PYTHIA/pythia/pyspen.F

   1
   2 C***********************************************************************
   3
   4       FUNCTION PYSPEN(XREIN,XIMIN,IREIM)
   5
   6 C...Calculates real and imaginary part of Spence function; see
   7 C...G. 't Hooft and M. Veltman, Nucl. Phys. B153 (1979) 365.
   8       COMMON/LUDAT1/MSTU(200),PARU(200),MSTJ(200),PARJ(200)
   9       SAVE /LUDAT1/
  10       DIMENSION B(0:14)
  11
  12       DATA B/
  13      & 1.000000E+00,        -5.000000E-01,         1.666667E-01,
  14      & 0.000000E+00,        -3.333333E-02,         0.000000E+00,
  15      & 2.380952E-02,         0.000000E+00,        -3.333333E-02,
  16      & 0.000000E+00,         7.575757E-02,         0.000000E+00,
  17      &-2.531135E-01,         0.000000E+00,         1.166667E+00/
  18
  19       XRE=XREIN
  20       XIM=XIMIN
  21       IF(ABS(1.-XRE).LT.1.E-6.AND.ABS(XIM).LT.1.E-6) THEN
  22         IF(IREIM.EQ.1) PYSPEN=PARU(1)**2/6.
  23         IF(IREIM.EQ.2) PYSPEN=0.
  24         RETURN
  25       ENDIF
  26
  27       XMOD=SQRT(XRE**2+XIM**2)
  28       IF(XMOD.LT.1.E-6) THEN
  29         IF(IREIM.EQ.1) PYSPEN=0.
  30         IF(IREIM.EQ.2) PYSPEN=0.
  31         RETURN
  32       ENDIF
  33
  34       XARG=SIGN(ACOS(XRE/XMOD),XIM)
  35       SP0RE=0.
  36       SP0IM=0.
  37       SGN=1.
  38       IF(XMOD.GT.1.) THEN
  39         ALGXRE=LOG(XMOD)
  40         ALGXIM=XARG-SIGN(PARU(1),XARG)
  41         SP0RE=-PARU(1)**2/6.-(ALGXRE**2-ALGXIM**2)/2.
  42         SP0IM=-ALGXRE*ALGXIM
  43         SGN=-1.
  44         XMOD=1./XMOD
  45         XARG=-XARG
  46         XRE=XMOD*COS(XARG)
  47         XIM=XMOD*SIN(XARG)
  48       ENDIF
  49       IF(XRE.GT.0.5) THEN
  50         ALGXRE=LOG(XMOD)
  51         ALGXIM=XARG
  52         XRE=1.-XRE
  53         XIM=-XIM
  54         XMOD=SQRT(XRE**2+XIM**2)
  55         XARG=SIGN(ACOS(XRE/XMOD),XIM)
  56         ALGYRE=LOG(XMOD)
  57         ALGYIM=XARG
  58         SP0RE=SP0RE+SGN*(PARU(1)**2/6.-(ALGXRE*ALGYRE-ALGXIM*ALGYIM))
  59         SP0IM=SP0IM-SGN*(ALGXRE*ALGYIM+ALGXIM*ALGYRE)
  60         SGN=-SGN
  61       ENDIF
  62
  63       XRE=1.-XRE
  64       XIM=-XIM
  65       XMOD=SQRT(XRE**2+XIM**2)
  66       XARG=SIGN(ACOS(XRE/XMOD),XIM)
  67       ZRE=-LOG(XMOD)
  68       ZIM=-XARG
  69
  70       SPRE=0.
  71       SPIM=0.
  72       SAVERE=1.
  73       SAVEIM=0.
  74       DO 100 I=0,14
  75       IF(MAX(ABS(SAVERE),ABS(SAVEIM)).LT.1E-30) GOTO 110
  76       TERMRE=(SAVERE*ZRE-SAVEIM*ZIM)/FLOAT(I+1)
  77       TERMIM=(SAVERE*ZIM+SAVEIM*ZRE)/FLOAT(I+1)
  78       SAVERE=TERMRE
  79       SAVEIM=TERMIM
  80       SPRE=SPRE+B(I)*TERMRE
  81       SPIM=SPIM+B(I)*TERMIM
  82   100 CONTINUE
  83
  84   110 IF(IREIM.EQ.1) PYSPEN=SP0RE+SGN*SPRE
  85       IF(IREIM.EQ.2) PYSPEN=SP0IM+SGN*SPIM
  86
  87       RETURN
  88       END