PYTHIA/pythia/pyi3au.F

   1
   2 C***********************************************************************
   3
   4       SUBROUTINE PYI3AU(EPS,RAT,Y3RE,Y3IM)
   5
   6 C...Calculates real and imaginary parts of the auxiliary function I3;
   7 C...see R. K. Ellis, I. Hinchliffe, M. Soldate and J. J. van der Bij,
   8 C...Nucl. Phys. B297 (1988) 221.
   9       COMMON/LUDAT1/MSTU(200),PARU(200),MSTJ(200),PARJ(200)
  10       SAVE /LUDAT1/
  11
  12       BE=0.5*(1.+SQRT(1.+RAT*EPS))
  13       IF(EPS.LT.1.) GA=0.5*(1.+SQRT(1.-EPS))
  14
  15       IF(EPS.LT.0.) THEN
  16         IF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN
  17           F3RE=PYSPEN(-0.25*EPS/(1.+0.25*(RAT-1.)*EPS),0.,1)-
  18      &    PYSPEN((1.-0.25*EPS)/(1.+0.25*(RAT-1.)*EPS),0.,1)+
  19      &    PYSPEN(0.25*(RAT+1.)*EPS/(1.+0.25*RAT*EPS),0.,1)-
  20      &    PYSPEN((RAT+1.)/RAT,0.,1)+0.5*(LOG(1.+0.25*RAT*EPS)**2-
  21      &    LOG(0.25*RAT*EPS)**2)+LOG(1.-0.25*EPS)*
  22      &    LOG((1.+0.25*(RAT-1.)*EPS)/(1.+0.25*RAT*EPS))+
  23      &    LOG(-0.25*EPS)*LOG(0.25*RAT*EPS/(1.+0.25*(RAT-1.)*EPS))
  24         ELSEIF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).GE.1.E-4) THEN
  25           F3RE=PYSPEN(-0.25*EPS/(BE-0.25*EPS),0.,1)-
  26      &    PYSPEN((1.-0.25*EPS)/(BE-0.25*EPS),0.,1)+
  27      &    PYSPEN((BE-1.+0.25*EPS)/BE,0.,1)-
  28      &    PYSPEN((BE-1.+0.25*EPS)/(BE-1.),0.,1)+
  29      &    0.5*(LOG(BE)**2-LOG(BE-1.)**2)+
  30      &    LOG(1.-0.25*EPS)*LOG((BE-0.25*EPS)/BE)+
  31      &    LOG(-0.25*EPS)*LOG((BE-1.)/(BE-0.25*EPS))
  32         ELSEIF(ABS(EPS).GE.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN
  33           F3RE=PYSPEN((GA-1.)/(GA+0.25*RAT*EPS),0.,1)-
  34      &    PYSPEN(GA/(GA+0.25*RAT*EPS),0.,1)+
  35      &    PYSPEN((1.+0.25*RAT*EPS-GA)/(1.+0.25*RAT*EPS),0.,1)-
  36      &    PYSPEN((1.+0.25*RAT*EPS-GA)/(0.25*RAT*EPS),0.,1)+
  37      &    0.5*(LOG(1.+0.25*RAT*EPS)**2-LOG(0.25*RAT*EPS)**2)+
  38      &    LOG(GA)*LOG((GA+0.25*RAT*EPS)/(1.+0.25*RAT*EPS))+
  39      &    LOG(GA-1.)*LOG(0.25*RAT*EPS/(GA+0.25*RAT*EPS))
  40         ELSE
  41           F3RE=PYSPEN((GA-1.)/(GA+BE-1.),0.,1)-
  42      &    PYSPEN(GA/(GA+BE-1.),0.,1)+PYSPEN((BE-GA)/BE,0.,1)-
  43      &    PYSPEN((BE-GA)/(BE-1.),0.,1)+0.5*(LOG(BE)**2-LOG(BE-1.)**2)+
  44      &    LOG(GA)*LOG((GA+BE-1.)/BE)+LOG(GA-1.)*LOG((BE-1.)/(GA+BE-1.))
  45         ENDIF
  46         F3IM=0.
  47       ELSEIF(EPS.LT.1.) THEN
  48         IF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN
  49           F3RE=PYSPEN(-0.25*EPS/(1.+0.25*(RAT-1.)*EPS),0.,1)-
  50      &    PYSPEN((1.-0.25*EPS)/(1.+0.25*(RAT-1.)*EPS),0.,1)+
  51      &    PYSPEN((1.-0.25*EPS)/(-0.25*(RAT+1.)*EPS),0.,1)-
  52      &    PYSPEN(1./(RAT+1.),0.,1)+LOG((1.-0.25*EPS)/(0.25*EPS))*
  53      &    LOG((1.+0.25*(RAT-1.)*EPS)/(0.25*(RAT+1.)*EPS))
  54           F3IM=-PARU(1)*LOG((1.+0.25*(RAT-1.)*EPS)/(0.25*(RAT+1.)*EPS))
  55         ELSEIF(ABS(EPS).LT.1.E-4.AND.ABS(RAT*EPS).GE.1.E-4) THEN
  56           F3RE=PYSPEN(-0.25*EPS/(BE-0.25*EPS),0.,1)-
  57      &    PYSPEN((1.-0.25*EPS)/(BE-0.25*EPS),0.,1)+
  58      &    PYSPEN((1.-0.25*EPS)/(1.-0.25*EPS-BE),0.,1)-
  59      &    PYSPEN(-0.25*EPS/(1.-0.25*EPS-BE),0.,1)+
  60      &    LOG((1.-0.25*EPS)/(0.25*EPS))*
  61      &    LOG((BE-0.25*EPS)/(BE-1.+0.25*EPS))
  62           F3IM=-PARU(1)*LOG((BE-0.25*EPS)/(BE-1.+0.25*EPS))
  63         ELSEIF(ABS(EPS).GE.1.E-4.AND.ABS(RAT*EPS).LT.1.E-4) THEN
  64           F3RE=PYSPEN((GA-1.)/(GA+0.25*RAT*EPS),0.,1)-
  65      &    PYSPEN(GA/(GA+0.25*RAT*EPS),0.,1)+
  66      &    PYSPEN(GA/(GA-1.-0.25*RAT*EPS),0.,1)-
  67      &    PYSPEN((GA-1.)/(GA-1.-0.25*RAT*EPS),0.,1)+
  68      &    LOG(GA/(1.-GA))*LOG((GA+0.25*RAT*EPS)/(1.+0.25*RAT*EPS-GA))
  69           F3IM=-PARU(1)*LOG((GA+0.25*RAT*EPS)/(1.+0.25*RAT*EPS-GA))
  70         ELSE
  71           F3RE=PYSPEN((GA-1.)/(GA+BE-1.),0.,1)-
  72      &    PYSPEN(GA/(GA+BE-1.),0.,1)+PYSPEN(GA/(GA-BE),0.,1)-
  73      &    PYSPEN((GA-1.)/(GA-BE),0.,1)+LOG(GA/(1.-GA))*
  74      &    LOG((GA+BE-1.)/(BE-GA))
  75           F3IM=-PARU(1)*LOG((GA+BE-1.)/(BE-GA))
  76          ENDIF
  77       ELSE
  78         RSQ=EPS/(EPS-1.+(2.*BE-1.)**2)
  79         RCTHE=RSQ*(1.-2.*BE/EPS)
  80         RSTHE=SQRT(MAX(0.,RSQ-RCTHE**2))
  81         RCPHI=RSQ*(1.+2.*(BE-1.)/EPS)
  82         RSPHI=SQRT(MAX(0.,RSQ-RCPHI**2))
  83         R=SQRT(RSQ)
  84         THE=ACOS(MAX(-0.999999,MIN(0.999999,RCTHE/R)))
  85         PHI=ACOS(MAX(-0.999999,MIN(0.999999,RCPHI/R)))
  86         F3RE=PYSPEN(RCTHE,RSTHE,1)+PYSPEN(RCTHE,-RSTHE,1)-
  87      &  PYSPEN(RCPHI,RSPHI,1)-PYSPEN(RCPHI,-RSPHI,1)+
  88      &  (PHI-THE)*(PHI+THE-PARU(1))
  89         F3IM=PYSPEN(RCTHE,RSTHE,2)+PYSPEN(RCTHE,-RSTHE,2)-
  90      &  PYSPEN(RCPHI,RSPHI,2)-PYSPEN(RCPHI,-RSPHI,2)
  91       ENDIF
  92
  93       Y3RE=2./(2.*BE-1.)*F3RE
  94       Y3IM=2./(2.*BE-1.)*F3IM
  95
  96       RETURN
  97       END