************************************************************* * * File: andim_nlo.f * * Returns the NLO anomalous dimensions in the * a_s=alpha_s/4pi notation * * Input variables: N : Mellin variable * NF : Number of flavours * * Functions: PSI from data/theo/harmsums/psi.f * * Output: P1NS : Complex valued Non-singlet LO anomalous * dimension in N space * * P1SG(2,2) : matrix of the complex valued LO * singlet anomalous dimensions in * N space * ************************************************************* SUBROUTINE ANDIM_NLO(N,NF,P1NS,P1SG) IMPLICIT none * include "../../commons/colfact.h" include "../../commons/consts.h" * DOUBLE COMPLEX DPSI,PSI, S1, S2 * * --------------------------------------------------------------------- * * Internal variables * INTEGER I,J DOUBLE COMPLEX NS,NT,NFO,NFI,NSI,NSE,NE,NN DOUBLE COMPLEX N1,N2,NM,NMS,N1S,N1T,N2S,N2T DOUBLE COMPLEX N3,N4,N5,N6 DOUBLE COMPLEX S11,S12,S13,S14,S15,S16 DOUBLE COMPLEX SPMOM,SLC,SLV,SSCHLM,SSTR2M,SSTR3M,SSCHLP DOUBLE COMPLEX SSTR2P,SSTR3P DOUBLE COMPLEX PPSA,PQGA,PGQA,PGGA,PQGB,PGQB,PGGB,PGQC,PGGC DOUBLE COMPLEX PNPA,PNMA,PNSB,PNSC * * --------------------------------------------------------------------- * * Input variables * DOUBLE COMPLEX N INTEGER NF * * Output variables * DOUBLE COMPLEX P1NS(3) DOUBLE COMPLEX P1SG(2,2) * * --------------------------------------------------------------------- * S1 = EMC + PSI(N+1d0) S2 = ZETA2 - DPSI(N+1d0,1) * NS = N * N NT = NS * N NFO = NT * N NFI = NFO * N NSI = NFI * N NSE = NSI * N NE = NSE * N NN = NE * N * NM = N - 1d0 N1 = N + 1d0 N2 = N + 2d0 NMS = NM * NM N1S = N1 * N1 N1T = N1S * N1 N2S = N2 * N2 N2T = N2S * N2 * * --------------------------------------------------------------------- * * ..Analytic continuations of the occuring sums as given in GRV (1990) * (with an improved parametrization of the moments of Sp(x)/(1+x).) * * N3 = N + 3D0 N4 = N + 4D0 N5 = N + 5D0 N6 = N + 6D0 S11 = S1 + 1D0/N1 S12 = S11 + 1D0/N2 S13 = S12 + 1D0/N3 S14 = S13 + 1D0/N4 S15 = S14 + 1D0/N5 S16 = S15 + 1D0/N6 SPMOM = 1.0000D0 * (ZETA2 - S1 / N ) / N - 1 0.9992D0 * (ZETA2 - S11/ N1) / N1 + 2 0.9851D0 * (ZETA2 - S12/ N2) / N2 - 3 0.9005D0 * (ZETA2 - S13/ N3) / N3 + 4 0.6621D0 * (ZETA2 - S14/ N4) / N4 - 5 0.3174D0 * (ZETA2 - S15/ N5) / N5 + 6 0.0699D0 * (ZETA2 - S16/ N6) / N6 * SLC = - 5D0/8D0 * ZETA3 SLV = - ZETA2/2D0* (PSI(N1/2D0) - PSI(N/2D0)) 1 + S1/NS + SPMOM SSCHLM = SLC - SLV SSTR2M = ZETA2 - DPSI (N1/2D0,1) SSTR3M = 0.5D0 * DPSI (N1/2D0,2) + ZETA3 SSCHLP = SLC + SLV SSTR2P = ZETA2 - DPSI(N2/2D0,1) SSTR3P = 0.5D0 * DPSI(N2/2D0,2) + ZETA3 * * --------------------------------------------------------------------- * * ..The contributions to P1NS as given in Gonzalez-Arroyo et al. (1979) * (Note that the anomalous dimensions in the literature often differ * from these moments of the splitting functions by factors -1 or -2, * in addition to possible different normalizations of the coupling) * PNMA = ( 16D0* S1 * (2D0* N + 1D0) / (NS * N1S) + 1 16D0* (2D0* S1 - 1D0/(N * N1)) * ( S2 - SSTR2M ) + 2 64D0* SSCHLM + 24D0* S2 - 3D0 - 8D0* SSTR3M - 3 8D0* (3D0* NT + NS -1D0) / (NT * N1T) + 4 16D0* (2D0* NS + 2D0* N +1D0) / (NT * N1T) ) * (-0.5D0) PNPA = ( 16D0* S1 * (2D0* N + 1D0) / (NS * N1S) + 1 16D0* (2D0* S1 - 1D0/(N * N1)) * ( S2 - SSTR2P ) + 2 64D0* SSCHLP + 24D0* S2 - 3D0 - 8D0* SSTR3P - 3 8D0* (3D0* NT + NS -1D0) / (NT * N1T) - 4 16D0* (2D0* NS + 2D0* N +1D0)/(NT * N1T) ) * (-0.5D0) PNSB = ( S1 * (536D0/9D0 + 8D0* (2D0* N + 1D0) / (NS * N1S)) - 1 (16D0* S1 + 52D0/3D0- 8D0/(N * N1)) * S2 - 43D0/6D0 - 2 (151D0* NFO + 263D0* NT + 97D0* NS + 3D0* N + 9D0) * 3 4D0/ (9D0* NT * N1T) ) * (-0.5D0) PNSC = ( -160D0/9D0* S1 + 32D0/3.* S2 + 4D0/3D0 + 1 16D0*(11D0*NS+5D0*N-3D0)/(9D0* NS * N1S))*(-0.5D0) * * --------------------------------------------------------------------- * * ..The contributions to P1SG as given in Floratos et al. (1981) * ..Pure singlet (PS) and QG * PPSA = (5d0* NFI + 32d0* NFO + 49d0* NT+38d0* NS + 28d0* N + 8d0) # / (NM * NT * N1T * N2S) * 2d0 * PQGA = (-2d0* S1 * S1 + 2d0* S2 - 2d0* SSTR2P) # * (NS + N + 2d0) / (N * N1 * N2) # + (8d0* S1 * (2d0* N + 3d0)) / (N1S * N2S) # + 2d0* (NN + 6d0* NE + 15d0* NSE + 25d0* NSI + 36d0* NFI # + 85d0* NFO + 128d0* NT + 104d0* NS + 64d0* N + 16d0) # / (NM * NT * N1T * N2T) PQGB = (2d0* S1 * S1 - 2d0* S2 + 5d0) * (NS + N + 2d0) # / (N * N1 * N2) - 4d0* S1 / NS # + (11d0* NFO + 26d0* NT + 15d0* NS + 8d0* N + 4d0) # / (NT * N1T * N2) * * --------------------------------------------------------------------- * * ..GQ and GG * PGQA = (- S1 * S1 + 5d0* S1 - S2) * (NS + N + 2d0) # / (NM * N * N1) - 2d0* S1 / N1S # - (12d0* NSI + 30d0* NFI + 43d0* NFO + 28d0* NT - NS # - 12d0* N - 4d0) / (2d0* NM * NT * N1T) PGQB = (S1*S1 + S2 - SSTR2P) * (NS + N + 2d0) / (NM * N * N1) # - S1 * (17d0* NFO + 41d0* NS - 22d0* N - 12d0) # / (3d0* NMS * NS * N1) # + (109d0* NN + 621d0* NE + 1400d0* NSE + 1678d0* NSI # + 695d0* NFI - 1031d0* NFO - 1304d0* NT - 152d0* NS # + 432d0* N + 144d0) / (9d0* NMS * NT * N1T * N2S) PGQC = (S1 - 8d0/3d0) * (NS + N + 2d0) / (NM * N * N1) + 1d0/ N1S PGQC = 4d0/3d0* PGQC * PGGA = - (2d0* NFI + 5d0* NFO + 8d0* NT + 7d0* NS- 2d0* N - 2d0) # * 8d0* S1 / (NMS * NS * N1S * N2S) - 67d0/9d0* S1 + 8d0/3d0 # - 4d0* SSTR2P * (NS + N + 1d0) / (NM * N * N1 * N2) # + 2d0* S1 * SSTR2P - 4d0* SSCHLP + 0.5d0 * SSTR3P # + (457d0* NN + 2742d0* NE + 6040d0* NSE + 6098d0* NSI # + 1567d0* NFI - 2344d0* NFO - 1632d0* NT + 560d0* NS # + 1488d0* N + 576d0) / (18d0* NMS * NT * N1T * N2T) PGGB = (38d0* NFO + 76d0* NT + 94d0* NS + 56d0* N + 12d0) *(-2d0) # / (9d0* NM * NS * N1S * N2) + 20d0/9d0* S1 - 4d0/3d0 PGGC = (2d0* NSI + 4d0* NFI + NFO - 10d0* NT - 5d0* NS - 4d0* N # - 4d0) * (-2d0) / (NM * NT * N1T * N2) - 1d0 * * Output to the array * DO I=1,2 DO J=1,2 P1SG(I,J)=0d0 ENDDO ENDDO do I=1,3 P1NS(I)=0d0 enddo * * NON SINGLET * * Plus P1NS(1) = CF *((CF-CA/2d0)* PNPA + CA* PNSB + TR*dble(NF)* PNSC) * Minus=Valence P1NS(2) = CF *((CF-CA/2d0)* PNMA + CA* PNSB + TR*dble(NF)* PNSC) P1NS(3) = P1NS(2) * * SINGLET * P1SG(1,1) = P1NS(1) + TR*dble(NF)*CF*PPSA*4d0 P1SG(1,2) = TR*dble(NF) * (CA * PQGA + CF * PQGB)*4d0 P1SG(2,1) = (CF*CF*PGQA + CF*CA*PGQB+TR*dble(NF)*CF*PGQC)*4d0 P1SG(2,2) = (CA*CA*PGGA + TR*dble(NF)*(CA*PGGB+CF*PGGC))*4d0 * * --------------------------------------------------------------------- * * RETURN END * * =================================================================av==