************************************************************************ * * NEUTRAL CURRENT * ************************************************************************ * * MassiveZeroCoefficientFunctions.f: * * This file contains all the exact asymptotic massive coefficient * functions as given in the paper below. * * Reference: hep-ph/9601302 (Appendix D) * * The following return the coefficients of the log dependent terms. * ************************************************************************ * * Order alphas coeficient functions (NLO) * Expansion parameter alphas/4*pi * ************************************************************************ * Equation (4.1): Gluon coefficient function for FL ************************************************************************ FUNCTION CLG1AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Output Variables * DOUBLE PRECISION CLG1AM0_A0 * CLG1AM0_A0 = TR * 16D0 * X * ( 1D0 - X ) * RETURN END * ************************************************************************ * Equation (4.2): Gluon coefficient function for F2 ************************************************************************ FUNCTION C2G1AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Output Variables * DOUBLE PRECISION C2G1AM0_AQ * C2G1AM0_AQ = TR * ( 4D0 - 8D0 * X + 8D0 * X**2 ) * RETURN END * ************************************************************************ FUNCTION C2G1AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Output Variables * DOUBLE PRECISION C2G1AM0_A0 * C2G1AM0_A0 = TR * ( ( 4D0 - 8D0 * X + 8D0 * X**2 ) 1 * DLOG( ( 1D0 - X ) / X ) - 4D0 + 32D0 * X 2 - 32D0 * X**2 ) * RETURN END * ************************************************************************ * * Order alphas^2 coeficient functions (NNLO) * Expansion parameter alphas/4*pi * ************************************************************************ * Equation (4.3): Gluon coefficient function for FL ************************************************************************ FUNCTION CLG2AM0_AF(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLM DOUBLE PRECISION C1 ** * Output Variables * DOUBLE PRECISION CLG2AM0_AF * DLX=DLOG(X) DLM=DLOG(1.0D0-X) * C1=64.0D0*X*(1.0D0-X)*DLM-128.0D0*X*DLX-32.0D0-160.0D0*X 1+544.0D0*X*X/3.0D0+32.0D0/X/3.0D0 * CLG2AM0_AF = TR * CA * C1 * RETURN END * ************************************************************************ FUNCTION CLG2AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLM DOUBLE PRECISION A1,B1 ** * Output Variables * DOUBLE PRECISION CLG2AM0_AQ * DLX=DLOG(X) DLM=DLOG(1.0D0-X) * A1=64.0D0*X*(1.0D0-X)*DLM-128.0D0*X*DLX-32.0D0-160.0D0*X 1+544.0D0*X*X/3.0D0+32.0D0/X/3.0D0 * B1=32.0D0*X*DLX+16.0D0*(1.0D0-2.0D0*X*X+X) * CLG2AM0_AQ = TR * ( CA * A1 + CF * B1 ) * RETURN END * ************************************************************************ FUNCTION CLG2AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLM,DLM2,DLP,S11,S11M DOUBLE PRECISION A2,B2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION CLG2AM0_A0 * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) DLM2=DLM*DLM DLP=DLOG(1.0D0+X) S11=WGPLG(1,1,1.0D0-X) S11M=WGPLG(1,1,-X) * A2=96.0D0*X*DLX2+(64.0D0*X*X-192.0D0*X)*DLX*DLM+(32.0D0 1-416.0D0*X*X+256.0D0*X)*DLX+32.0D0*X*(1.0D0-X)*DLM2+( 2-32.0D0+928.0D0*X*X/3.0D0-288.0D0*X+32.0D0/X/3.0D0)*DLM 3+64.0D0*X*X*ZETA2-128.0D0*X*S11+64.0D0*X*(1.0D0+X)*(S11M 4+DLX*DLP)+32.0D0/3.0D0-1696*X*X/9.0D0+544.0D0*X/3.0D0 5-32.0D0/X/9.0D0 * B2=-(64.0D0*X*X*X/5.0D0+64.0D0*X/3.0D0)*DLX2+32.0D0*X 1*(S11+DLX*DLM)+(-208.0D0/15.0D0+192.0D0*X*X/5.0D0 2-416.0D0*X/5.0D0-64.0D0/X/15.0D0)*DLX+(16.0D0-64.0D0*X*X 3+48.0D0*X)*DLM+(128.0D0*X*X*X/5.0D0-64.0D0*X/3.0D0)*ZETA2 4+(128.0D0*X*X*X/5.0D0-64.0D0*X/3.0D0+64.0D0/X/X/15.0D0) 5*(S11M+DLX*DLP)-256.0D0/15.0D0+672.0D0*X*X/5.0D0-608.0D0 6*X/5.0D0+64.0D0/X/15.0D0 * CLG2AM0_A0 = TR * ( CA * A2 + CF * B2 ) * RETURN END * ************************************************************************ * Equation (4.4): Gluon coefficient function for F2 ************************************************************************ FUNCTION C2G2AM0_AQF(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLM DOUBLE PRECISION C1 ** * Output Variables * DOUBLE PRECISION C2G2AM0_AQF * DLX=DLOG(X) DLM=DLOG(1.0D0-X) * C1=-248.0D0*X*X/3.0D0+64.0D0*X+8.0D0+32.0D0/X/3.0D0 1+(32.0D0*X*X-32.0D0*X+16.0D0)*DLM+(64.0D0*X+16.0D0)*DLX * C2G2AM0_AQF = TR * CA * C1 * RETURN END * ************************************************************************ FUNCTION C2G2AM0_AF(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLM,DLM2 DOUBLE PRECISION S11 DOUBLE PRECISION C2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2G2AM0_AF * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) DLM2=DLM*DLM S11=WGPLG(1,1,1.0D0-X) * C2=(-16.0D0+32.0D0*X-32.0D0*X*X)*ZETA2+1124.0D0*X*X/3.0D0 1-968.0D0*X/3.0D0-172.0D0/3.0D0+16.0D0/X/3.0D0+(16.0D0 2-32.0D0*X+32.0D0*X*X)*DLM2-(8.0D0+32.0D0*X)*DLX2+(248.0D0 3*X*X/3.0D0-256.0D0*X-8.0D0)*DLX+(32.0D0/X/3.0D0-8.0D0 4+192.0D0*X-632.0D0*X*X/3.0D0)*DLM+(96.0D0*X-32.0D0*X*X) 5*DLX*DLM+(64.0D0*X+16.0D0)*S11 * C2G2AM0_AF = TR * CA * C2 * RETURN END * ************************************************************************ FUNCTION C2G2AM0_AQ2(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLM DOUBLE PRECISION A1,B1 ** * Output Variables * DOUBLE PRECISION C2G2AM0_AQ2 * DLX=DLOG(X) DLM=DLOG(1.0D0-X) * A1=16.0D0/X/3.0D0-124.0D0*X*X/3.0D0+32.0D0*X+4.0D0 1+(16.0D0*X*X-16.0D0*X+8.0D0)*DLM+(32.0D0*X+8.0D0)*DLX * B1=-2.0D0+8.0D0*X+(16.0D0*X*X-16.0D0*X+8.0D0)*DLM 1+(-16.0D0*X*X+8.0D0*X-4.0D0)*DLX * C2G2AM0_AQ2 = TR * ( CA * A1 + CF * B1 ) * RETURN END * ************************************************************************ FUNCTION C2G2AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLM,DLM2,DLP DOUBLE PRECISION S111MX,S11MX DOUBLE PRECISION A2,B2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2G2AM0_AQ * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) DLM2=DLM*DLM DLP=DLOG(1.0D0+X) S111MX=WGPLG(1,1,1.0D0-X) S11MX=WGPLG(1,1,-X) * A2=-(16.0D0+32.0D0*X*X)*ZETA2+1628.0D0*X*X/9.0D0 1-368.0D0*X/3.0D0-220.0D0/3.0D0+208.0D0/X/9.0D0 2+(16.0D0*X*X-16.0D0*X+8.0D0)*DLM2-(48.0D0*X+16.0D0) 3*DLX2+(-536.0D0*X*X/3.0D0+160.0D0*X-8.0D0+32.0D0/X/3.0D0) 4*DLM+(200.0D0*X*X-192.0D0*X)*DLX+(96.0D0*X-32.0D0*X*X) 5*DLX*DLM+(64.0D0*X+16.0D0)*S111MX-(32.0D0*X*X+32.0D0*X+16.0D0) 6*(S11MX+DLX*DLP) * B2=(-64.0D0*X*X+64.0D0*X-32.0D0)*ZETA2+16.0D0*X*X-68.0D0*X 1+36.0D0+(32.0D0*X*X-32.0D0*X+16.0D0)*DLM2+(32.0D0*X*X 2-16.0D0*X+8.0D0)*DLX2+(-80.0D0*X*X+96.0D0*X-28.0D0)*DLM 3+(80.0D0*X*X-48.0D0*X+8.0D0)*DLX+(-64.0D0*X*X+48.0D0*X 4-24.0D0)*DLX*DLM+(8.0D0-16.0D0*X)*S111MX * C2G2AM0_AQ = TR * ( CA * A2 + CF * B2 ) * RETURN END * ************************************************************************ FUNCTION C2G2AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLX3,DLM,DLM2,DLM3,DLP,DLP2 DOUBLE PRECISION S11,S121MX,S12MX,S211MX,S21MX,S111MX,S11MX DOUBLE PRECISION Z,S21Z,S21MZ DOUBLE PRECISION A31,A32,A33,A34,A3 DOUBLE PRECISION B31,B32,B33,B34,B3 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2G2AM0_A0 * DLX=DLOG(X) DLX2=DLX*DLX DLX3=DLX2*DLX DLM=DLOG(1.0D0-X) DLM2=DLM*DLM DLM3=DLM2*DLM DLP=DLOG(1.0D0+X) DLP2=DLP*DLP S11=WGPLG(1,1,1.0D0-X) S121MX=WGPLG(1,2,1.0D0-X) S12MX=WGPLG(1,2,-X) S211MX=WGPLG(2,1,1.0D0-X) S21MX=WGPLG(2,1,-X) S111MX=WGPLG(1,1,1.0D0-X) S11MX=WGPLG(1,1,-X) Z=(1.0D0-X)/(1.0D0+X) S21Z=WGPLG(2,1,Z) S21MZ=WGPLG(2,1,-Z) * A31=DLX3*(16.0D0/3.0D0+16.0D0*X)+ 1DLX2*DLM*(-8.0D0+16.0D0*X*X-64.0D0*X)+ 2DLX2*DLP*(12.0D0+32.0D0*X*X+24.0D0*X)+ 3DLX2*(-114.0D0*X*X+184.0D0*X)+ 4DLX*DLM2*(-16.0D0*X*X+48.0D0*X)+ 5DLX*DLM*DLP*(-16.0D0-32.0D0*X*X-32.0D0*X)+ 6DLX*DLM*(16.0D0+292.0D0*X*X-288.0D0*X)+ 7DLX*DLP2*(8.0D0+16.0D0*X) A32=DLX*DLP*(-48.0D0+208.0D0*X*X/3.0D0+16.0D0*X- 132.0D0/X/3.0D0)+ 2DLX*ZETA2*(-16.0D0+32.0D0*X*X-160.0D0*X)+ 3DLX*S111MX*(+32.0D0*X)+ 4DLX*S11MX*(24.0D0+32.0D0*X*X+48.0D0*X)+ 5DLX*(292.0D0/3.0D0-5780.0D0*X*X/9.0D0+332.0D0*X)+ 6DLM2*(-6.0D0-214.0D0*X*X/3.0D0+64.0D0*X+16.0D0/X/3.0D0)+ 7ZETA2*DLM*(-40.0D0-64.0D0*X*X+48.0D0*X) A33=DLM*S111MX*(16.0D0+64.0D0*X)+ 1DLM*S11MX*(-16.0D0-32.0D0*X*X-32.0D0*X)+ 2DLM*(-112.0D0/3.0D0+2996.0D0*X*X/9.0D0-860.0D0*X/3.0D0 3+208.0D0/X/9.0D0)+ 4ZETA2*DLP*(8.0D0+16.0D0*X)+ 5DLP*S11MX*(16.0D0+32.0D0*X)+ 6S21MZ*(-16.0D0-32.0D0*X*X-32.0D0*X)+ 7S21Z*(16.0D0+32.0D0*X*X+32.0D0*X) A34=ZETA2*(-4.0D0+796.0D0*X*X/3.0D0-208.0D0*X-32.0D0/X)+ 1ZETA3*(-12.0D0-8.0D0*X*X-56.0D0*X)+ 2S111MX*(20.0D0+80.0D0*X*X/3.0D0-64.0D0*X+64.0D0/X/3.0D0)+ 3S211MX*(-16.0D0-128.0D0*X)+ 4S121MX*(40.0D0+144.0D0*X)+ 5S11MX*(-48.0D0+208.0D0*X*X/3.0D0+16.0D0*X-32.0D0/X/3.0D0)+ 6S21MX*(-24.0D0-48.0D0*X)+ 7S12MX*(16.0D0+32.0D0*X)+80.0D0/X/9.0D0+ 8466.0D0/9.0D0-878.0D0*X*X/9.0D0+260.0D0*X/9.0D0 A3=A31+A32+A33+A34 * B31=DLX3*(-8.0D0/3.0D0-32.0D0*X*X/3.0D0+16.0D0*X/3.0D0)+ 1DLX2*DLM*(16.0D0+48.0D0*X*X-32.0D0*X)+ 2DLX2*DLP*(16.0D0+16.0D0*X*X+32.0D0*X)+ 3DLX2*(-4.0D0-96.0D0*X*X*X/5.0D0-52.0D0*X*X+8.0D0*X/3.0D0)+ 4DLX*DLM2*(-20.0D0-48.0D0*X*X+40.0D0*X)+ 5DLX*DLM*(24.0D0+168.0D0*X*X-160.0D0*X)+ 6DLX*DLP2*(-32.0D0-32.0D0*X*X-64.0D0*X)+ 7DLX*DLP*(96.0D0+192.0D0*X*X*X/5.0D0+128.0D0*X/3.0D0) B32=16.0D0*DLX*DLP/X/X/15.0D0-16.0D0*DLX/X/15.0D0+ 1DLX*ZETA2*(32.0D0+64.0D0*X*X-64.0D0*X)+ 2DLX*S111MX*(32.0D0*X*X)+ 3DLX*S11MX*(-32.0D0-32.0D0*X*X+64.0D0*X)+ 4DLX*(-712.0D0/15.0D0-672.0D0*X*X/5.0D0+136.0D0*X/5.0D0)+ 5DLM3*(8.0D0+16.0D0*X*X-16.0D0*X)+ 6DLM2*(-22.0D0-84.0D0*X*X+88.0D0*X)+ 7ZETA2*DLM*(-32.0D0*X*X) B33=DLM*S111MX*(8.0D0-16.0D0*X)+ 1DLM*(28.0D0+96.0D0*X*X-132.0D0*X)+ 2ZETA2*DLP*(-32.0D0-32.0D0*X*X-64.0D0*X)+ 3DLP*S11MX*(-64.0D0-64.0D0*X*X-128.0D0*X)+ 4ZETA2*(48.0D0+192.0D0*X*X*X/5.0D0+104.0D0*X*X- 5208.0D0*X/3.0D0)+ 6ZETA3*(112.0D0+192.0D0*X*X-96.0D0*X) B34=S111MX*(-24.0D0+64.0D0*X*X-48.0D0*X)+ 1S211MX*(-24.0D0-32.0D0*X*X+48.0D0*X)+ 2S121MX*(-32.0D0+64.0D0*X)+ 3S11MX*(96.0D0+192.0D0*X*X*X/5.0D0+128.0D0*X/3.0D0)+ 416.0D0*S11MX/X/X/15.0D0+16.0D0/X/15.0D0+ 5S21MX*(96.0D0+96.0D0*X*X-64.0D0*X)+ 6S12MX*(-64.0D0-64.0D0*X*X-128.0D0*X)- 7904.0D0/15.0D0+328.0D0*X*X/5.0D0+68.0D0*X/5.0D0 B3=B31+B32+B33+B34 * C2G2AM0_A0 = TR * ( CA * A3 + CF * B3 ) * RETURN END * ************************************************************************ * Equation (4.5): Heavy quark coefficient function for FL ************************************************************************ FUNCTION CLPS2AM0_AF(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX DOUBLE PRECISION C1 ** * Output Variables * DOUBLE PRECISION CLPS2AM0_AF * DLX=DLOG(X) * C1=32.0D0/3.0D0/X+64.0D0*X*X/3.0D0 1-32.0D0-32.0D0*X*DLX * CLPS2AM0_AF = CF * TR * C1 * RETURN END * ************************************************************************ FUNCTION CLPS2AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX DOUBLE PRECISION A1 ** * Output Variables * DOUBLE PRECISION CLPS2AM0_AQ * DLX=DLOG(X) * A1=-32.0D0*X*DLX-32.0D0+64.0D0*X*X/3.0D0+32.0D0/X/3.0D0 * CLPS2AM0_AQ = CF * TR * A1 * RETURN END * ************************************************************************ FUNCTION CLPS2AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLM,SPX DOUBLE PRECISION A2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION CLPS2AM0_A0 * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) SPX=WGPLG(1,1,1.0D0-X) * A2=32.0D0*X*(DLX2-DLX*DLM-SPX)+(-32.0D0+64.0D0*X*X/3.0D0 1+32.0D0/X/3.0D0)*DLM+(32.0D0-64.0D0*X*X-32.0D0*X)*DLX 2+32.0D0/3.0D0+320.0D0*X*X/9.0D0-128.0D0*X/3.0D0 3-32.0D0/X/9.0D0 * CLPS2AM0_A0 = CF * TR * A2 * RETURN END * ************************************************************************ * Equation (4.6): Heavy quark coefficient function for F2 ************************************************************************ FUNCTION C2PS2AM0_AQF(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX DOUBLE PRECISION C1 ** * Output Variables * DOUBLE PRECISION C2PS2AM0_AQF * DLX=DLOG(X) * C1=-32.0D0*X*X/3.0D0-8.0D0*X+8.0D0+32.0D0/X/3.0D0 1+16.0D0*(1.0D0+X)*DLX * C2PS2AM0_AQF = CF * TR * C1 * RETURN END * ************************************************************************ FUNCTION C2PS2AM0_AF(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLM,SPX DOUBLE PRECISION C2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2PS2AM0_AF * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) SPX=WGPLG(1,1,1.0D0-X) * C2=128.0D0*X*X/3.0D0+16.0D0*X/3.0D0-160.0D0/3.0D0 1+16.0D0/X/3.0D0+8.0D0*(1.0D0+X)*(-DLX2+2.0D0*DLX*DLM 2+2.0D0*SPX)+(-32.0D0*X*X/3.0D0-8.0D0*X+8.0D0+32.0D0/X/3.0D0) 3*DLM+(32.0D0*X*X/3.0D0-40.0D0*X-8.0D0)*DLX * C2PS2AM0_AF = CF * TR * C2 * RETURN END * ************************************************************************ FUNCTION C2PS2AM0_AQ2(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX DOUBLE PRECISION A1 ** * Output Variables * DOUBLE PRECISION C2PS2AM0_AQ2 * DLX=DLOG(X) * A1=-16.0D0*X*X/3.0D0-4.0D0*X+4.0D0+16.0D0/X/3.0D0 1+8.0D0*(1.0D0+X)*DLX * C2PS2AM0_AQ2 = CF * TR * A1 * RETURN END * ************************************************************************ FUNCTION C2PS2AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLM,S11 DOUBLE PRECISION A2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2PS2AM0_AQ * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) S11=WGPLG(1,1,1.0D0-X) * A2=-64.0D0*X*X/9.0D0+160.0D0*X/3.0D0-208.0D0/3.0D0 1+208.0D0/X/9.0D0+32.0D0*X*X*DLX+16.0D0*(1.0D0+X)*(-DLX2+DLX*DLM 2+S11)+(-32.0D0*X*X/3.0D0-8.0D0*X+8.0D0+32.0D0/X/3.0D0) 3*DLM * C2PS2AM0_AQ = CF * TR * A2 * RETURN END * ************************************************************************ FUNCTION C2PS2AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Internal Variables * DOUBLE PRECISION DLX,DLX2,DLX3,DLM,DLM2,DLP,S11,S12,S21,S11M DOUBLE PRECISION A3 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2PS2AM0_A0 * DLX=DLOG(X) DLX2=DLX*DLX DLX3=DLX*DLX2 DLM=DLOG(1.0D0-X) DLM2=DLM*DLM DLP=DLOG(1.0D0+X) S11=WGPLG(1,1,1.0D0-X) S12=WGPLG(1,2,1.0D0-X) S21=WGPLG(2,1,1.0D0-X) S11M=WGPLG(1,1,-X) * A3=(1.0D0+X)*(16.0D0*DLX3/3.0D0-16.0D0*DLX2*DLM+8.0D0 1*DLX*DLM2-32.0D0*ZETA2*DLX+16.0D0*DLM*S11+32.0D0*S12 2-16.0D0*S21)+(40.0D0*X-16.0D0*X*X)*DLX2+32.0D0*X*X*DLX 3*DLM+(280.0D0/3.0D0-704.0D0*X*X/9.0D0-88.0D0*X)*DLX 4+(4.0D0-16.0D0*X*X/3.0D0-4.0D0*X+16.0D0/X/3.0D0)*DLM2 5+(-208.0D0/3.0D0-64.0D0*X*X/9.0D0+160.0D0*X/3.0D0 6+208.0D0/X/9.0D0)*DLM+(-16.0D0+64.0D0*X*X/3.0D0-16.0D0*X 7-32.0D0/X)*ZETA2+(16.0D0-16.0D0*X+64.0D0/X/3.0D0 8+32.0D0*X*X/3.0D0)*S11+(-32.0D0-32.0D0*X*X/3.0D0-32.0D0 9*X-32.0D0/X/3.0D0)*(S11M+DLX*DLP)+304.0D0/9.0D0+832.0D0 1*X*X/9.0D0-1216.0D0*X/9.0D0+80.0D0/X/9.0D0 * C2PS2AM0_A0 = CF * TR * A3 * RETURN END * ************************************************************************ * Equation (4.7): Non-singlet quark coefficient function for FL ************************************************************************ FUNCTION CLNS2AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Output Variables * DOUBLE PRECISION CLNS2AM0_AQ * CLNS2AM0_AQ = 16D0 * CF * TR * X / 3D0 * RETURN END * ************************************************************************ FUNCTION CLNS2AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Output Variables * DOUBLE PRECISION CLNS2AM0_A0 * CLNS2AM0_A0 = 16D0 * CF * TR * ( X * DLOG( 1D0 - X ) 1 - 2D0 * X * DLOG(X) - 25D0 * X / 6D0 + 1D0 ) / 3D0 * RETURN END * ************************************************************************ * Equation (4.8): Light quark coefficient function for F2 * Regular part ************************************************************************ FUNCTION C2NS2AM0_AQ2(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION B1 ** * Output Variables * DOUBLE PRECISION C2NS2AM0_AQ2 * B1=(-1D0-X)*2.0D0 * C2NS2AM0_AQ2 = 2D0 * CF * TR * B1 / 3D0 * RETURN END * ************************************************************************ FUNCTION C2NS2AM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLX,DLM DOUBLE PRECISION A1 ** * Output Variables * DOUBLE PRECISION C2NS2AM0_AQ * DLX=DLOG(X) DLM=DLOG(1.0D0-X) * A1=((-8.0D0*(1.0D0+X*X)*DLX/(1.0D0-X)+13.0D0*X+1.0D0) 1 + (-1D0-X)*(4.0D0*DLM-29.0D0/3.0D0)) * C2NS2AM0_AQ = 2D0 * CF * TR * A1 / 3D0 * RETURN END * ************************************************************************ FUNCTION C2NS2AM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLX,DLX2,DLM,DLM2,SPX DOUBLE PRECISION A2,B2 DOUBLE PRECISION WGPLG ** * Output Variables * DOUBLE PRECISION C2NS2AM0_A0 * DLX=DLOG(X) DLX2=DLX*DLX DLM=DLOG(1.0D0-X) DLM2=DLM*DLM SPX=WGPLG(1,1,1.0D0-X) * A2=(1.0D0+13.0D0*X)*DLM-(3.0D0+23.0D0*X)*DLX+29.0D0/6.0D0 1-295.0D0*X/6.0D0+(1.0D0+X*X)*(-4.0D0*SPX-8.0D0*DLX 1*DLM+6.0D0*DLX2+67.0D0*DLX/3.0D0)/(1.0D0-X) * B2=(-1D0-X)*(-4.0D0*ZETA2+2.0D0*DLM2 1-29.0D0*DLM/3.0D0+359D0/18.0D0) * C2NS2AM0_A0 = 2D0 * CF * TR * ( A2 + B2 ) / 3D0 * RETURN END * ************************************************************************ * Equation (4.8): Light quark coefficient function for F2 * Singular part ************************************************************************ FUNCTION C2NS2BM0_AQ2(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION Z ** * Output Variables * DOUBLE PRECISION C2NS2BM0_AQ2 * Z = 2D0 / ( 1D0 - X ) * C2NS2BM0_AQ2 = Z * 4D0 * CF * TR / 3D0 * RETURN END * ************************************************************************ FUNCTION C2NS2BM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLM,Z ** * Output Variables * DOUBLE PRECISION C2NS2BM0_AQ * DLM = DLOG( 1D0 - X ) Z = 2D0 / ( 1D0 - X ) * C2NS2BM0_AQ = Z * 2D0 * CF * TR * ( 4D0 * DLM - 29D0 / 3D0 ) / 3D0 * RETURN END * ************************************************************************ FUNCTION C2NS2BM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLM,DLM2,Z ** * Output Variables * DOUBLE PRECISION C2NS2BM0_A0 * DLM = DLOG( 1D0 - X ) DLM2 = DLM * DLM Z = 2D0 / ( 1D0 - X ) * C2NS2BM0_A0 = Z * 2D0 * CF * TR * ( - 4D0 * ZETA2 + 2D0 * DLM2 1 - 29D0 * DLM / 3D0 + 359D0 / 18D0 ) / 3D0 * RETURN END * ************************************************************************ * Equation (4.10): Light quark coefficient function for F2 * Local part ************************************************************************ FUNCTION C2NS2CM0_AQ2(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLM ** * Output Variables * DOUBLE PRECISION C2NS2CM0_AQ2 * DLM = DLOG( 1D0 - X ) * C2NS2CM0_AQ2 = 8D0 * CF * TR * DLM / 3D0 + 2D0 * CF * TR * RETURN END * ************************************************************************ FUNCTION C2NS2CM0_AQ(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLM,DLM2 ** * Output Variables * DOUBLE PRECISION C2NS2CM0_AQ * DLM = DLOG( 1D0 - X ) DLM2 = DLM * DLM * C2NS2CM0_AQ = 4D0 * CF * TR * ( 2D0 * DLM2 - 29D0 * DLM / 3D0 ) 1 / 3D0 - CF * TR * ( 32D0 * ZETA2 / 3D0 + 38D0 / 3D0 ) * RETURN END * ************************************************************************ FUNCTION C2NS2CM0_A0(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" INCLUDE "../commons/consts.h" ** * Input Variables * DOUBLE PRECISION X ** * Input Variables * DOUBLE PRECISION DLM,DLM2,DLM3 ** * Output Variables * DOUBLE PRECISION C2NS2CM0_A0 * DLM = DLOG( 1D0 - X ) DLM2 = DLM * DLM DLM3 = DLM2 * DLM * C2NS2CM0_A0 = 4D0 * CF * TR * ( - 4D0 * ZETA2 * DLM 1 + 2D0 * DLM3 / 3D0 - 29D0 * DLM2 / 6D0 2 + 359D0 * DLM / 18D0 ) / 3D0 3 + CF * TR * ( 268D0 * ZETA2 / 9D0 + 265D0 / 9D0 ) * RETURN END * ************************************************************************ * * CHARGED CURRENT * ************************************************************************ FUNCTION CG1ACCM0_AL(X) * IMPLICIT NONE * INCLUDE "../commons/ColorFactors.h" ** * Input Variables * DOUBLE PRECISION X ** * Output Variables * DOUBLE PRECISION CG1ACCM0_AL * CG1ACCM0_AL = 2D0 * TR * ( X**2 + ( 1D0 - X )**2 ) * RETURN END * ************************************************************************ * Logarithmically divergents term to be added to the MSbar ZM * coefficient functions to obtain the massless limit of the IC * contributions. ************************************************************************ function DICa(xi,z) * implicit none * include "../commons/ColorFactors.h" include "../commons/kfacQ.h" ** * Input Variables * double precision xi,z ** * Internal Variables * double precision lnk ** * Output Variables * double precision DICa * lnk = dlog(xi/kfacQ) ! ln(muF2/mh2) * DICa = 2d0 * CF * ( 1d0 + z ) * ( - lnk + 1d0 1 + 2d0 * dlog( 1d0 - z ) ) * return end * ************************************************************************ function DICb(xi,z) * implicit none * include "../commons/ColorFactors.h" include "../commons/kfacQ.h" ** * Input Variables * double precision xi,z ** * Internal Variables * double precision lnk ** * Output Variables * double precision DICb * lnk = dlog(xi/kfacQ) ! ln(muF2/mh2) * DICb = 4d0 * CF * ( lnk - 1d0 - 2d0 * dlog( 1d0 - z ) ) 1 / ( 1d0 - z ) * return end * ************************************************************************ function DICc(xi,z) * implicit none * include "../commons/ColorFactors.h" include "../commons/kfacQ.h" ** * Input Variables * double precision xi,z ** * Internal Variables * double precision lnk ** * Output Variables * double precision DICc * lnk = dlog(xi/kfacQ) ! ln(muF2/mh2) * DICc = 4d0 * CF * ( 3d0 * lnk / 4d0 + 1d0 1 + ( lnk - 1d0 ) * dlog( 1d0 - z ) - dlog( 1d0 - z )**2 ) * return end