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subroutine nbodydec(rm)
c
c Revision : 1.0
c
c input: rm: Resonance mass
c
c {\tt nbodydec} performs the decay of a resonance with mass rm in
c its local rest frame into nexit particles with 4-momenta and
c masses stored in the array pnew (see comment to SUB jdecay).
c The accessible many-body phase-space is homogenously populated,
c i.e. each configuration has equal probability. The theory behind
c this approach can be found in M.M. Block and J.D. Jackson, Z.
c Phys. C 3, 255 (1980). The original routine is contained in CPC
c (Code ACGJ). It has been modified for uQMD purposes.
c More documentation and better readability are to follow.
implicit none
integer j,i,imin1
include 'newpart.f'
real*8 rm
real*8 p4loc(0:3), p1loc(3), ploc(3)
real*8 M(mprt), MEFFloc(mprt), MASS
real*8 M1,F1,M11
real*8 z3, v2, ptot, costheta, z4, v1, reci1, z9, delx2, xi,
+ z10, pp1dot,ener1,p2, p1s, z5, sintheta, phii,psin,
+ p1sq, u, u1, ximin,ximax,delu,energy,pi,wmax,w,esys,z2,s,
+ z8,reci,b, delxi,a,delz,ranf
LOGICAL MASSLESS
integer ntry
p4loc(0) = rm
p4loc(1) = 0d0
p4loc(2) = 0d0
p4loc(3) = 0d0
wmax = 1d0
PI=4d0*ATAN(1d0)
C
M1=0d0 !Initialize M1=sum of all masses.
MASSLESS=.FALSE.
C Read masses.
DO I=1,nexit
m(i) = pnew(5,i)
M1=M1+M(I) ! M1= sum of all masses.
ENDDO
IF (M1.EQ.0.) THEN ! If massless.
MASSLESS=.TRUE.
WMAX=1d0
ENDIF
MEFFloc(1)=M(1) !Initialize Meff(1)
C Initialize ESYS.
ESYS=SQRT(p4loc(0)*p4loc(0)+p4loc(1)*p4loc(1)+
+ p4loc(2)*p4loc(2)+p4loc(3)*p4loc(3))
C
C Main Calculation
C
ntry=0
60 W=1d0 !Initial weight, for each new event.
ntry=ntry+1
MASS=M1 !Initial M=total mass of ALL particles.
ENERGY=p4loc(0) !Initialize E to E*=cms energy.
DO I=nexit-1,2,-1 !Loop over all N-2 effective masses needed.
U1=M(I+1)/ENERGY
U=U1**2
MASS=MASS-M(I+1)
C MASS=SUM of all rest masses of the REMAINING particles.
XIMIN=(MASS/ENERGY)**2 !This is Xi,minimum.
DELU=1d0-U1
XIMAX=DELU**2 !This is Xi,maximum,where
!XIMIN <= XI <= XIMAX.
DELXI=XIMAX-XIMIN ! DELXI=delta (XI)=XIMAX-XIMIN.
B=(1d0+U-XIMIN) ! Used in FAST event generator.
A=dble(I)*B ! A=commonly used factor.
IMIN1=I-1 ! IMIN1=commonly used factor.
DELZ=(A-dble(IMIN1)*DELXI)*DELXI**IMIN1 ! DELZ=Zmax-Zmin
C
C Here, we introduce the FAST generators.
C
RECI=1d0/dble(I)
S=1d0/(dble(I)-dble(IMIN1)*DELXI/B) ! The probability
! for the distribution i*(i-1)*y**(i-2)*(1-y).
100 Z2=ranf(0)
IF (Z2.LT.S) THEN ! The distribution i*(i-1)*y**(i-2)*(1-y).
Z8=ranf(0)
Z9=ranf(0)
RECI1=1d0/dble(IMIN1)
DELX2=DELXI*Z8**RECI*Z9**RECI1
ELSE
Z10=ranf(0)
DELX2=DELXI*Z10**RECI ! The probability distribution
! i*y**(i-1)
ENDIF
IF (DELX2.EQ.0.) GOTO 100 ! Guards against division by 0.
ctp060202 110 XI=XIMIN+DELX2 ! XI=XImin+deltaXI.
XI=XIMIN+DELX2 ! XI=XImin+deltaXI.
! We reweight (multiply) W by
! DELZ*F1*[(XI/(XI-XIMIN))**(I-2)]/(1+U-XI) .
W=W*DELZ*F1(U,XI)*((XI/DELX2)**(I-2))/(1d0+U-XI)
MEFFloc(I)=ENERGY*SQRT(XI) ! Store effective mass I, and
! update E for next effective mass.
ENERGY=MEFFloc(I)
ENDDO
V1=(M(1)/ENERGY)**2 ! Set up final weight, with particles 1 and 2.
V2=(M(2)/ENERGY)**2
W=W*F1(V1,V2) ! We now have the FINAL weight.
!We find WMAX, the max weight, here.
c IF (W.GT.WMAX) WMAX=W ! Update WMAX.
! This routine selects W=1 (unweighted events).
Z3=ranf(0)
IF (W.LT.WMAX*Z3.and.ntry.le.1000) THEN
GOTO 60
ENDIF
! We have accepted event, so see if we Lorentz transform it.
M11=p4loc(0)
p1loc(1)=p4loc(1)
p1loc(2)=p4loc(2)
p1loc(3)=p4loc(3)
!Iterate over all blob masses, MEFF(I), where MEFF(1)=M(1),MEFF(N)=E*.
DO 2500 I=nexit,2,-1
ENERGY=.5d0*(M11+(M(I)**2-MEFFloc(I-1)**2)/M11)
PTOT=SQRT(ENERGY**2-M(I)**2)
!Find RANDOM cos(theta*)=COSTHETA, random PHI*=PHI
! SINTHETA=SIN(THETHA*)
Z4=ranf(0)
COSTHETA=2d0*Z4-1d0 ! -PI <= THETA* <= PI
SINTHETA=SQRT(1d0-COSTHETA**2)
Z5=ranf(0)
PHII=2d0*PI*Z5 ! 0 <= PHI* <= 2*PI, random PHII
PSIN=PTOT*SINTHETA !Commonly used combination.
! Calculate momentum compon. of particle I, ploc(k), k=1 to 3.
ploc(1)=PSIN*COS(PHII) ! x-component.
ploc(2)=PSIN*SIN(PHII) !y-component.
ploc(3)=PTOT*COSTHETA ! z-component.
P1SQ=p1loc(1)**2+p1loc(2)**2+p1loc(3)**2
P1S=SQRT(P1SQ)
ENER1=SQRT(P1SQ+M11**2)
! Calculate Plab(i) =
!P*(i) + betagamma(i)*
! [Energy + betagamma(j).ploc(j)/(gamma+1)],
!where . means DOT product, i,j=x,y,z.
PP1DOT=ploc(1)*p1loc(1)+ploc(2)*p1loc(2)+ploc(3)*p1loc(3) ! DOT product.
A=(ENERGY+PP1DOT/M11/(1d0+ENER1/M11))/M11
! Plab=P1 for particle I;store in matrix OUT(K,I,3), update
! new M11 and new p1loc()=ploc()-p1loc().
P2=0d0
DO J=1,3
ploc(J)=ploc(J)+A*p1loc(J) !Store new ploc().
P2=P2+ploc(J)*ploc(J) !Get square of ploc() vector.
p1loc(J)=p1loc(J)-ploc(J) !Update p1loc()
ENDDO
ENERGY=SQRT(P2+M(I)**2) !Store new ENERGY.
M11=MEFFloc(I-1) ! Update M11.
c WRITE (5,2600) M(I),ENERGY,ploc(1),ploc(2),ploc(3)
pnew(5,i) = m(i)
pnew(4,i) = sqrt(m(i)**2+ploc(1)**2+ploc(2)**2+ploc(3)**2)
pnew(1,i) = ploc(1)
pnew(2,i) = ploc(2)
pnew(3,i) = ploc(3)
2500 ENDDO
c2600 FORMAT(0P,F7.4,2X,G13.7,5X,G13.7,3X,G13.7,3X,G13.7)
P2=0d0 ! Do LAST particle here.
DO J=1,3
ploc(J)=p1loc(J) ! Store last ploc().
P2=P2+ploc(J)*ploc(J)
ENDDO
ENERGY=SQRT(P2+M(1)**2) ! Store last ENERGY.
c WRITE (5,2600) M(1),ENERGY,ploc(1),ploc(2),ploc(3)
c WRITE (5,*)
pnew(5,1) = m(1)
pnew(4,1) = sqrt(m(1)**2+ploc(1)**2+ploc(2)**2+ploc(3)**2)
pnew(1,1) = ploc(1)
pnew(2,1) = ploc(2)
pnew(3,1) = ploc(3)
RETURN
END
!-------------------------------------------------------------------------
FUNCTION F1(V1,V2)
! Function F1(V1,V2)=SQR(1+(V1-V2)**2-2*(V1+V2))=2*(P*)/(E*).
implicit none
REAL*8 F1, F2, V1, V2
F2=1d0+(V1-V2)**2-2d0*(V1+V2)
IF (F2.LE.0d0) THEN
F1=0d0
ELSE
F1=SQRT(F2) ! Guard against sqr(-).
ENDIF
END
function M_inv_2(v01,vx1,vy1,vz1,
+ v02,vx2,vy2,vz2)
real*8 M_inv_2,v01,vx1,vy1,vz1,
+ v02,vx2,vy2,vz2
M_inv_2 = sqrt((v01+v02)**2
+ -(vx1+vx2)**2
+ -(vy1+vy2)**2
+ -(vz1+vz2)**2)
return
end
function M_inv_3(v01,vx1,vy1,vz1,
+ v02,vx2,vy2,vz2,
+ v03,vx3,vy3,vz3)
real*8 M_inv_3,v01,vx1,vy1,vz1,
+ v02,vx2,vy2,vz2,
+ v03,vx3,vy3,vz3
M_inv_3 = sqrt((v01+v02+v03)**2
+ -(vx1+vx2+vx3)**2
+ -(vy1+vy2+vy3)**2
+ -(vz1+vz2+vz3)**2)
return
end
subroutine jdecay(rm)
C input px,py,pz : CM-momenta of total system
C rm: Mass of resonance (sqrt(s))
c for pnew and pgen :
c first index: 1=px, 2=py, 3=pz, 4=E, 5=m0
c second index: particle number
implicit none
include 'newpart.f'
real*8 pgen(5,mprt),rnd(mprt),u(3),beta(3),wt,tmp
real*8 wtmax,rm,sum,pi,sum1,sum2,pcms,ranf,gamma,bp,phi,qcm,r1234
parameter(pi=3.141592654)
integer n,nadd1,i,j,ii,k
c
pgen(1,1)=0d0
pgen(2,1)=0d0
pgen(3,1)=0d0
pgen(5,1)=rm
pgen(4,1)=rm
c
nadd1=nexit-1
c
pgen(5,nexit)=pnew(5,nexit)
c Two body decay
c ---------------
if(nexit.eq.2) goto 400
sum=0d0
c sum: sum of masses in the outgoing channel
do 20 n=1,nexit
sum=sum+pnew(5,n)
20 continue
c calculate maximum phase-space weight wtmax
c ------------------------------------
wtmax=0.5d0
sum1=pgen(5,1)
sum2=sum-pnew(5,1)
do 200 i=1,nadd1
wtmax=wtmax*pcms(sum1,sum2,pnew(5,i))
sum1=sum1-pnew(5,i)
sum2=sum2-pnew(5,i+1)
200 continue
c generate uniform nexit-body phase space
c --------------------------------------
300 continue
c first generate nexit random numbers with decreasing value
c as excess energy distribution weights
rnd(1)=ranf(1)
do 110 i=2,nexit
rnd(i)=ranf(1)
do 120 j=i,2,-1
if(rnd(j).gt.rnd(j-1)) then
tmp=rnd(j-1)
rnd(j-1)=rnd(j)
rnd(j)=tmp
endif
120 continue
110 continue
c last weight has to be zero
rnd(nexit)=0d0
c now ?
wt=1d0
sum1=sum
do 330 i=2,nexit
sum1=sum1-pnew(5,i-1)
pgen(5,i)=sum1+rnd(i)*(pgen(5,1)-sum)
if(pgen(5,1)-sum.lt.0.0) write(6,*)'glrrrrrp'
wt=wt*pcms(pgen(5,i-1),pgen(5,i),pnew(5,i-1))
330 continue
r1234=ranf(1)
if(wt.lt.r1234*wtmax) goto 300
c carry out two-body decays in pgen frames
c ----------------------------------------
400 continue
do 410 i=1,nadd1
qcm=pcms(pgen(5,i),pgen(5,i+1),pnew(5,i))
c u(3) is cos(theta)
u(3)=2d0*ranf(1)-1d0
phi=2d0*pi*ranf(1)
u(1)=sqrt(1d0-u(3)**2)*cos(phi)
u(2)=sqrt(1d0-u(3)**2)*sin(phi)
do 420 j=1,3
pnew(j,i)=qcm*u(j)
pgen(j,i+1)=-pnew(j,i)
420 continue
pnew(4,i)=sqrt(qcm**2+pnew(5,i)**2)
pgen(4,i+1)=sqrt(qcm**2+pgen(5,i+1)**2)
410 continue
do 430 j=1,4
pnew(j,nexit)=pgen(j,nexit)
430 continue
c boost pgen frames to lab frame
c -------------------------------------------------
do 500 ii=1,nadd1
i=nexit-ii
do 510 j=1,3
beta(j)=pgen(j,i)/pgen(4,i)
510 continue
gamma=pgen(4,i)/pgen(5,i)
do 520 k=i,nexit
bp=beta(1)*pnew(1,k)+beta(2)*pnew(2,k)+beta(3)*pnew(3,k)
do 530 j=1,3
pnew(j,k)=pnew(j,k)+gamma*beta(j)*(pnew(4,k)
& +bp*gamma/(gamma+1d0))
530 continue
pnew(4,k)=gamma*(pnew(4,k)+bp)
520 continue
500 continue
return
end