh,sigqqh,rg,rgn
491 common /thikpa/ fmax,xmin
492 common /pyjets/ n,npad,k(4000,5),p(4000,5),v(4000,5)
493 common /plglur/ glur(1000,4),kglu(1000,6),nrg,nrgm
494 common /factor/ cfac, kf
495 common /pleave/ taul, temlev
496 common /parimp/ b1, psib1, rb1, rb2
497 common /plen/ epartc, um
498 common /plos/ elr,rsk
499 common /numje1/ nuj1, nuj2
500 save /pyjets/, /plglur/
504 * find minimum of nuclear thikness function with subroutine plsear
505 psib1=pi*(2.d0*pyr(0)-1.d0)
506 call plsear (fmax1,xmin1)
510 * generate vertex of jet production
516 if(ff1.gt.f.and.iv.le.100000) goto 1
518 rb1=dsqrt(abs(r0*r0+b1*b1/4.d0+r0*b1*dcos(psib1)))
519 rb2=dsqrt(abs(r0*r0+b1*b1/4.d0-r0*b1*dcos(psib1)))
523 * find maximum of angular spectrum of radiated gluons with subroutine gluang
525 temax=0.5d0*(1.d0+dsqrt(5.d0))*0.0863d0
528 * reset all radiated gluon 4-momenta and codes to zero -------------------
539 * generate changing 4-momentum of partons due to rescattering and energy loss
540 * (for partons with |eta|<3 and p>5 GeV/c)
541 nuj1=7 ! minimum number of rescattered parton
542 nuj2=n ! maximum number of rescattered parton
543 do 2 ip=nuj1,nuj2 ! cycle on travelling partons
546 ks=k(ip,1) ! parton status code
547 kf=k(ip,2) ! parton identificator
549 epart=abs(pyp(ip,10)) ! parton total momentum
550 etar=pyp(ip,19) ! parton pseudorapidity
551 if(epart.ge.5.d0.and.abs(etar).le.3.d0) then
552 if(ka.eq.21.or.ka.eq.1.or.ka.eq.2.or.ka.eq.3.
553 > or.ka.eq.4.or.ka.eq.5.or.ka.eq.6.or.ka.eq.7.
555 if(ks.eq.2.or.ks.eq.1.or.ks.eq.21) then
556 phir=pyp(ip,15) ! parton azimuthal angle
557 tetr=pyp(ip,13) ! parton polar angle
558 yrr=pyp(ip,17) ! parton rapidity
559 stetr=max(dsin(tetr),1.d-04) ! parton sin(theta)
565 cfac=1.d0 ! for gluon
567 cfac=0.44444444d0 ! for quark
570 * boost from laboratory system to system of hard parton
572 bet0=(r0*dcos(psib1)+0.5d0*b1)/rb1
573 if(bet0.le.-1.d0) bet0=-0.99999d0
574 if(bet0.ge.1.d0) bet0=0.99999d0
576 if(psib1.lt.0.d0) bet=-1.d0*bet
578 if(phip.gt.pi) phip=phip-2.d0*pi
579 if(phip.lt.-1.d0*pi) phip=phip+2.d0*pi
580 call pyrobo(0,0,0.d0,phir1,0.d0,0.d0,0.d0)
581 call pyrobo(0,0,tetr1,0.d0,0.d0,0.d0,0.d0)
583 * calculate proper time of parton leaving QGP
584 aphin=(r0*r0-b1*b1/4.d0)/(rb1*rb2)
585 if(aphin.le.-1.d0) aphin=-0.99999d0
586 if(aphin.ge.1.d0) aphin=0.99999d0
588 if(psib1.le.0.d0) phin=-1.d0*phin
590 if(phid.gt.pi) phid=phid-2.d0*pi
591 if(phid.lt.-1.d0*pi) phid=phid+2.d0*pi
592 taul1=abs(dsqrt(abs(RA*RA-(rb1*dsin(phip))**2))-rb1*dcos(phip))
593 taul2=abs(dsqrt(abs(RA*RA-(rb2*dsin(phid))**2))-rb2*dcos(phid))
594 taul=min(taul1,taul2) ! escape time taul
595 temlev=plt(taul) ! QGP temperature at taul
596 if(taul.le.tau0) goto 100 ! escape from QGP if taul<tau0
598 * start parton rescattering in QGP with proper time iterations
601 xi=-10.d0*dlog(max(pyr(0),1.d-10))/(sigpl*pln(tau))
602 vel=abs(p(ip,3))/dsqrt(p(ip,3)**2+p(ip,5)**2) ! parton velocity
603 if(vel.lt.0.3d0) goto 4
605 if(tau.ge.taul.or.tfs.le.TC) goto 100 ! escape if tau>taul or >taupl
607 * transform parton 4-momentum due to next scattering with subroutine pljetr
608 epartc=p(ip,4) ! parton energy
609 um=p(ip,5) ! parton mass
610 sigtr=pls(tfs)*cfac*((p(ip,4)/pyp(ip,8))**2)
611 prob=sigpl/(sigtr/stetr+sigpl)
614 if(irasf.gt.100000) goto 100
615 if(ran.lt.prob) goto 3
618 pass=50.6d0/(pln(tau)*sigtr)
621 call pljetr(tau,pass,pltp,ipar,epart)
624 * set 4-momentum (in lab system) of next radiated gluon for parton number >8
625 * and fill arrays of radiated gluons in common block plglur
627 if(abs(elr).gt.0.1d0.and.ip.gt.8) then
632 if(fte1.gt.fte2) goto 6
633 tgl=te1 ! gaussian angular spectrum
634 c tgl=0.d0 ! collinear angular spectrum
635 c tgl=((0.5d0*pi*epartc)**pyr(0))/epartc ! broad-angular spectrum
636 pgl=pi*(2.d0*pyr(0)-1.d0)
637 pxgl=abs(elr)*(dcos(phir)*dcos(tgl)/dcosh(yrr)+
638 > dcos(phir)*dsin(tgl)*dcos(pgl)*dsinh(yrr)/dcosh(yrr)-
639 > dsin(phir)*dsin(tgl)*dsin(pgl))
640 pygl=abs(elr)*(dsin(phir)*dcos(tgl)/dcosh(yrr)+
641 > dsin(phir)*dsin(tgl)*dcos(pgl)*dsinh(yrr)/dcosh(yrr)+
642 > dcos(phir)*dsin(tgl)*dsin(pgl))
643 pzgl=abs(elr)*(dsinh(yrr)*dcos(tgl)-dsin(tgl)*dcos(pgl))
645 ptgl=dsqrt(abs(pxgl*pxgl+pygl*pygl))
646 psgl=dsqrt(abs(ptgl*ptgl+pzgl*pzgl))
648 glur(nrg,1)=abs(elr) ! energy
649 glur(nrg,3)=datan(dpgl) ! phi
650 if(pxgl.lt.0.d0) then
651 if(pygl.ge.0.d0) then
652 glur(nrg,3)=glur(nrg,3)+pi
654 glur(nrg,3)=glur(nrg,3)-pi
657 glur(nrg,4)=0.5d0*dlog(max(1.d-9,(psgl+pzgl)/(psgl-pzgl))) ! eta
658 glur(nrg,2)=glur(nrg,1)/dcosh(glur(nrg,4)) ! pt
660 kglu(nrg,1)=2 ! status code
661 kglu(nrg,2)=21 ! particle identificator
662 kglu(nrg,3)=k(ipar,3) ! parent line number
663 kglu(nrg,4)=0 ! special colour info
664 kglu(nrg,5)=0 ! special colour info
665 kglu(nrg,6)=ipar ! associated parton number
668 write(6,*) 'Warning! Number of emitted gluons is too large!'
671 * set parton "thermalization" if pt<T
672 if(abs(p(ip,3)).gt.pltp3) goto 3
674 if(p(ip,3).ge.0.d0) then
680 if(iraz.gt.100000) goto 100
681 ep0=-0.15d0*(dlog(max(1.d-10,pyr(0)))+dlog(max(1.d-10,pyr(0)))+
682 > dlog(max(1.d-10,pyr(0))))
683 if(ep0.le.p(ip,5).or.ep0.ge.100.d0) goto 5
684 pp0=dsqrt(abs(ep0**2-p(ip,5)**2))
686 if(pyr(0).gt.probt) goto 5
687 ctp0=2.d0*pyr(0)-1.d0
688 stp0=dsqrt(abs(1.d0-ctp0**2))
689 php0=pi*(2.d0*pyr(0)-1.d0)
690 p(ip,1)=pp0*stp0*dcos(php0)
691 p(ip,2)=pp0*stp0*dsin(php0)
692 p(ip,3)=sigp*pp0*ctp0
693 p(ip,4)=dsqrt(p(ip,1)**2+p(ip,2)**2+p(ip,3)**2+p(ip,5)**2)
695 * boost to laboratory system
696 100 call pyrobo(0,0,tetr,phir,0.d0,0.d0,0.d0)
704 ******************************* END PLEVNT *************************
706 ******************************* PLJETR *****************************
707 SUBROUTINE PLJETR(tau,y,x,ip,epart)
708 * transform parton 4-momentum due to scattering in plasma at time = tau
709 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
710 IMPLICIT INTEGER(I-N)
711 INTEGER PYK,PYCHGE,PYCOMP
714 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
715 common /plpar2/ pln0,taupl,tauh,sigpl,sigh,sigplh,sigqqh,rg,rgn
716 common /pyjets/ n,npad,k(4000,5),p(4000,5),v(4000,5)
717 common /pljdat/ ej, z, ygl, alfs, um, epa
718 common /pleave/ taul, temlev
719 common /radcal/ aa, bb
720 common /factor/ cfac, kf
721 common /plos/ elr,rsk
726 tauu=x ! redenote temerature tauu=x
727 i=ip ! redenote parton number i=ip
731 * boost to system of comoving plasma constituent
732 phir=pyp(i,15) ! parton phi
733 tetr=pyp(i,13) ! parton theta
734 stetr=max(dsin(tetr),1.d-08) ! parton sin(theta)
737 call pyrobo(0,0,0.d0,phir1,0.d0,0.d0,0.d0)
738 call pyrobo(0,0,tetr1,0.d0,0.d0,0.d0,0.d0)
739 pp=pyp(i,8) ! parton total momentum
740 ppl=abs(p(i,3)) ! parton pz
741 um=p(i,5) ! parton mass
742 epa=p(i,4) ! parton energy
743 ppt=pyp(i,10) ! parton pt
744 pphi=pyp(i,15) ! parton phi
746 if(ppl.lt.3.d0) goto 222 ! no energy loss if pz<3 GeV/c
748 * generation hard parton-plasma scattering with momentum transfer rsk
749 221 ep0=-1.*tauu*(dlog(max(1.d-10,pyr(0)))+dlog(max(1.d-10,
750 > pyr(0)))+dlog(max(1.d-10,pyr(0)))) ! energy of 'thermal' parton
752 if(ep0.lt.1.d-10.and.iter.le.100000) goto 221
753 scm=2.*ep0*epa+um*um+ep0*ep0
754 qm2=(scm-((um+ep0)**2))*(scm-((um-ep0)**2))/scm
756 alf=6.d0*pi/((33.d0-2.d0*nf)*dlog(max(bub,1.d-10)))
757 z=pi*4.d0*tauu*tauu*alf*(1.+nf/6.d0)
758 bubs=dsqrt(abs(z))/TC
759 alfs=6.d0*pi/((33.d0-2.d0*nf)*dlog(max(bubs,1.d-10)))
761 phmax2=max(phmin2,qm2)
762 fqmax2=1.d0/(dlog(max(phmin2/(TC*TC),1.d-10)))**2
764 tp=1.d0/(rn1/phmax2+(1.d0-rn1)/phmin2)
765 ftp=1.d0/(dlog(max(tp/(TC*TC),1.d-10)))**2
768 if(fprob.lt.rn2) goto 12
770 if(rsk.gt.ppl) rsk=ppl
772 * calculate radiative energy loss per given scattering with subroutin plfun1
773 ygl=y*cfac ! mean gluon free path in GeV^{-1}
774 elp=ygl*z ! mimimum radiated energy in LPM regime
776 bb=ej ! maximum radiated energy
777 bbi=max(dsqrt(abs(z)),1.000001d0*elp)
778 aa=min(bb,bbi) ! minimum radiated energy
782 CALL SIMPA(aa,bb,hh,REPS,AEPS,plfun1,om,resun,AIH,AIABS)
783 * ! integral over omega for radiative loss
784 call radsear(ermax1,eomin1)
787 11 resu=eomin*pyr(0)+aa
791 if(fres.gt.fres1.and.iraz.lt.100000) goto 11
792 elr=resu*resun ! energy of radiated gluon
794 * to chancel radiative energy loss (optional case)
796 * to chancel collisional energy loss (optional case)
799 * determine the direction of parton moving
800 if(p(i,3).ge.0.d0) then
806 * calculate new 4-momentum of hard parton
808 epan=max(epa-rsk*rsk/(2.d0*ep0)-abs(elr),1.d0)
809 pptn=dsqrt(abs(rsk*rsk+(rsk**4)*(1.d0-epa*epa/(ppl*ppl))/
810 > (4.d0*ep0*ep0)-(rsk**4)*epa/(2.d0*ep0*ppl*ppl)-(rsk**4)/
812 ppln=dsqrt(abs(epan*epan-pptn*pptn-p(i,5)**2))
813 p(i,1)=pptn*dcos(phirs) ! px
814 p(i,2)=pptn*dsin(phirs) ! py
815 p(i,3)=sigp*ppln ! pz
818 * boost to system of hard parton
819 222 call pyrobo(0,0,tetr,phir,0.d0,0.d0,0.d0)
823 ******************************* END PLJETR **************************
825 ******************************** PLSEAR ***************************
826 SUBROUTINE PLSEAR (fmax,xmin)
827 * finding maximum and 'sufficient minimum of nucleus thikness function.
828 * xm, fm are outputs.
829 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
830 IMPLICIT INTEGER(I-N)
831 INTEGER PYK,PYCHGE,PYCOMP
833 common /parimp/ b1, psib1, rb1, rb2
834 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
836 rm1=dsqrt(abs(RA*RA-b1*b1/4.d0*(dsin(psib1)**2)))+
837 > b1*dcos(psib1)/2.d0
838 rm2=dsqrt(abs(RA*RA-b1*b1/4.d0*(dsin(psib1)**2)))-
839 > b1*dcos(psib1)/2.d0
852 ****************************** END PLSEAR **************************
854 ******************************** RADSEAR ***************************
855 SUBROUTINE RADSEAR (fmax,xmin)
856 * find maximum and 'sufficient minimum of radiative energy loss distribution
857 * xm, fm are outputs.
858 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
859 IMPLICIT INTEGER(I-N)
860 INTEGER PYK,PYCHGE,PYCOMP
862 common /radcal/ aa, bb
867 x=aa+xmin*(j-1)/999.d0
876 ****************************** END RADSEAR **************************
878 ********************************* BIPSEAR ***************************
879 SUBROUTINE BIPSEAR (fmax,xmin)
880 * find maximum and 'sufficient minimum' of jet production cross section
881 * as a function of impact paramater (xm, fm are outputs)
882 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
883 IMPLICIT INTEGER(I-N)
884 INTEGER PYK,PYCHGE,PYCOMP
886 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
900 ****************************** END RADSEAR **************************
902 **************************** SIMPA **********************************
903 SUBROUTINE SIMPA (A1,B1,H1,REPS1,AEPS1,FUNCT,X,
905 * calculate intergal of function FUNCT(X) on the interval from A1 to B1
906 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
907 IMPLICIT INTEGER(I-N)
909 H=dSIGN ( H1, B1-A1 )
929 IF( (X0+4.d0*H-B)*S)5,5,6
941 23 IF(F(K)-10.d16)10,11,10
942 11 F(K)=FUNCT(X)/3.d0
944 9 DI3=DI3+P(K)*ABS(F(K))
945 DI1=(F(1)+4.*F(3)+F(5))*2.d0*H
949 13 IF (AEPS) 12,14,12
950 12 EPS=ABS((AIABS+DI3)*REPS)
953 16 DELTA=ABS(DI2-DI1)
954 IF(DELTA-EPS)20,21,21
955 20 IF(DELTA-EPS/8.d0)17,14,14
970 18 DI1=DI2+(DI2-DI1)/15.d0
988 ************************* END SIMPA *******************************
990 ************************* PARINV **********************************
991 SUBROUTINE PARINV(X,A,F,N,R)
992 * gives interpolation of function F(X) with arrays A(N) and F(N)
993 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
994 IMPLICIT INTEGER(I-N)
996 IF(X.LT.A(1))GO TO 11
1016 R=B4*((X-B2)*(X-B3))/((B1-B2)*(B1-B3))+B5*((X-B1)*(X-B3))/
1017 1 ((B2-B1)*(B2-B3))+B6*((X-B1)*(X-B2))/((B3-B1)*(B3-B2))
1019 6 IF(K2.NE.N)GO TO 3
1023 IF(C.LT.0.1d-7) GO TO 5
1027 C41 FORMAT(25H X IS OUT OF THE INTERVAL,3H X=,F15.9)
1032 IF(C.LT.0.1d-7) GO TO 12
1038 C************************** END PARINV *************************************
1040 * function to calculate quark-quark scattering differential cross section
1041 double precision FUNCTION PLSIGH(Z)
1042 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1043 IMPLICIT INTEGER(I-N)
1044 INTEGER PYK,PYCHGE,PYCOMP
1045 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1047 beta=(33.d0-2.d0*nf)/(12.d0*pi)
1048 alfs=1.d0/(beta*dlog(max(1.d-10,z/(TC*TC))))
1049 PLSIGH=8.d0*pi*alfs*alfs/(9.d0*z*z)
1053 * function to calculate differential radiated gluon spectrum in BDMS model
1054 double precision FUNCTION PLFUN1(or)
1055 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1056 IMPLICIT INTEGER(I-N)
1057 INTEGER PYK,PYCHGE,PYCOMP
1058 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1059 common /pljdat/ ej, z, ygl, alfs, um, epa
1060 common /pleave/ taul, temlev
1061 common /factor/ cfac, kf
1063 x=min((1.d0-ygl*z/or),or/ej)
1064 if(x.le.0.d0) x=0.d0
1065 if(x.ge.1.d0) x=0.9999d0
1067 if(x.ge.0.5d0) x=1.-x
1068 spinf=0.5*(1.+(1.d0-x)**4+x**4)/(1.d0-x)
1070 spinf=1.d0-x+0.5d0*x*x
1072 ak=ygl*z/(or*(1.d0-x))
1074 uu=0.5d0*al*dsqrt(abs(0.5d0*(1.d0-x+cfac*x*x)*ak*
1075 > dlog(max(16.d0/ak,1.d-10))))/ygl
1076 * if quark production outside the QGP then
1077 * arg=(((dsin(uu)*cosh(uu))**2)+((dcos(uu)*sinh(uu))**2))/(2.d0*uu*uu);
1078 * here quark production inside the QGP
1079 arg=((dcos(uu)*cosh(uu))**2)+((dsin(uu)*sinh(uu))**2)
1080 gl1=(ygl/(cfac*z))**0.3333333d0
1081 gl2=(um/epa)**1.333333d0
1082 dc=1.d0/((1.d0+((gl1*gl2*or)**1.5d0))**2) ! massive parton
1083 c dc=1.d0 !massless parton
1084 plfun1=dc*3.d0*alfs*ygl*dlog(max(arg,1.d-20))*spinf/(pi*al*or)
1088 * function to calculate time-dependence of QGP viscosity (if mvisc=1,2)
1089 double precision FUNCTION PLVISC(X)
1090 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1091 IMPLICIT INTEGER(I-N)
1092 INTEGER PYK,PYCHGE,PYCOMP
1093 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1100 elseif(mvisc.eq.1) then
1101 a=3.4d0*(1.d0+0.12d0*(2.d0*nf+1.d0))
1102 b=15.d0*(1.d0+0.06d0*nf)
1103 c=4.d0*pi*pi*(10.5d0*nf/a+16.d0/b)/675.d0
1105 c=(1.7d0*nf+1.d0)*0.342d0/(1.d0+nf/6.d0)
1108 alf=6.d0*pi/((33.d0-2.d0*nf)*dlog(max(bub,1.d-10)))
1110 PLVISC=c*(T**3)/(alf*alf*dlog(max(1.d-10,alf1)))
1114 * function to calculate time-dependence of QGP number density
1115 double precision FUNCTION PLN(X)
1116 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1117 IMPLICIT INTEGER(I-N)
1118 INTEGER PYK,PYCHGE,PYCOMP
1119 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1120 common /plpar2/ pln0,taupl,tauh,sigpl,sigh,sigplh,sigqqh,rg,rgn
1121 common /plevol/ taup(5000),temp(5000),denp(5000),enep(5000)
1123 pi2=3.14159d0*3.14159d0
1126 call parinv(t,taup,denp,5000,res)
1128 res=1.2d0*(16.d0+9.d0*nf)*((5.06d0*TC)**3)/pi2
1134 * function to calculate time-dependence of QGP temperature
1135 double precision FUNCTION PLT(X)
1136 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1137 IMPLICIT INTEGER(I-N)
1138 INTEGER PYK,PYCHGE,PYCOMP
1139 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1140 common /plpar2/ pln0,taupl,tauh,sigpl,sigh,sigplh,sigqqh,rg,rgn
1141 common /plevol/ taup(5000),temp(5000),denp(5000),enep(5000)
1145 call parinv(t,taup,temp,5000,res)
1153 * function to caculate time-dependence of parton-plasma integral cross section
1154 double precision FUNCTION PLS(X)
1155 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1156 IMPLICIT INTEGER(I-N)
1157 INTEGER PYK,PYCHGE,PYCOMP
1159 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1160 common /plpar2/ pln0,taupl,tauh,sigpl,sigh,sigplh,sigqqh,rg,rgn
1161 common /plen/ epartc, um
1165 alf=6.d0*pi/((33.d0-2.d0*nf)*dlog(max(bub,1.d-10)))
1166 ZZ0=4.d0*t*t*pi*alf*(1.d0+nf/6.d0)
1167 scm=4.d0*t*epartc+um*um+4.d0*t*t
1168 ZZ1=max((scm-((um+2.d0*t)**2))*(scm-((um-2.d0*t)**2))/scm,ZZ0)
1172 CALL SIMPA(ZZ0,ZZ1,HH1,REPS,AEPS,plsigh,ZZ,RESS,AIH,AIABS)
1173 PLS=0.39d0*2.25d0*2.25d0*RESS*(16.d0+4.d0*nf)/(16.d0+9.d0*nf)
1177 * function to calculate nuclear thikness function
1178 double precision FUNCTION PLTHIK(X)
1179 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1180 IMPLICIT INTEGER(I-N)
1181 INTEGER PYK,PYCHGE,PYCOMP
1182 common /parimp/ b1, psib1, rb1, rb2
1183 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1185 r12=bu*bu+b1*b1/4.d0+bu*b1*dcos(psib1)
1186 r22=bu*bu+b1*b1/4.d0-bu*b1*dcos(psib1)
1187 PLTHIK=dsqrt(abs((RA*RA-r12)*(RA*RA-r22)))*bu
1191 * function to calculate angular distribution of emitted gluons
1192 double precision function gluang(x)
1193 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1194 IMPLICIT INTEGER(I-N)
1196 gluang=x*dexp(-1.d0*(x-s)*(x-s)/(2.d0*s*s))
1200 * function to calculate jet production vs. centrality
1201 double precision function funbip(x)
1202 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1203 IMPLICIT INTEGER(I-N)
1204 INTEGER PYK,PYCHGE,PYCOMP
1205 common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
1206 dimension bip(15), bipr(15), pjet(15)
1207 data bip/0.d0,0.5d0,1.5d0,2.5d0,3.5d0,4.5d0,5.5d0,6.5d0,7.5d0,
1208 > 8.5d0,9.5d0,10.5d0,11.5d0,12.5d0,13.5d0/
1209 data pjet/200000.d0,217558.d0,625570.d0,949850.d0,1.17128d+06,
1210 > 1.30123d+06,1.32297d+06,1.18483d+06,1.02584d+06,839982.d0,
1211 > 621238.d0,399300.d0,227456.d0,113982.d0,41043.d0/
1214 bipr(i)=bip(i)*RA/6.8d0
1216 call parinv (bu,bipr,pjet,15,res)
1221 * function integrated at calculation of initial QGP temperature vs. centrality
1222 double precision function ftaa(x)
1223 IMPLICIT DOUBLE PRECISION(A-H, O-Z)
1224 IMPLICIT INTEGER(I-N)
1225 INTEGER PYK,PYCHGE,PYCOMP
1228 ftaa=(1.d0-br*x*x/a)*dlog(1.d0+x*x*(1.d0-br))/(a*a)
1231 **************************************************************************