pythiaeRHIC/pythia/pygfxx.f

0001
0002 C*********************************************************************
0003
0004 C...PYGFXX
0005 C...Auxiliary to PYRGHM.
0006
0007       SUBROUTINE PYGFXX(MA,TANB,MQ,MUR,MD,MTOP,AT,AB,XMU,XMGL,VH,
0008      *  STOP1,STOP2,SBOT1,SBOT2,DELTAMT,DELTAMB)
0009       IMPLICIT DOUBLE PRECISION(A-H,M,O-Z)
0010       DIMENSION VH(2,2),VH3T(2,2),VH3B(2,2),AL(2,2)
0011 C...Commonblocks.
0012       INTEGER MSTU,MSTJ,KCHG
0013       COMMON/PYDAT1/MSTU(200),PARU(200),MSTJ(200),PARJ(200)
0014       COMMON/PYDAT2/KCHG(500,4),PMAS(500,4),PARF(2000),VCKM(4,4)
0015       SAVE /PYDAT1/,/PYDAT2/
0016
0017       G(X,Y) = 2.D0 - (X+Y)/(X-Y)*DLOG(X/Y)
0018
0019       T(X,Y,Z) = (X**2*Y**2*LOG(X**2/Y**2) + X**2*Z**2*LOG(Z**2/X**2)
0020      * + Y**2*Z**2*LOG(Y**2/Z**2))/((X**2-Y**2)*(Y**2-Z**2)*(X**2-Z**2))
0021
0022       IF(DABS(XMU).LT.0.000001D0) XMU = 0.000001D0
0023       MQ2 = MQ**2
0024       MUR2 = MUR**2
0025       MD2 = MD**2
0026       TANBA = TANB
0027       SINBA = TANBA/DSQRT(TANBA**2+1D0)
0028       COSBA = SINBA/TANBA
0029
0030       SINB = TANB/DSQRT(TANB**2+1D0)
0031       COSB = SINB/TANB
0032
0033       PI = PARU(1)
0034       MZ = PMAS(23,1)
0035       MW = PMAS(24,1)
0036       SW = 1D0-MW**2/MZ**2
0037       V  = 174.1D0
0038
0039       ALPHA3 = 0.12D0/(1D0+23/12D0/PI*0.12D0*LOG(MTOP**2/MZ**2))
0040       G2 = DSQRT(0.0336D0*4D0*PI)
0041       G1 = DSQRT(0.0101D0*4D0*PI)
0042
0043       IF(MQ.GT.MUR) MST = MQ
0044       IF(MUR.GT.MQ.OR.MUR.EQ.MQ) MST = MUR
0045
0046       MSUSYT = DSQRT(MST**2  + MTOP**2)
0047
0048       IF(MQ.GT.MD) MSB = MQ
0049       IF(MD.GT.MQ.OR.MD.EQ.MQ) MSB = MD
0050
0051       MB = PYMRUN(5,MSB**2)
0052       MSUSYB = DSQRT(MSB**2 + MB**2)
0053       TT = LOG(MSUSYT**2/MTOP**2)
0054       TB = LOG(MSUSYB**2/MTOP**2)
0055
0056       RMTOP = MTOP/(1D0+4D0*ALPHA3/3D0/PI)
0057       HT = RMTOP/(V*SINB)
0058       HTST = RMTOP/V
0059       HB = MB/V/COSB
0060       G32 = ALPHA3*4D0*PI
0061       BT2 = -(8D0*G32 - 9D0*HT**2/2D0 - HB**2/2D0)/(4D0*PI)**2
0062       BB2 = -(8D0*G32 - 9D0*HB**2/2D0 - HT**2/2D0)/(4D0*PI)**2
0063       AL2 = 3D0/8D0/PI**2*HT**2
0064 C      BT2ST = -(8.*G32 - 9.*HTST**2/2.)/(4.*PI)**2
0065 C      ALST = 3./8./PI**2*HTST**2
0066       AL1 = 3D0/8D0/PI**2*HB**2
0067
0068       AL(1,1) = AL1
0069       AL(1,2) = (AL2+AL1)/2D0
0070       AL(2,1) = (AL2+AL1)/2D0
0071       AL(2,2) = AL2
0072
0073       IF(MA.GT.MTOP) THEN
0074         VI = V*(1D0 + 3D0/32D0/PI**2*HTST**2*
0075      *        LOG(MTOP**2/MA**2))
0076         H1I = VI* COSBA
0077         H2I = VI*SINBA
0078         H1T = H1I*(1D0+3D0/8D0/PI**2*HB**2*LOG(MA**2/MSUSYT**2))**.25D0
0079         H2T = H2I*(1D0+3D0/8D0/PI**2*HT**2*LOG(MA**2/MSUSYT**2))**.25D0
0080         H1B = H1I*(1D0+3D0/8D0/PI**2*HB**2*LOG(MA**2/MSUSYB**2))**.25D0
0081         H2B = H2I*(1D0+3D0/8D0/PI**2*HT**2*LOG(MA**2/MSUSYB**2))**.25D0
0082       ELSE
0083         VI = V
0084         H1I = VI*COSB
0085         H2I = VI*SINB
0086         H1T=H1I*(1D0+3D0/8D0/PI**2*HB**2*LOG(MTOP**2/MSUSYT**2))**.25D0
0087         H2T=H2I*(1D0+3D0/8D0/PI**2*HT**2*LOG(MTOP**2/MSUSYT**2))**.25D0
0088         H1B=H1I*(1D0+3D0/8D0/PI**2*HB**2*LOG(MTOP**2/MSUSYB**2))**.25D0
0089         H2B=H2I*(1D0+3D0/8D0/PI**2*HT**2*LOG(MTOP**2/MSUSYB**2))**.25D0
0090       ENDIF
0091
0092       TANBST = H2T/H1T
0093       SINBT = TANBST/DSQRT(1D0+TANBST**2)
0094
0095       TANBSB = H2B/H1B
0096       SINBB = TANBSB/DSQRT(1D0+TANBSB**2)
0097       COSBB = SINBB/TANBSB
0098
0099       DELTAMT = 0D0
0100       DELTAMB = 0D0
0101
0102       MTOP4 = RMTOP**4*(1D0+2D0*BT2*TT- AL2*TT - 4D0*DELTAMT)
0103       MTOP2 = DSQRT(MTOP4)
0104       MBOT4 = MB**4*(1D0+2D0*BB2*TB - AL1*TB)
0105      * /(1D0+DELTAMB)**4
0106       MBOT2 = DSQRT(MBOT4)
0107
0108       STOP12 = (MQ2 + MUR2)*.5D0 + MTOP2
0109      *  +1D0/8D0*(G2**2+G1**2)*(H1T**2-H2T**2)
0110      *  +SQRT(((G2**2-5D0*G1**2/3D0)/4D0*(H1T**2-H2T**2) +
0111      *  MQ2 - MUR2)**2*0.25D0 + MTOP2*(AT-XMU/TANBST)**2)
0112       STOP22 = (MQ2 + MUR2)*.5D0 + MTOP2
0113      *  +1D0/8D0*(G2**2+G1**2)*(H1T**2-H2T**2)
0114      *   - SQRT(((G2**2-5D0*G1**2/3D0)/4D0*(H1T**2-H2T**2) +
0115      *  MQ2 - MUR2)**2*0.25D0
0116      *  + MTOP2*(AT-XMU/TANBST)**2)
0117       IF(STOP22.LT.0.) GOTO 120
0118       SBOT12 = (MQ2 + MD2)*.5D0
0119      *   - 1D0/8D0*(G2**2+G1**2)*(H1B**2-H2B**2)
0120      *  + SQRT(((G1**2/3D0-G2**2)/4D0*(H1B**2-H2B**2) +
0121      *  MQ2 - MD2)**2*0.25D0 + MBOT2*(AB-XMU*TANBSB)**2)
0122       SBOT22 = (MQ2 + MD2)*.5D0
0123      *   - 1D0/8D0*(G2**2+G1**2)*(H1B**2-H2B**2)
0124      *   - SQRT(((G1**2/3D0-G2**2)/4D0*(H1B**2-H2B**2) +
0125      *   MQ2 - MD2)**2*0.25D0 + MBOT2*(AB-XMU*TANBSB)**2)
0126       IF(SBOT22.LT.0.) SBOT22 = 10000D0
0127
0128       STOP1 = DSQRT(STOP12)
0129       STOP2 = DSQRT(STOP22)
0130       SBOT1 = DSQRT(SBOT12)
0131       SBOT2 = DSQRT(SBOT22)
0132
0133 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
0134 C
0135 C     HERE IS THE DEFINITION OF DELTAMB AND DELTAMT, WHICH
0136 C     ARE THE VERTEX CORRECTIONS TO THE BOTTOM AND TOP QUARK
0137 C     MASS, KEEPING THE DOMINANT QCD AND TOP YUKAWA COUPLING
0138 C     INDUCED CORRECTIONS.
0139 C
0140 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
0141
0142       X=SBOT1
0143       Y=SBOT2
0144       Z=XMGL
0145       IF(X.EQ.Y) X = X - 0.00001D0
0146       IF(X.EQ.Z) X = X - 0.00002D0
0147       IF(Y.EQ.Z) Y = Y - 0.00003D0
0148
0149       T1=T(X,Y,Z)
0150       X=STOP1
0151       Y=STOP2
0152       Z=XMU
0153       IF(X.EQ.Y) X = X - 0.00001D0
0154       IF(X.EQ.Z) X = X - 0.00002D0
0155       IF(Y.EQ.Z) Y = Y - 0.00003D0
0156       T2=T(X,Y,Z)
0157       DELTAMB = -2*ALPHA3/3D0/PI*XMGL*(AB-XMU*TANB)*T1
0158      *  + HT**2/(4D0*PI)**2*(AT-XMU/TANB)*XMU*TANB*T2
0159       X=STOP1
0160       Y=STOP2
0161       Z=XMGL
0162       IF(X.EQ.Y) X = X - 0.00001D0
0163       IF(X.EQ.Z) X = X - 0.00002D0
0164       IF(Y.EQ.Z) Y = Y - 0.00003D0
0165       T3=T(X,Y,Z)
0166       DELTAMT = -2D0*ALPHA3/3D0/PI*(AT-XMU/TANB)*XMGL*T3
0167
0168 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
0169 C
0170 C   HERE THE NEW VALUES OF THE TOP AND BOTTOM QUARK MASSES AT
0171 C   THE SCALE MS ARE DEFINED, TO BE USED IN THE EFFECTIVE
0172 C   POTENTIAL APPROXIMATION. THEY ARE JUST THE OLD ONES, BUT
0173 C   INCLUDING THE FINITE CORRECTIONS DELTAMT AND DELTAMB.
0174 C   THE DELTAMB CORRECTIONS CAN BECOME LARGE AND ARE RESUMMED
0175 C   TO ALL ORDERS, AS SUGGESTED IN THE TWO RECENT WORKS BY M. CARENA,
0176 C   S. MRENNA AND C.E.M. WAGNER, AS WELL AS IN THE WORK BY M. CARENA,
0177 C   D. GARCIA, U. NIERSTE AND C.E.M. WAGNER, TO APPEAR. THE TOP
0178 C   QUARK MASS CORRECTIONS ARE SMALL AND ARE KEPT IN THE PERTURBATIVE
0179 C   FORMULATION.  THE FUNCTION T(X,Y,Z) IS NECESSARY FOR THE
0180 C   CALCULATION. THE ENTRIES ARE MASSES AND NOT THEIR SQUARES !
0181 C
0182 C
0183 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
0184
0185       MTOP4 = RMTOP**4*(1D0+2D0*BT2*TT- AL2*TT - 4D0*DELTAMT)
0186       MTOP2 = DSQRT(MTOP4)
0187       MBOT4 = MB**4*(1D0+2D0*BB2*TB - AL1*TB)
0188      * /(1D0+DELTAMB)**4
0189       MBOT2 = DSQRT(MBOT4)
0190
0191       STOP12 = (MQ2 + MUR2)*.5D0 + MTOP2
0192      *   +1D0/8D0*(G2**2+G1**2)*(H1T**2-H2T**2)
0193      *   +SQRT(((G2**2-5D0*G1**2/3D0)/4D0*(H1T**2-H2T**2) +
0194      *   MQ2 - MUR2)**2*0.25D0 + MTOP2*(AT-XMU/TANBST)**2)
0195       STOP22 = (MQ2 + MUR2)*.5D0 + MTOP2
0196      *  +1D0/8D0*(G2**2+G1**2)*(H1T**2-H2T**2)
0197      *   - SQRT(((G2**2-5D0*G1**2/3D0)/4D0*(H1T**2-H2T**2) +
0198      *  MQ2 - MUR2)**2*0.25D0
0199      *  + MTOP2*(AT-XMU/TANBST)**2)
0200
0201       IF(STOP22.LT.0.) GOTO 120
0202       SBOT12 = (MQ2 + MD2)*.5D0
0203      *   - 1D0/8D0*(G2**2+G1**2)*(H1B**2-H2B**2)
0204      *  + SQRT(((G1**2/3D0-G2**2)/4D0*(H1B**2-H2B**2) +
0205      *  MQ2 - MD2)**2*0.25D0 + MBOT2*(AB-XMU*TANBSB)**2)
0206       SBOT22 = (MQ2 + MD2)*.5D0
0207      *   - 1D0/8D0*(G2**2+G1**2)*(H1B**2-H2B**2)
0208      *   - SQRT(((G1**2/3D0-G2**2)/4D0*(H1B**2-H2B**2) +
0209      *   MQ2 - MD2)**2*0.25D0 + MBOT2*(AB-XMU*TANBSB)**2)
0210       IF(SBOT22.LT.0.) GOTO 120
0211
0212
0213       STOP1 = DSQRT(STOP12)
0214       STOP2 = DSQRT(STOP22)
0215       SBOT1 = DSQRT(SBOT12)
0216       SBOT2 = DSQRT(SBOT22)
0217
0218 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
0219 CCC   D-TERMS
0220 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
0221       STW=SW
0222
0223       F1T=(MQ2-MUR2)/(STOP12-STOP22)*(.5D0-4D0/3D0*STW)*
0224      *         LOG(STOP1/STOP2)
0225      *        +(.5D0-2D0/3D0*STW)*LOG(STOP1*STOP2/(MQ2+MTOP2))
0226      *        + 2D0/3D0*STW*LOG(STOP1*STOP2/(MUR2+MTOP2))
0227
0228       F1B=(MQ2-MD2)/(SBOT12-SBOT22)*(-.5D0+2D0/3D0*STW)*
0229      *        LOG(SBOT1/SBOT2)
0230      *        +(-.5D0+1D0/3D0*STW)*LOG(SBOT1*SBOT2/(MQ2+MBOT2))
0231      *        - 1D0/3D0*STW*LOG(SBOT1*SBOT2/(MD2+MBOT2))
0232
0233       F2T=DSQRT(MTOP2)*(AT-XMU/TANBST)/(STOP12-STOP22)*
0234      *         (-.5D0*LOG(STOP12/STOP22)
0235      *        +(4D0/3D0*STW-.5D0)*(MQ2-MUR2)/(STOP12-STOP22)*
0236      *         G(STOP12,STOP22))
0237
0238       F2B=DSQRT(MBOT2)*(AB-XMU*TANBSB)/(SBOT12-SBOT22)*
0239      *         (.5D0*LOG(SBOT12/SBOT22)
0240      *        +(-2D0/3D0*STW+.5D0)*(MQ2-MD2)/(SBOT12-SBOT22)*
0241      *        G(SBOT12,SBOT22))
0242
0243       VH3B(1,1) = MBOT4/(COSBB**2)*(LOG(SBOT1**2*SBOT2**2/
0244      *  (MQ2+MBOT2)/(MD2+MBOT2))
0245      *  + 2D0*(AB*(AB-XMU*TANBSB)/(SBOT1**2-SBOT2**2))*
0246      *  LOG(SBOT1**2/SBOT2**2)) +
0247      *  MBOT4/(COSBB**2)*(AB*(AB-XMU*TANBSB)/
0248      *  (SBOT1**2-SBOT2**2))**2*G(SBOT12,SBOT22)
0249
0250       VH3T(1,1) =
0251      *  MTOP4/(SINBT**2)*(XMU*(-AT+XMU/TANBST)/(STOP1**2
0252      * -STOP2**2))**2*G(STOP12,STOP22)
0253
0254       VH3B(1,1)=VH3B(1,1)+
0255      *    MZ**2*(2*MBOT2*F1B-DSQRT(MBOT2)*AB*F2B)
0256
0257       VH3T(1,1) = VH3T(1,1) +
0258      *  MZ**2*(DSQRT(MTOP2)*XMU/TANBST*F2T)
0259
0260       VH3T(2,2) = MTOP4/(SINBT**2)*(LOG(STOP1**2*STOP2**2/
0261      *  (MQ2+MTOP2)/(MUR2+MTOP2))
0262      *  + 2D0*(AT*(AT-XMU/TANBST)/(STOP1**2-STOP2**2))*
0263      *  LOG(STOP1**2/STOP2**2)) +
0264      *  MTOP4/(SINBT**2)*(AT*(AT-XMU/TANBST)/
0265      *  (STOP1**2-STOP2**2))**2*G(STOP12,STOP22)
0266
0267       VH3B(2,2) =
0268      *  MBOT4/(COSBB**2)*(XMU*(-AB+XMU*TANBSB)/(SBOT1**2
0269      * -SBOT2**2))**2*G(SBOT12,SBOT22)
0270
0271       VH3T(2,2)=VH3T(2,2)+
0272      *    MZ**2*(-2*MTOP2*F1T+DSQRT(MTOP2)*AT*F2T)
0273       VH3B(2,2) = VH3B(2,2) -MZ**2*DSQRT(MBOT2)*XMU*TANBSB*F2B
0274       VH3T(1,2) = -
0275      *   MTOP4/(SINBT**2)*XMU*(AT-XMU/TANBST)/
0276      * (STOP1**2-STOP2**2)*(LOG(STOP1**2/STOP2**2) + AT*
0277      * (AT - XMU/TANBST)/(STOP1**2-STOP2**2)*G(STOP12,STOP22))
0278
0279       VH3B(1,2) =
0280      * - MBOT4/(COSBB**2)*XMU*(AB-XMU*TANBSB)/
0281      * (SBOT1**2-SBOT2**2)*(LOG(SBOT1**2/SBOT2**2) + AB*
0282      * (AB - XMU*TANBSB)/(SBOT1**2-SBOT2**2)*G(SBOT12,SBOT22))
0283
0284
0285       VH3T(1,2)=VH3T(1,2) +
0286      *MZ**2*(MTOP2/TANBST*F1T-DSQRT(MTOP2)*(AT/TANBST+XMU)/2D0*F2T)
0287
0288       VH3B(1,2)=VH3B(1,2) +
0289      *MZ**2*(-MBOT2*TANBSB*F1B+DSQRT(MBOT2)*(AB*TANBSB+XMU)/2D0*F2B)
0290
0291       VH3T(2,1) = VH3T(1,2)
0292       VH3B(2,1) = VH3B(1,2)
0293
0294 C      TQ = LOG((MQ2 + MTOP2)/MTOP2)
0295 C      TU = LOG((MUR2+MTOP2)/MTOP2)
0296 C      TQD = LOG((MQ2 + MB**2)/MB**2)
0297 C      TD = LOG((MD2+MB**2)/MB**2)
0298
0299       DO 110 I = 1,2
0300         DO 100 J = 1,2
0301           VH(I,J) =
0302      *   6D0/(8D0*PI**2*(H1T**2+H2T**2))
0303      *   *VH3T(I,J)*0.5D0*(1D0-AL(I,J)*TT/2D0) +
0304      *   6D0/(8D0*PI**2*(H1B**2+H2B**2))
0305      *   *VH3B(I,J)*0.5D0*(1D0-AL(I,J)*TB/2D0)
0306   100   CONTINUE
0307   110 CONTINUE
0308
0309       GOTO 150
0310   120 DO 140 I =1,2
0311         DO 130 J = 1,2
0312           VH(I,J) = -1D15
0313   130   CONTINUE
0314   140 CONTINUE
0315
0316
0317   150 RETURN
0318       END