PYTHIA6/pyquen.F

   1 *----------------------------------------------------------------------
   2 *
   3 *  Filename             : PYQUEN.F
   4 *
   5 *  First version created: 20-AUG-1997   Author : Igor Lokhtin
   6 *  Last revision        : 23-SEP-2004
   7 *
   8 *======================================================================
   9 *
  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)
  14 *
  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.
  17 *
  18 *
  19 *======================================================================
  20
  21       SUBROUTINE PYQUEN(A,ifb,bfix)
  22       IMPLICIT DOUBLE PRECISION(A-H, O-Z)
  23       IMPLICIT INTEGER(I-N)
  24       INTEGER PYK,PYCHGE,PYCOMP
  25       external pydata
  26       external pyp,pyr,pyk,pyjoin,pyshow
  27       external ftaa,funbip
  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
  35       common /bintaa/ br
  36       common /plfpar/ bgen
  37       save /pyjets/, /pydat1/, /pysubs/, /plglur/, /plquar/
  38       dimension ijoik(2),ijoin(1000),nis(500),nss(500),nas(500),nus(500)
  39
  40 * set initial event paramters
  41       AW=A                                 ! atomic weight
  42       RA=1.15d0*AW**0.333333d0             ! nucleus radius in fm
  43       RA2=2.d0*RA
  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)
  48 *
  49       pi=3.14159d0
  50
  51 * avoid stopping run if pythia does not conserve energy due to collisional loss
  52       mstu(21)=1
  53
  54 * generate impact parameter of A-A collision with jet production
  55       if(ifb.eq.0) then
  56        if(bfix.lt.0.d0) then
  57         write(6,*) 'Impact parameter less than zero!'
  58         bfix=0.d0
  59        end if
  60        if (bfix.gt.RA2) then
  61         write(6,*) 'Impact parameter larger than two nuclear radius!'
  62         bfix=RA2
  63        end if
  64        b1=bfix
  65       else
  66        call bipsear(fmax1,xmin1)
  67        fmax=fmax1
  68        xmin=xmin1
  69  11    bb1=xmin*pyr(0)
  70        ff1=fmax*pyr(0)
  71        fb=funbip(bb1)
  72        if(ff1.gt.fb) goto 11
  73        b1=bb1
  74       end if
  75       bgen=b1
  76
  77 * calculate initial QGP temperature as function of centrality
  78       sb0=pi*RA*RA
  79       sb=RA*RA*(pi-2.d0*dasin(0.5d0*b1/RA))-b1*dsqrt(abs(RA*RA-
  80      >   b1*b1/4.d0))
  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,
  84      >           aih,aiabs)
  85       rtaa=rtaa0*(1.d0-br*(1.d0+(1.d0-0.25d0*br)*dlog(1.d0/br)+
  86      >     4.d0*rest/pi))
  87       T00=((rtaa*sb0)/(rtaa0*sb))**0.25d0
  88       T0=T00*(AW/207.d0)**0.166667d0
  89
  90 * generate single event with partonic energy loss
  91       ehard=ckin(3)
  92       if(b1.le.1.85d0*RA) then
  93        call plinit(ehard)
  94        call plevnt(ehard)
  95       end if
  96
  97 * reset all in-vacuum radiated guark 4-momenta and codes to zero
  98       do i=1,1000
  99        do j=1,5
 100         pqua(i,j)=0.d0
 101         kqua(i,j)=0
 102        end do
 103       end do
 104       nrq=0
 105
 106 * generate final state shower in vacuum if it was excluded before
 107       nrgm=nrg                        ! fix number of in-medium emitted gluons
 108       ip1=0
 109       ip2=0
 110       ip01=0
 111       ip02=0
 112       ip001=0
 113       ip002=0
 114       if(mstj(41).ne.0) goto 5
 115       mstj(41)=1
 116       nn=n
 117       do i=9,nn
 118        if(k(i,3).eq.7) then
 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
 122        end if
 123        if(k(i,3).eq.8) then
 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
 127        end if
 128       end do
 129
 130       n1=n
 131       call pyshow(ip1,0,qmax1)    ! vacuum showering for first hard parton
 132       if(n.eq.n1) ip1=0
 133       n2=n
 134       call pyshow(ip2,0,qmax2)    ! vacuum showering for second hard parton
 135       if(n.eq.n2) ip2=0
 136       if(n.eq.nn) goto 5
 137
 138 * find two leading partons after showering
 139       do i=nn+1,n
 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
 142       end do
 143       ptle1=0.d0
 144       ptle2=0.d0
 145       do i=nn+1,n
 146        if (k(i,1).eq.14) goto 3
 147        if(i.ge.ip002.and.ip002.gt.0) then
 148         ptl02=pyp(i,10)
 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
 152         end if
 153        elseif(ip001.gt.0) then
 154         ptl01=pyp(i,10)
 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
 158         end if
 159        end if
 160  3     continue
 161       end do
 162
 163 * replace two hard partons by two leading partons in original event record
 164       if(ip1.gt.0) then
 165        do j=1,5
 166         v(ip1,j)=v(ip01,j)
 167         p(ip1,j)=p(ip01,j)
 168        end do
 169        k(ip1,1)=kfh1
 170       end if
 171       if(ip2.gt.0) then
 172        do j=1,5
 173         v(ip2,j)=v(ip02,j)
 174         p(ip2,j)=p(ip02,j)
 175        end do
 176        k(ip2,1)=kfh2
 177       end if
 178
 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
 182       do i=nn+1,n
 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
 185         nrq=nrq+1
 186         do j=1,5
 187          kqua(nrq,j)=k(i,j)
 188          pqua(nrq,j)=p(i,j)
 189         end do
 190          kqua(nrq,1)=2
 191         goto 12
 192        end if
 193        if(i.ge.ip002.and.ip002.gt.0) then
 194         ish=ip2
 195        else
 196         ish=ip1
 197        end if
 198        nrg=nrg+1
 199        nur=nrg
 200  7     ishm=kglu(nur-1,6)
 201        if(ish.ge.ishm.or.nur.le.2) goto 6   ! adding gluons in 'plglur' arrays
 202        do j=1,6
 203         kglu(nur,j)=kglu(nur-1,j)
 204        end do
 205        do j=1,4
 206         glur(nur,j)=glur(nur-1,j)
 207        end do
 208        nur=nur-1
 209        goto 7
 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
 220  12    continue
 221        do j=1,5                              ! remove partons from event list
 222         v(i,j)=0.d0
 223         k(i,j)=0
 224         p(i,j)=0.d0
 225        end do
 226       end do
 227       n=nn
 228
 229  5    continue
 230
 231 * stop generate event if there are no additional gluons
 232       if(nrg.lt.1) goto 1
 233
 234 * define number of stirngs (ns) and number of entries in strings before
 235 * in-medium radiation (nis(ns))
 236       ns=0
 237       nes=0
 238       i0=0
 239       i1=0
 240       do i=1,500
 241        nis(i)=0
 242        nas(i)=0
 243        nss(i)=0
 244        nus(i)=0
 245       end do
 246       do i=9,n
 247        ks=k(i,1)
 248        ksp=k(i-1,1)
 249        if(ks.eq.2) then
 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
 254         nss(ns+1)=nes
 255         ns=ns+1
 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
 258        end if
 259       end do
 260       i0=n-nes-i1             ! first i0 lines not included in strings
 261       do i=1,ns
 262        nss(i)=nss(i)+i0
 263       end do
 264
 265 * move fragmented particles in bottom of event list
 266       i=i0+1
 267  2    ks=k(i,1)
 268       ksp=k(i-1,1)
 269       if(ks.ne.2.and.ksp.ne.2) then
 270        n=n+1
 271        do j=1,5
 272         v(n,j)=v(i,j)
 273         k(n,j)=k(i,j)
 274         p(n,j)=p(i,j)
 275        end do
 276        do in=i+1,n
 277         do j=1,5
 278          v(in-1,j)=v(in,j)
 279          k(in-1,j)=k(in,j)
 280          p(in-1,j)=p(in,j)
 281         end do
 282        end do
 283        do ip=1,nrg
 284         ku=kglu(ip,6)
 285         if(ku.gt.i) kglu(ip,6)=ku-1
 286        end do
 287        n=n-1
 288       else
 289        i=i+1
 290       end if
 291       if(i.le.n-i1) goto 2
 292
 293 * define number of additional entries in strings, nas(ns)
 294       do i=1,nrg
 295        kas=kglu(i,6)
 296        if(kas.le.nss(1)) then
 297         nas(1)=nas(1)+1
 298        else
 299         do j=2,ns
 300          if(kas.le.nss(j).and.kas.gt.nss(j-1))
 301      >   nas(j)=nas(j)+1
 302         end do
 303        end if
 304       end do
 305       do j=1,ns
 306        do i=1,j
 307         nus(j)=nus(j)+nas(i)
 308        end do
 309       end do
 310
 311 * add emitted gluons in event list
 312       nu=n
 313       n=n+nrg
 314       do i=nu,nu-i1,-1
 315        is=i+nrg
 316        do j=1,5
 317         v(is,j)=v(i,j)
 318         k(is,j)=k(i,j)
 319         p(is,j)=p(i,j)
 320        end do
 321       end do
 322       do ia=ns-1,1,-1
 323        do i=nss(ia+1)-1,nss(ia),-1
 324         is=i+nus(ia)
 325         do j=1,5
 326          v(is,j)=v(i,j)
 327          k(is,j)=k(i,j)
 328          p(is,j)=p(i,j)
 329         end do
 330        end do
 331       end do
 332
 333       do i=1,nrg
 334        if(i.le.nus(1)) then
 335        ia=nss(1)-1+i
 336        else
 337         do in=2,ns
 338          if(i.le.nus(in).and.i.gt.nus(in-1))
 339      >   ia=nss(in)-1+i
 340         end do
 341        end if
 342        eg=glur(i,1)
 343        ptg=glur(i,2)
 344        phig=glur(i,3)
 345        etag=glur(i,4)
 346        do j=1,5
 347         v(ia,j)=0.d0
 348         k(ia,j)=kglu(i,j)
 349        end do
 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)
 354        p(ia,4)=eg
 355        p(ia,5)=0.d0
 356       end do
 357
 358 * rearrange partons to form strings in event list
 359       do ij=1,1000
 360        ijoin(ij)=0
 361       end do
 362       do i=1,ns
 363        njoin=nis(i)+nas(i)
 364        if(i.eq.1) then
 365         do j=1,njoin
 366          ijoin(j)=i0+j
 367         end do
 368        else
 369         do j=1,njoin
 370          ijoin(j)=nss(i-1)+nus(i-1)+j
 371         end do
 372        end if
 373        call pyjoin(njoin,ijoin)
 374       end do
 375
 376 * add in-vacuum emitted quark pairs
 377       if(nrq.lt.2) goto 1
 378       do i=1,nrq,2
 379        n=n+2
 380        do j=1,5
 381         v(n-1,j)=0.d0
 382         k(n-1,j)=kqua(i,j)
 383         p(n-1,j)=pqua(i,j)
 384        end do
 385        in=i+1
 386  4     ktest=k(n-1,2)+kqua(in,2)
 387        if(ktest.eq.0.or.in.eq.nrq) goto 8
 388        in=in+1
 389        goto 4
 390  8     do j=1,5
 391         v(n,j)=0.d0
 392         k(n,j)=kqua(in,j)
 393         p(n,j)=pqua(in,j)
 394        end do
 395        if(in.gt.i+1) then
 396         do j=1,5
 397          kqua(in,j)=kqua(i+1,j)
 398          pqua(in,j)=pqua(i+1,j)
 399         end do
 400        end if
 401       end do
 402
 403       do ij=1,2
 404        ijoik(ij)=0
 405       end do
 406       do i=1,nrq-1,2
 407        k(n+1-i,1)=1
 408        ijoik(1)=n-i
 409        ijoik(2)=n+1-i
 410        call pyjoin(2,ijoik)
 411       end do
 412
 413  1    continue
 414
 415       return
 416       end
 417
 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
 424       external plvisc
 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)
 428       save /plevol/
 429 *
 430       pi=3.14159d0
 431       pi2=pi*pi
 432
 433 * set number degrees of freedom in QGP
 434       hgd=3.d0
 435       rg=(16.d0+10.5d0*nf)/hgd
 436       rgn=(16.d0+9.d0*nf)/hgd
 437
 438 * set 'fiction' sigma for parton rescattering in QGP
 439       sigqq=4.2d0
 440       sigpl=2.25d0*2.25d0*sigqq*(16.d0+4.d0*nf)/(16.d0+9.d0*nf)
 441
 442 * set intial plasma temperature, density and energy density in perfect
 443 * (if mvisc=0) or viscous (mvisc=1,2) QGP with PLVISC subroitine
 444       hst=0.15d0
 445       if(mvisc.eq.2.and.T0.gt.0.6d0) hst=0.25d0
 446       T01=T0*5.06d0
 447       TC1=TC*5.06d0
 448       pln0=(16.d0+9.d0*nf)*1.2d0*(T01**3)/pi2
 449       ened0=pi2*(16.d0+10.5d0*nf)*(T01**4)/30.d0
 450       hh=hst*tau0
 451       tau=tau0                          ! proper time
 452       T=T01                             ! temperature
 453       den=pln0                          ! number density
 454       ened=ened0                        ! energy density
 455
 456 * create array of parameters to configurate QGP time evolution
 457       DO I=1,5000
 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
 463      >       *ened/tau)+ened
 464        T1=(30.d0*ened1/((16.d0+10.5d0*nf)*pi2))**0.25d0
 465        tau1=tau+0.5d0*hh
 466        ened=hh*(1.3333d0*plvisc(T1)/(tau1*tau1)-1.3333d0
 467      >      *ened1/tau1)+ened
 468        TPR=T
 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
 471        tau=tau+hh
 472        if(TPR.gt.TC1.and.T.le.TC1) taupl=tau-0.5d0*hh  ! QGP lifetime taupl
 473       END DO
 474       tauh=taupl*rg                                    ! mixed phase lifetime
 475
 476       return
 477       end
 478 ******************************** END PLINIT **************************
 479
 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
 488       external pyp,pyr,pyk
 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/
 501 *
 502       pi=3.14159d0
 503
 504 * find minimum of nuclear thikness function with subroutine plsear
 505       psib1=pi*(2.d0*pyr(0)-1.d0)
 506       call plsear (fmax1,xmin1)
 507       fmax=fmax1
 508       xmin=xmin1
 509
 510 * generate vertex of jet production
 511       iv=0
 512  1    rr1=xmin*pyr(0)
 513       ff1=fmax*pyr(0)
 514       f=plthik(rr1)
 515       iv=iv+1
 516       if(ff1.gt.f.and.iv.le.100000) goto 1
 517       r0=rr1
 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)))
 520       rb1=max(rb1,1.d-4)
 521       rb2=max(rb2,1.d-4)
 522
 523 * find maximum of angular spectrum of radiated gluons with subroutine gluang
 524       temin=0.5d0*pi
 525       temax=0.5d0*(1.d0+dsqrt(5.d0))*0.0863d0
 526       ftemax=gluang(temax)
 527
 528 * reset all radiated gluon 4-momenta and codes to zero -------------------
 529       do i=1,1000
 530        do j=1,4
 531         glur(i,j)=0.d0
 532         kglu(i,j)=0
 533        end do
 534        kglu(i,5)=0
 535        kglu(i,6)=0
 536       end do
 537       nrg=0
 538
 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
 544        irasf=0
 545        iraz=0
 546        ks=k(ip,1)                       ! parton status code
 547        kf=k(ip,2)                       ! parton identificator
 548        ka=abs(kf)
 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.
 554      >  or.ka.eq.8) then
 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)
 560         phir1=-1.d0*phir
 561         tetr1=-1.d0*tetr
 562
 563 * set colour factor
 564         if(kf.eq.21) then
 565          cfac=1.d0                      ! for gluon
 566         else
 567          cfac=0.44444444d0              ! for quark
 568         end if
 569
 570 * boost from laboratory system to system of hard parton
 571         ipar=ip
 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
 575         bet=dacos(bet0)
 576         if(psib1.lt.0.d0) bet=-1.d0*bet
 577         phip=phir-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)
 582
 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
 587         phin=dacos(aphin)
 588         if(psib1.le.0.d0) phin=-1.d0*phin
 589         phid=phip-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
 597
 598 * start parton rescattering in QGP with proper time iterations
 599         tau=tau0
 600  3      tfs=plt(tau)
 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
 604         tau=tau+xi*vel
 605         if(tau.ge.taul.or.tfs.le.TC) goto 100  ! escape if tau>taul or >taupl
 606
 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)
 612         ran=pyr(0)
 613         irasf=irasf+1
 614         if(irasf.gt.100000) goto 100
 615         if(ran.lt.prob) goto 3
 616         pltp=plt(tau)
 617         pltp3=3.d0*pltp
 618         pass=50.6d0/(pln(tau)*sigtr)
 619         elr=0.d0
 620         rsk=0.d0
 621         call pljetr(tau,pass,pltp,ipar,epart)
 622         irasf=0
 623
 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
 626         if(nrg.le.1000) then
 627          if(abs(elr).gt.0.1d0.and.ip.gt.8) then
 628           nrg=nrg+1
 629  6        te1=temin*pyr(0)
 630           fte1=ftemax*pyr(0)
 631           fte2=gluang(te1)
 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))
 644      >      /dcosh(yrr)
 645           ptgl=dsqrt(abs(pxgl*pxgl+pygl*pygl))
 646           psgl=dsqrt(abs(ptgl*ptgl+pzgl*pzgl))
 647           dpgl=pygl/pxgl
 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
 653            else
 654             glur(nrg,3)=glur(nrg,3)-pi
 655            end if
 656           end if
 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
 659 * set gluon codes
 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
 666          end if
 667         else
 668          write(6,*) 'Warning! Number of emitted gluons is too large!'
 669         end if
 670
 671 * set parton "thermalization" if pt<T
 672         if(abs(p(ip,3)).gt.pltp3) goto 3
 673  4      continue
 674         if(p(ip,3).ge.0.d0) then
 675          sigp=1.d0
 676         else
 677          sigp=-1.d0
 678         end if
 679  5      iraz=iraz+1
 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))
 685         probt=pp0/ep0
 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)
 694
 695 * boost to laboratory system
 696  100    call pyrobo(0,0,tetr,phir,0.d0,0.d0,0.d0)
 697        end if
 698        end if
 699        end if
 700  2    continue
 701
 702       return
 703       end
 704 ******************************* END PLEVNT *************************
 705
 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
 712       external plfun1, pls
 713       external pyp,pyr
 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
 722       save /pyjets/
 723 *
 724       pi=3.14159d0
 725       spi=dsqrt(pi)
 726       tauu=x                            ! redenote temerature tauu=x
 727       i=ip                              ! redenote parton number i=ip
 728       iter=0
 729       iraz=0
 730
 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)
 735       phir1=-1.d0*phir
 736       tetr1=-1.d0*tetr
 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
 745
 746       if(ppl.lt.3.d0) goto 222          ! no energy loss if pz<3 GeV/c
 747
 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
 751        iter=iter+1
 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
 755        bub=4.d0*tauu/TC
 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)))
 760        phmin2=z
 761        phmax2=max(phmin2,qm2)
 762        fqmax2=1.d0/(dlog(max(phmin2/(TC*TC),1.d-10)))**2
 763  12    rn1=pyr(0)
 764        tp=1.d0/(rn1/phmax2+(1.d0-rn1)/phmin2)
 765        ftp=1.d0/(dlog(max(tp/(TC*TC),1.d-10)))**2
 766        fprob=ftp/fqmax2
 767        rn2=pyr(0)
 768        if(fprob.lt.rn2) goto 12
 769        rsk=dsqrt(abs(tp))
 770        if(rsk.gt.ppl) rsk=ppl
 771
 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
 775        ej=ppl
 776        bb=ej                           ! maximum radiated energy
 777        bbi=max(dsqrt(abs(z)),1.000001d0*elp)
 778        aa=min(bb,bbi)                  ! minimum radiated energy
 779        hh=0.00001d0*(bb-aa)
 780        REPS=0.01d0
 781        AEPS=1.d-8
 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)
 785        ermax=ermax1
 786        eomin=eomin1
 787  11    resu=eomin*pyr(0)+aa
 788        fres=ermax*pyr(0)
 789        fres1=plfun1(resu)
 790        iraz=iraz+1
 791        if(fres.gt.fres1.and.iraz.lt.100000) goto 11
 792        elr=resu*resun                   ! energy of radiated gluon
 793
 794 * to chancel radiative energy loss (optional case)
 795 c       elr=0.d0
 796 * to chancel collisional energy loss (optional case)
 797 c       rsk=0.d0
 798
 799 * determine the direction of parton moving
 800        if(p(i,3).ge.0.d0) then
 801         sigp=1.d0
 802        else
 803         sigp=-1.d0
 804        end if
 805
 806 * calculate new 4-momentum of hard parton
 807        phirs=2.d0*pi*pyr(0)
 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)/
 811      >      (4.d0*ppl*ppl)))
 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
 816        p(i,4)=epan                           ! E
 817
 818 * boost to system of hard parton
 819  222   call pyrobo(0,0,tetr,phir,0.d0,0.d0,0.d0)
 820
 821       return
 822       end
 823 ******************************* END PLJETR **************************
 824
 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
 832        external plthik
 833        common /parimp/ b1, psib1, rb1, rb2
 834        common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
 835
 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
 840        xmin=min(rm1,rm2)
 841        fmax=0.d0
 842        do 10 j=1,1000
 843         x=xmin*(j-1)/999.d0
 844         f=plthik(x)
 845         if(f.gt.fmax) then
 846          fmax=f
 847         end if
 848   10   continue
 849
 850        return
 851        end
 852 ****************************** END PLSEAR **************************
 853
 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
 861       external plfun1
 862       common /radcal/ aa, bb
 863
 864       xmin=bb-aa
 865       fmax=0.d0
 866       do j=1,1000
 867        x=aa+xmin*(j-1)/999.d0
 868        f=plfun1(x)
 869        if(f.gt.fmax) then
 870         fmax=f
 871        end if
 872       end do
 873
 874       return
 875       end
 876 ****************************** END RADSEAR **************************
 877
 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
 885       external funbip
 886       common /plpar1/ tau0,T0,TC,sigqq,AW,RA,mvisc,nf
 887
 888       xmin=2.*RA
 889       fmax=0.d0
 890       do j=1,1000
 891        x=xmin*(j-1)/999.d0
 892        f=funbip(x)
 893        if(f.gt.fmax) then
 894         fmax=f
 895        end if
 896       end do
 897
 898       return
 899       end
 900 ****************************** END RADSEAR **************************
 901
 902 **************************** SIMPA **********************************
 903       SUBROUTINE SIMPA (A1,B1,H1,REPS1,AEPS1,FUNCT,X,
 904      1                     AI,AIH,AIABS)
 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)
 908       DIMENSION F(7), P(5)
 909       H=dSIGN ( H1, B1-A1 )
 910       S=dSIGN (1.d0, H )
 911       A=A1
 912       B=B1
 913       AI=0.0d0
 914       AIH=0.0d0
 915       AIABS=0.0d0
 916       P(2)=4.d0
 917       P(4)=4.d0
 918       P(3)=2.d0
 919       P(5)=1.d0
 920       IF(B-A)1,2,1
 921  1    REPS=ABS(REPS1)
 922       AEPS=ABS(AEPS1)
 923       DO 3 K=1,7
 924  3    F(K)=10.d16
 925       X=A
 926       C=0.d0
 927       F(1)=FUNCT(X)/3.d0
 928  4    X0=X
 929       IF( (X0+4.d0*H-B)*S)5,5,6
 930  6    H=(B-X0)/4.d0
 931       IF ( H ) 7,2,7
 932  7    DO 8 K=2,7
 933  8    F(K)=10.d16
 934       C=1.d0
 935  5    DI2=F (1)
 936       DI3=ABS( F(1) )
 937       DO 9 K=2,5
 938       X=X+H
 939       IF((X-B)*S)23,24,24
 940  24   X=B
 941  23   IF(F(K)-10.d16)10,11,10
 942  11   F(K)=FUNCT(X)/3.d0
 943  10   DI2=DI2+P(K)*F(K)
 944  9    DI3=DI3+P(K)*ABS(F(K))
 945       DI1=(F(1)+4.*F(3)+F(5))*2.d0*H
 946       DI2=DI2*H
 947       DI3=DI3*H
 948       IF (REPS) 12,13,12
 949  13   IF (AEPS) 12,14,12
 950  12   EPS=ABS((AIABS+DI3)*REPS)
 951       IF(EPS-AEPS)15,16,16
 952  15   EPS=AEPS
 953  16   DELTA=ABS(DI2-DI1)
 954       IF(DELTA-EPS)20,21,21
 955  20   IF(DELTA-EPS/8.d0)17,14,14
 956  17   H=2.d0*H
 957       F(1)=F(5)
 958       F(2)=F(6)
 959       F(3)=F(7)
 960       DO 19 K=4,7
 961  19   F(K)=10.d16
 962       GO TO 18
 963  14   F(1)=F(5)
 964       F(3)=F(6)
 965       F(5)=F(7)
 966       F(2)=10.d16
 967       F(4)=10.d16
 968       F(6)=10.d16
 969       F(7)=10.d16
 970  18   DI1=DI2+(DI2-DI1)/15.d0
 971       AI=AI+DI1
 972       AIH=AIH+DI2
 973       AIABS=AIABS+DI3
 974       GO TO 22
 975  21   H=H/2.d0
 976       F(7)=F(5)
 977       F(6)=F(4)
 978       F(5)=F(3)
 979       F(3)=F(2)
 980       F(2)=10.d16
 981       F(4)=10.d16
 982       X=X0
 983       C=0.
 984       GO TO 5
 985  22   IF(C)2,4,2
 986  2    RETURN
 987       END
 988 ************************* END SIMPA *******************************
 989
 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)
 995       DIMENSION A(N),F(N)
 996       IF(X.LT.A(1))GO TO 11
 997       IF(X.GT.A(N))GO TO 4
 998       K1=1
 999       K2=N
1000  2    K3=K2-K1
1001       IF(K3.LE.1)GO TO 6
1002       K3=K1+K3/2
1003       IF(A(K3)-X) 7,8,9
1004  7    K1=K3
1005       GOTO2
1006  9    K2=K3
1007       GOTO2
1008  8    P=F(K3)
1009       RETURN
1010  3    B1=A(K1)
1011       B2=A(K1+1)
1012       B3=A(K1+2)
1013       B4=F(K1)
1014       B5=F(K1+1)
1015       B6=F(K1+2)
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))
1018       RETURN
1019  6    IF(K2.NE.N)GO TO 3
1020       K1=N-2
1021       GOTO3
1022  4    C=ABS(X-A(N))
1023       IF(C.LT.0.1d-7) GO TO 5
1024       K1=N-2
1025  13   CONTINUE
1026 C13   PRINT 41,X
1027 C41   FORMAT(25H X IS OUT OF THE INTERVAL,3H X=,F15.9)
1028       GO TO 3
1029  5    R=F(N)
1030       RETURN
1031  11   C=ABS(X-A(1))
1032       IF(C.LT.0.1d-7) GO TO 12
1033       K1=1
1034       GOTO 13
1035  12   R=F(1)
1036       RETURN
1037       END
1038 C************************** END PARINV *************************************
1039
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
1046        pi=3.14159d0
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)
1050        return
1051        end
1052
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
1062       pi=3.14159d0
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
1066       if(kf.eq.21) then
1067        if(x.ge.0.5d0) x=1.-x
1068        spinf=0.5*(1.+(1.d0-x)**4+x**4)/(1.d0-x)
1069       else
1070        spinf=1.d0-x+0.5d0*x*x
1071       end if
1072       ak=ygl*z/(or*(1.d0-x))
1073       al=taul*5.06d0
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)
1085       return
1086       end
1087
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
1094       pi=3.14159d0
1095       T=X
1096       TC1=5.06d0*TC
1097       if(X.le.TC1) T=TC1
1098       if(mvisc.eq.0) then
1099        c=0.d0
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
1104       else
1105        c=(1.7d0*nf+1.d0)*0.342d0/(1.d0+nf/6.d0)
1106       end if
1107       bub=4.d0*T/TC1
1108       alf=6.d0*pi/((33.d0-2.d0*nf)*dlog(max(bub,1.d-10)))
1109       alf1=1.d0/alf
1110       PLVISC=c*(T**3)/(alf*alf*dlog(max(1.d-10,alf1)))
1111       return
1112       end
1113
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)
1122        save /plevol/
1123        pi2=3.14159d0*3.14159d0
1124        t=X
1125        if(t.lt.taupl) then
1126         call parinv(t,taup,denp,5000,res)
1127        else
1128         res=1.2d0*(16.d0+9.d0*nf)*((5.06d0*TC)**3)/pi2
1129        end if
1130        PLN=res
1131        return
1132        end
1133
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)
1142        save /plevol/
1143        t=X
1144        if(t.lt.taupl) then
1145         call parinv(t,taup,temp,5000,res)
1146        else
1147         res=TC
1148        end if
1149         PLT=res
1150        return
1151        end
1152
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
1158        external plsigh
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
1162        t=X
1163        pi=3.14159d0
1164        bub=4.d0*t/TC
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)
1169        HH1=0.01d0*ZZ1
1170        REPS=0.01d0
1171        AEPS=1.d-8
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)
1174        return
1175        end
1176
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
1184        bu=X
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
1188        return
1189        end
1190
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)
1195       s=0.0863d0
1196       gluang=x*dexp(-1.d0*(x-s)*(x-s)/(2.d0*s*s))
1197       return
1198       end
1199
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/
1212       bu=x
1213       do i=1,15
1214        bipr(i)=bip(i)*RA/6.8d0
1215       end do
1216       call parinv (bu,bipr,pjet,15,res)
1217       funbip=res
1218       return
1219       end
1220
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
1226       common/bintaa/ br
1227       a=1.d0+x*x
1228       ftaa=(1.d0-br*x*x/a)*dlog(1.d0+x*x*(1.d0-br))/(a*a)
1229       return
1230       end
1231 **************************************************************************