/* Copyright (C) 1991-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see . */ /* This header is separate from features.h so that the compiler can include it implicitly at the start of every compilation. It must not itself include or any other header that includes because the implicit include comes before any feature test macros that may be defined in a source file before it first explicitly includes a system header. GCC knows the name of this header in order to preinclude it. */ /* We do support the IEC 559 math functionality, real and complex. */ /* wchar_t uses ISO/IEC 10646 (2nd ed., published 2011-03-15) / Unicode 6.0. */ /* We do not support C11 . */ FUNCTION FORMOM(XMAA,XMOM) C ================================================================== C formfactorfor pi-pi0 gamma final state C R. Decker, Z. Phys C36 (1987) 487. C ================================================================== COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMMON / DECPAR / GFERMI,GV,GA,CCABIB,SCABIB,GAMEL REAL*4 GFERMI,GV,GA,CCABIB,SCABIB,GAMEL COMMON /TESTA1/ KEYA1 COMPLEX BWIGN,FORMOM DATA ICONT /1/ * THIS INLINE FUNCT. CALCULATES THE SCALAR PART OF THE PROPAGATOR BWIGN(XM,AM,GAMMA)=1./CMPLX(XM**2-AM**2,GAMMA*AM) * HADRON CURRENT FRO =0.266*AMRO**2 ELPHA=- 0.1 AMROP = 1.7 GAMROP= 0.26 AMOM =0.782 GAMOM =0.0085 AROMEG= 1.0 GCOUP=12.924 GCOUP=GCOUP*AROMEG FQED =SQRT(4.0*3.1415926535/137.03604) FORMOM=FQED*FRO**2/SQRT(2.0)*GCOUP**2*BWIGN(XMOM,AMOM,GAMOM) $ *(BWIGN(XMAA,AMRO,GAMRO)+ELPHA*BWIGN(XMAA,AMROP,GAMROP)) $ *(BWIGN( 0.0,AMRO,GAMRO)+ELPHA*BWIGN( 0.0,AMROP,GAMROP)) END C======================================================================= COMPLEX FUNCTION FK1AB(XMSQ,INDX) C ================================================================== C complex form-factor for a1+a1prime. AJW 1/98 C ================================================================== COMPLEX F1,F2,AMPA,AMPB INTEGER IFIRST,INDX DATA IFIRST/0/ IF (IFIRST.EQ.0) THEN IFIRST = 1 XM1 = PKORB(1,19) XG1 = PKORB(2,19) XM2 = PKORB(1,20) XG2 = PKORB(2,20) XM1SQ = XM1*XM1 GF1 = GFUN(XM1SQ) GG1 = XM1*XG1/GF1 XM2SQ = XM2*XM2 GF2 = GFUN(XM2SQ) GG2 = XM2*XG2/GF2 END IF IF (INDX.EQ.1) THEN AMPA = CMPLX(PKORB(3,81),0.) AMPB = CMPLX(PKORB(3,82),0.) ELSE IF (INDX.EQ.2) THEN AMPA = CMPLX(PKORB(3,83),0.) AMPB = CMPLX(PKORB(3,84),0.) ELSEIF (INDX.EQ.3) THEN AMPA = CMPLX(PKORB(3,85),0.) AMPB = CMPLX(PKORB(3,86),0.) ELSEIF (INDX.EQ.4) THEN AMPA = CMPLX(PKORB(3,87),0.) AMPB = CMPLX(PKORB(3,88),0.) END IF GF = GFUN(XMSQ) FG1 = GG1*GF FG2 = GG2*GF F1 = CMPLX(-XM1SQ,0.0)/CMPLX(XMSQ-XM1SQ,FG1) F2 = CMPLX(-XM2SQ,0.0)/CMPLX(XMSQ-XM2SQ,FG2) FK1AB = AMPA*F1+AMPB*F2 RETURN END FUNCTION FORM1(MNUM,QQ,S1,SDWA) C ================================================================== C formfactorfor F1 for 3 scalar final state C R. Fisher, J. Wess and F. Wagner Z. Phys C3 (1980) 313 C H. Georgi, Weak interactions and modern particle theory, C The Benjamin/Cummings Pub. Co., Inc. 1984. C R. Decker, E. Mirkes, R. Sauer, Z. Was Karlsruhe preprint TTP92-25 C and erratum !!!!!! C ================================================================== C COMPLEX FORM1,WIGNER,WIGFOR,FPIKM,BWIGM COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMPLEX FORMA1,FORMK1,FORMRO,FORMKS COMPLEX FA1A1P,FK1AB,F3PI C IF (MNUM.EQ.0) THEN C ------------ 3 pi hadronic state (a1) C FORMRO = FPIKM(SQRT(S1),AMPI,AMPI) C FORMRO = F3PI(1,QQ,S1,SDWA) C FORMA1 = FA1A1P(QQ) C FORM1 = FORMA1*FORMRO FORM1 = F3PI(1,QQ,S1,SDWA) ELSEIF (MNUM.EQ.1) THEN C ------------ K- pi- K+ (K*0 K-) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPI,AMK) FORMA1 = FA1A1P(QQ) FORM1 = FORMA1*FORMKS ELSEIF (MNUM.EQ.2) THEN C ------------ K0 pi- K0B (K*- K0) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPI,AMK) FORMA1 = FA1A1P(QQ) FORM1 = FORMA1*FORMKS ELSEIF (MNUM.EQ.3) THEN C ------------ K- pi0 K0 (K*0 K-) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPI,AMK) FORMA1 = FA1A1P(QQ) FORM1 = FORMA1*FORMKS ELSEIF (MNUM.EQ.4) THEN C ------------ pi0 pi0 K- (K*-pi0) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPI,AMK) FORMK1 = FK1AB(QQ,3) FORM1 = FORMK1*FORMKS ELSEIF (MNUM.EQ.5) THEN C ------------ K- pi- pi+ (rho0 K-) FORMK1 = FK1AB(QQ,4) FORMRO = FPIKM(SQRT(S1),AMPI,AMPI) FORM1 = FORMK1*FORMRO ELSEIF (MNUM.EQ.6) THEN C ------------ pi- K0B pi0 (pi- K*0B) FORMK1 = FK1AB(QQ,1) FORMKS = BWIGM(S1,AMKST,GAMKST,AMK,AMPI) FORM1 = FORMK1*FORMKS ELSEIF (MNUM.EQ.7) THEN C -------------- eta pi- pi0 final state FORM1=0.0 ENDIF END FUNCTION FORM2(MNUM,QQ,S1,SDWA) C ================================================================== C formfactorfor F2 for 3 scalar final state C R. Fisher, J. Wess and F. Wagner Z. Phys C3 (1980) 313 C H. Georgi, Weak interactions and modern particle theory, C The Benjamin/Cummings Pub. Co., Inc. 1984. C R. Decker, E. Mirkes, R. Sauer, Z. Was Karlsruhe preprint TTP92-25 C and erratum !!!!!! C ================================================================== C COMPLEX FORM2,WIGNER,WIGFOR,FPIKM,BWIGM COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMPLEX FORMA1,FORMK1,FORMRO,FORMKS COMPLEX FA1A1P,FK1AB,F3PI IF (MNUM.EQ.0) THEN C ------------ 3 pi hadronic state (a1) C FORMRO = FPIKM(SQRT(S1),AMPI,AMPI) C FORMRO = F3PI(2,QQ,S1,SDWA) C FORMA1 = FA1A1P(QQ) C FORM2 = FORMA1*FORMRO FORM2 = F3PI(2,QQ,S1,SDWA) ELSEIF (MNUM.EQ.1) THEN C ------------ K- pi- K+ (rho0 pi-) FORMRO = FPIKM(SQRT(S1),AMK,AMK) FORMA1 = FA1A1P(QQ) FORM2 = FORMA1*FORMRO ELSEIF (MNUM.EQ.2) THEN C ------------ K0 pi- K0B (rho0 pi-) FORMRO = FPIKM(SQRT(S1),AMK,AMK) FORMA1 = FA1A1P(QQ) FORM2 = FORMA1*FORMRO ELSEIF (MNUM.EQ.3) THEN C ------------ K- pi0 K0 (rho- pi0) FORMRO = FPIKM(SQRT(S1),AMK,AMK) FORMA1 = FA1A1P(QQ) FORM2 = FORMA1*FORMRO ELSEIF (MNUM.EQ.4) THEN C ------------ pi0 pi0 K- (K*-pi0) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPI,AMK) FORMK1 = FK1AB(QQ,3) FORM2 = FORMK1*FORMKS ELSEIF (MNUM.EQ.5) THEN C ------------ K- pi- pi+ (K*0B pi-) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPI,AMK) FORMK1 = FK1AB(QQ,1) FORM2 = FORMK1*FORMKS C ELSEIF (MNUM.EQ.6) THEN C ------------ pi- K0B pi0 (rho- K0B) FORMRO = FPIKM(SQRT(S1),AMPI,AMPI) FORMK1 = FK1AB(QQ,2) FORM2 = FORMK1*FORMRO C ELSEIF (MNUM.EQ.7) THEN C -------------- eta pi- pi0 final state FORM2=0.0 ENDIF C END COMPLEX FUNCTION BWIGM(S,M,G,XM1,XM2) C ********************************************************** C P-WAVE BREIT-WIGNER FOR RHO C ********************************************************** REAL S,M,G,XM1,XM2 REAL PI,QS,QM,W,GS DATA INIT /0/ C ------------ PARAMETERS -------------------- IF (INIT.EQ.0) THEN INIT=1 PI=3.141592654 C ------- BREIT-WIGNER ----------------------- ENDIF IF (S.GT.(XM1+XM2)**2) THEN QS=SQRT(ABS((S -(XM1+XM2)**2)*(S -(XM1-XM2)**2)))/SQRT(S) QM=SQRT(ABS((M**2-(XM1+XM2)**2)*(M**2-(XM1-XM2)**2)))/M W=SQRT(S) GS=G*(M/W)**2*(QS/QM)**3 ELSE GS=0.0 ENDIF BWIGM=M**2/CMPLX(M**2-S,-SQRT(S)*GS) RETURN END COMPLEX FUNCTION FPIKM(W,XM1,XM2) C ********************************************************** C PION FORM FACTOR C ********************************************************** COMPLEX BWIGM REAL ROM,ROG,ROM1,ROG1,BETA1,PI,PIM,S,W EXTERNAL BWIG DATA INIT /0/ C C ------------ PARAMETERS -------------------- IF (INIT.EQ.0 ) THEN INIT=1 PI=3.141592654 PIM=.140 ROM=0.773 ROG=0.145 ROM1=1.370 ROG1=0.510 BETA1=-0.145 ENDIF C ----------------------------------------------- S=W**2 FPIKM=(BWIGM(S,ROM,ROG,XM1,XM2)+BETA1*BWIGM(S,ROM1,ROG1,XM1,XM2)) & /(1+BETA1) RETURN END COMPLEX FUNCTION FPIKMD(W,XM1,XM2) C ********************************************************** C PION FORM FACTOR C ********************************************************** COMPLEX BWIGM REAL ROM,ROG,ROM1,ROG1,PI,PIM,S,W EXTERNAL BWIG DATA INIT /0/ C C ------------ PARAMETERS -------------------- IF (INIT.EQ.0 ) THEN INIT=1 PI=3.141592654 PIM=.140 ROM=0.773 ROG=0.145 ROM1=1.500 ROG1=0.220 ROM2=1.750 ROG2=0.120 BETA=6.5 DELTA=-26.0 ENDIF C ----------------------------------------------- S=W**2 FPIKMD=(DELTA*BWIGM(S,ROM,ROG,XM1,XM2) $ +BETA*BWIGM(S,ROM1,ROG1,XM1,XM2) $ + BWIGM(S,ROM2,ROG2,XM1,XM2)) & /(1+BETA+DELTA) RETURN END FUNCTION FORM3(MNUM,QQ,S1,SDWA) C ================================================================== C formfactorfor F3 for 3 scalar final state C R. Fisher, J. Wess and F. Wagner Z. Phys C3 (1980) 313 C H. Georgi, Weak interactions and modern particle theory, C The Benjamin/Cummings Pub. Co., Inc. 1984. C R. Decker, E. Mirkes, R. Sauer, Z. Was Karlsruhe preprint TTP92-25 C and erratum !!!!!! C ================================================================== C COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMPLEX FORM3,BWIGM COMPLEX FORMA1,FORMK1,FORMRO,FORMKS COMPLEX FA1A1P,FK1AB,F3PI C IF (MNUM.EQ.0) THEN C ------------ 3 pi hadronic state (a1) C FORMRO = FPIKM(SQRT(S1),AMPI,AMPI) C FORMRO = F3PI(3,QQ,S1,SDWA) C FORMA1 = FA1A1P(QQ) C FORM3 = FORMA1*FORMRO FORM3 = F3PI(3,QQ,S1,SDWA) ELSEIF (MNUM.EQ.3) THEN C ------------ K- pi0 K0 (K*- K0) FORMKS = BWIGM(S1,AMKST,GAMKST,AMPIZ,AMK) FORMA1 = FA1A1P(QQ) FORM3 = FORMA1*FORMKS ELSEIF (MNUM.EQ.6) THEN C ------------ pi- K0B pi0 (K*- pi0) FORMKS = BWIGM(S1,AMKST,GAMKST,AMK,AMPI) FORMK1 = FK1AB(QQ,3) FORM3 = FORMK1*FORMKS ELSE FORM3=CMPLX(0.,0.) ENDIF END FUNCTION FORM4(MNUM,QQ,S1,S2,S3) C ================================================================== C formfactorfor F4 for 3 scalar final state C R. Decker, in preparation C R. Decker, E. Mirkes, R. Sauer, Z. Was Karlsruhe preprint TTP92-25 C and erratum !!!!!! C ================================================================== C COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMPLEX FORM4,WIGNER,FPIKM REAL*4 M C ---- this formfactor is switched off .. . FORM4=CMPLX(0.0,0.0) END FUNCTION FORM5(MNUM,QQ,S1,S2) C ================================================================== C formfactorfor F5 for 3 scalar final state C G. Kramer, W. Palmer, S. Pinsky, Phys. Rev. D30 (1984) 89. C G. Kramer, W. Palmer Z. Phys. C25 (1984) 195. C R. Decker, E. Mirkes, R. Sauer, Z. Was Karlsruhe preprint TTP92-25 C and erratum !!!!!! C ================================================================== C COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMPLEX FORM5,WIGNER,FPIKM,FPIKMD,BWIGM IF (MNUM.EQ.0) THEN C ------------ 3 pi hadronic state (a1) FORM5=0.0 ELSEIF (MNUM.EQ.1) THEN C ------------ K- pi- K+ ELPHA=-0.2 FORM5=FPIKMD(SQRT(QQ),AMPI,AMPI)/(1+ELPHA) $ *( FPIKM(SQRT(S2),AMPI,AMPI) $ +ELPHA*BWIGM(S1,AMKST,GAMKST,AMPI,AMK)) ELSEIF (MNUM.EQ.2) THEN C ------------ K0 pi- K0B ELPHA=-0.2 FORM5=FPIKMD(SQRT(QQ),AMPI,AMPI)/(1+ELPHA) $ *( FPIKM(SQRT(S2),AMPI,AMPI) $ +ELPHA*BWIGM(S1,AMKST,GAMKST,AMPI,AMK)) ELSEIF (MNUM.EQ.3) THEN C ------------ K- K0 pi0 FORM5=0.0 ELSEIF (MNUM.EQ.4) THEN C ------------ pi0 pi0 K- FORM5=0.0 ELSEIF (MNUM.EQ.5) THEN C ------------ K- pi- pi+ ELPHA=-0.2 FORM5=BWIGM(QQ,AMKST,GAMKST,AMPI,AMK)/(1+ELPHA) $ *( FPIKM(SQRT(S1),AMPI,AMPI) $ +ELPHA*BWIGM(S2,AMKST,GAMKST,AMPI,AMK)) ELSEIF (MNUM.EQ.6) THEN C ------------ pi- K0B pi0 ELPHA=-0.2 FORM5=BWIGM(QQ,AMKST,GAMKST,AMPI,AMKZ)/(1+ELPHA) $ *( FPIKM(SQRT(S2),AMPI,AMPI) $ +ELPHA*BWIGM(S1,AMKST,GAMKST,AMPI,AMK)) ELSEIF (MNUM.EQ.7) THEN C -------------- eta pi- pi0 final state FORM5=FPIKMD(SQRT(QQ),AMPI,AMPI)*FPIKM(SQRT(S1),AMPI,AMPI) ENDIF C END SUBROUTINE CURRX(MNUM,PIM1,PIM2,PIM3,PIM4,HADCUR) C ================================================================== C hadronic current for 4 pi final state C R. Fisher, J. Wess and F. Wagner Z. Phys C3 (1980) 313 C R. Decker Z. Phys C36 (1987) 487. C M. Gell-Mann, D. Sharp, W. Wagner Phys. Rev. Lett 8 (1962) 261. C ================================================================== COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMMON / DECPAR / GFERMI,GV,GA,CCABIB,SCABIB,GAMEL REAL*4 GFERMI,GV,GA,CCABIB,SCABIB,GAMEL C ARBITRARY FIXING OF THE FOUR PI X-SECTION NORMALIZATION COMMON /ARBIT/ ARFLAT,AROMEG REAL PIM1(4),PIM2(4),PIM3(4),PIM4(4),PAA(4) COMPLEX HADCUR(4),FORM1,FORM2,FORM3,FPIKM COMPLEX BWIGN REAL PA(4),PB(4) REAL AA(4,4),PP(4,4) DATA PI /3.141592653589793238462643/ DATA FPI /93.3E-3/ BWIGN(A,XM,XG)=1.0/CMPLX(A-XM**2,XM*XG) C C --- masses and constants G1=12.924 G2=1475.98 G =G1*G2 ELPHA=-.1 AMROP=1.7 GAMROP=0.26 AMOM=.782 GAMOM=0.0085 ARFLAT=1.0 AROMEG=1.0 C FRO=0.266*AMRO**2 COEF1=2.0*SQRT(3.0)/FPI**2*ARFLAT COEF2=FRO*G*AROMEG C --- initialization of four vectors DO 7 K=1,4 DO 8 L=1,4 8 AA(K,L)=0.0 HADCUR(K)=CMPLX(0.0) PAA(K)=PIM1(K)+PIM2(K)+PIM3(K)+PIM4(K) PP(1,K)=PIM1(K) PP(2,K)=PIM2(K) PP(3,K)=PIM3(K) 7 PP(4,K)=PIM4(K) C IF (MNUM.EQ.1) THEN C =================================================================== C pi- pi- p0 pi+ case ==== C =================================================================== QQ=PAA(4)**2-PAA(3)**2-PAA(2)**2-PAA(1)**2 C --- loop over thre contribution of the non-omega current DO 201 K=1,3 SK=(PP(K,4)+PIM4(4))**2-(PP(K,3)+PIM4(3))**2 $ -(PP(K,2)+PIM4(2))**2-(PP(K,1)+PIM4(1))**2 C -- definition of AA matrix C -- cronecker delta DO 202 I=1,4 DO 203 J=1,4 203 AA(I,J)=0.0 202 AA(I,I)=1.0 C ... and the rest ... DO 204 L=1,3 IF (L.NE.K) THEN DENOM=(PAA(4)-PP(L,4))**2-(PAA(3)-PP(L,3))**2 $ -(PAA(2)-PP(L,2))**2-(PAA(1)-PP(L,1))**2 DO 205 I=1,4 DO 205 J=1,4 SIG= 1.0 IF(J.NE.4) SIG=-SIG AA(I,J)=AA(I,J) $ -SIG*(PAA(I)-2.0*PP(L,I))*(PAA(J)-PP(L,J))/DENOM 205 CONTINUE ENDIF 204 CONTINUE C --- lets add something to HADCURR FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKM(SQRT(QQ),AMPI,AMPI) C FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKMD(SQRT(QQ),AMPI,AMPI) CCCCCCCCCCCCCCCCC FORM1=WIGFOR(SK,AMRO,GAMRO) (tests) C FIX=1.0 IF (K.EQ.3) FIX=-2.0 DO 206 I=1,4 DO 206 J=1,4 HADCUR(I)= $ HADCUR(I)+CMPLX(FIX*COEF1)*FORM1*AA(I,J)*(PP(K,J)-PP(4,J)) 206 CONTINUE C --- end of the non omega current (3 possibilities) 201 CONTINUE C C C --- there are two possibilities for omega current C --- PA PB are corresponding first and second pi-s DO 301 KK=1,2 DO 302 I=1,4 PA(I)=PP(KK,I) PB(I)=PP(3-KK,I) 302 CONTINUE C --- lorentz invariants QQA=0.0 SS23=0.0 SS24=0.0 SS34=0.0 QP1P2=0.0 QP1P3=0.0 QP1P4=0.0 P1P2 =0.0 P1P3 =0.0 P1P4 =0.0 DO 303 K=1,4 SIGN=-1.0 IF (K.EQ.4) SIGN= 1.0 QQA=QQA+SIGN*(PAA(K)-PA(K))**2 SS23=SS23+SIGN*(PB(K) +PIM3(K))**2 SS24=SS24+SIGN*(PB(K) +PIM4(K))**2 SS34=SS34+SIGN*(PIM3(K)+PIM4(K))**2 QP1P2=QP1P2+SIGN*(PAA(K)-PA(K))*PB(K) QP1P3=QP1P3+SIGN*(PAA(K)-PA(K))*PIM3(K) QP1P4=QP1P4+SIGN*(PAA(K)-PA(K))*PIM4(K) P1P2=P1P2+SIGN*PA(K)*PB(K) P1P3=P1P3+SIGN*PA(K)*PIM3(K) P1P4=P1P4+SIGN*PA(K)*PIM4(K) 303 CONTINUE C FORM2=COEF2*(BWIGN(QQ,AMRO,GAMRO)+ELPHA*BWIGN(QQ,AMROP,GAMROP)) C FORM3=BWIGN(QQA,AMOM,GAMOM)*(BWIGN(SS23,AMRO,GAMRO)+ C $ BWIGN(SS24,AMRO,GAMRO)+BWIGN(SS34,AMRO,GAMRO)) FORM3=BWIGN(QQA,AMOM,GAMOM) C DO 304 K=1,4 HADCUR(K)=HADCUR(K)+FORM2*FORM3*( $ PB (K)*(QP1P3*P1P4-QP1P4*P1P3) $ +PIM3(K)*(QP1P4*P1P2-QP1P2*P1P4) $ +PIM4(K)*(QP1P2*P1P3-QP1P3*P1P2) ) 304 CONTINUE 301 CONTINUE C ELSE C =================================================================== C pi0 pi0 p0 pi- case ==== C =================================================================== QQ=PAA(4)**2-PAA(3)**2-PAA(2)**2-PAA(1)**2 DO 101 K=1,3 C --- loop over thre contribution of the non-omega current SK=(PP(K,4)+PIM4(4))**2-(PP(K,3)+PIM4(3))**2 $ -(PP(K,2)+PIM4(2))**2-(PP(K,1)+PIM4(1))**2 C -- definition of AA matrix C -- cronecker delta DO 102 I=1,4 DO 103 J=1,4 103 AA(I,J)=0.0 102 AA(I,I)=1.0 C C ... and the rest ... DO 104 L=1,3 IF (L.NE.K) THEN DENOM=(PAA(4)-PP(L,4))**2-(PAA(3)-PP(L,3))**2 $ -(PAA(2)-PP(L,2))**2-(PAA(1)-PP(L,1))**2 DO 105 I=1,4 DO 105 J=1,4 SIG=1.0 IF(J.NE.4) SIG=-SIG AA(I,J)=AA(I,J) $ -SIG*(PAA(I)-2.0*PP(L,I))*(PAA(J)-PP(L,J))/DENOM 105 CONTINUE ENDIF 104 CONTINUE C --- lets add something to HADCURR FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKM(SQRT(QQ),AMPI,AMPI) C FORM1= FPIKM(SQRT(SK),AMPI,AMPI) *FPIKMD(SQRT(QQ),AMPI,AMPI) CCCCCCCCCCCCC FORM1=WIGFOR(SK,AMRO,GAMRO) (tests) DO 106 I=1,4 DO 106 J=1,4 HADCUR(I)= $ HADCUR(I)+CMPLX(COEF1)*FORM1*AA(I,J)*(PP(K,J)-PP(4,J)) 106 CONTINUE C --- end of the non omega current (3 possibilities) 101 CONTINUE ENDIF END FUNCTION WIGFOR(S,XM,XGAM) COMPLEX WIGFOR,WIGNOR WIGNOR=CMPLX(-XM**2,XM*XGAM) WIGFOR=WIGNOR/CMPLX(S-XM**2,XM*XGAM) END SUBROUTINE CURINF C HERE the form factors of M. Finkemeier et al. start C it ends with the string: M. Finkemeier et al. END COMMON /INOUT/ INUT, IOUT WRITE (UNIT = IOUT,FMT = 99) WRITE (UNIT = IOUT,FMT = 98) c print *, 'here is curinf' 99 FORMAT( . /, ' *************************************************** ', . /, ' YOU ARE USING THE 4 PION DECAY MODE FORM FACTORS ', . /, ' WHICH HAVE BEEN DESCRIBED IN:', . /, ' R. DECKER, M. FINKEMEIER, P. HEILIGER AND H.H. JONSSON', . /, ' "TAU DECAYS INTO FOUR PIONS" ', . /, ' UNIVERSITAET KARLSRUHE PREPRINT TTP 94-13 (1994);', . /, ' LNF-94/066(IR); HEP-PH/9410260 ', . /, ' ', . /, ' PLEASE NOTE THAT THIS ROUTINE IS USING PARAMETERS', . /, ' RELATED TO THE 3 PION DECAY MODE (A1 MODE), SUCH AS', . /, ' THE A1 MASS AND WIDTH (TAKEN FROM THE COMMON /PARMAS/)', . /, ' AND THE 2 PION VECTOR RESONANCE FORM FACTOR (BY USING', . /, ' THE ROUTINE FPIKM)' , . /, ' THUS IF YOU DECIDE TO CHANGE ANY OF THESE, YOU WILL' , . /, ' HAVE TO REFIT THE 4 PION PARAMETERS IN THE COMMON' ) 98 FORMAT( . ' BLOCK /TAU4PI/, OR YOU MIGHT GET A BAD DISCRIPTION' , . /, ' OF TAU -> 4 PIONS' , . /, ' for these formfactors set in routine CHOICE for', . /, ' mnum.eq.102 -- AMRX=1.42 and GAMRX=.21', . /, ' mnum.eq.101 -- AMRX=1.3 and GAMRX=.46 PROB1,PROB2=0.2', . /, ' to optimize phase space parametrization', . /, ' *************************************************** ', . /, ' coded by M. Finkemeier and P. Heiliger, 29. sept. 1994', . /, ' incorporated to TAUOLA by Z. Was 17. jan. 1995', c . /, ' fitted on (day/month/year) by ... ', c . /, ' to .... data ', . /, ' changed by: Z. Was on 17.01.95', . /, ' changes by: M. Finkemeier on 30.01.95' ) END C SUBROUTINE CURINI COMMON /TAU4PI/ GOMEGA,GAMMA1,GAMMA2,ROM1,ROG1,BETA1, . ROM2,ROG2,BETA2 REAL*4 GOMEGA,GAMMA1,GAMMA2,ROM1,ROG1,BETA1, . ROM2,ROG2,BETA2 GOMEGA = 1.4 GAMMA1 = 0.38 GAMMA2 = 0.38 ROM1 = 1.35 ROG1 = 0.3 BETA1 = 0.08 ROM2 = 1.70 ROG2 = 0.235 BETA2 = -0.0075 END COMPLEX FUNCTION BWIGA1(QA) C ================================================================ C breit-wigner enhancement of a1 C ================================================================ COMPLEX WIGNER COMMON / PARMAS/ AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU, % AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1, % AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU, % AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1, % AMK,AMKZ,AMKST,GAMKST WIGNER(A,B,C)=CMPLX(1.0,0.0)/CMPLX(A-B**2,B*C) GAMAX=GAMA1*GFUN(QA)/GFUN(AMA1**2) BWIGA1=-AMA1**2*WIGNER(QA,AMA1,GAMAX) RETURN END COMPLEX FUNCTION BWIGEPS(QEPS) C ============================================================= C breit-wigner enhancement of epsilon C ============================================================= REAL QEPS,MEPS,GEPS MEPS=1.300 GEPS=.600 BWIGEPS=CMPLX(MEPS**2,-MEPS*GEPS)/ % CMPLX(MEPS**2-QEPS,-MEPS*GEPS) RETURN END COMPLEX FUNCTION FRHO4(W,XM1,XM2) C =========================================================== C rho-type resonance factor with higher radials, to be used C by CURR for the four pion mode C =========================================================== COMPLEX BWIGM COMMON /TAU4PI/ GOMEGA,GAMMA1,GAMMA2,ROM1,ROG1,BETA1, . ROM2,ROG2,BETA2 REAL*4 GOMEGA,GAMMA1,GAMMA2,ROM1,ROG1,BETA1, . ROM2,ROG2,BETA2 REAL ROM,ROG,PI,PIM,S,W EXTERNAL BWIG DATA INIT /0/ C C ------------ PARAMETERS -------------------- IF (INIT.EQ.0 ) THEN INIT=1 PI=3.141592654 PIM=.140 ROM=0.773 ROG=0.145 ENDIF C ----------------------------------------------- S=W**2 c print *,'rom2,rog2 =',rom2,rog2 FRHO4=(BWIGM(S,ROM,ROG,XM1,XM2)+BETA1*BWIGM(S,ROM1,ROG1,XM1,XM2) & +BETA2*BWIGM(S,ROM2,ROG2,XM1,XM2)) & /(1+BETA1+BETA2) RETURN END SUBROUTINE CURR(MNUM,PIM1,PIM2,PIM3,PIM4,HADCUR) C ================================================================== C Hadronic current for 4 pi final state, according to: C R. Decker, M. Finkemeier, P. Heiliger, H.H.Jonsson, TTP94-13 C C See also: C R. Fisher, J. Wess and F. Wagner Z. Phys C3 (1980) 313 C R. Decker Z. Phys C36 (1987) 487. C M. Gell-Mann, D. Sharp, W. Wagner Phys. Rev. Lett 8 (1962) 261. C ================================================================== COMMON /TAU4PI/ GOMEGA,GAMMA1,GAMMA2,ROM1,ROG1,BETA1, . ROM2,ROG2,BETA2 REAL*4 GOMEGA,GAMMA1,GAMMA2,ROM1,ROG1,BETA1, . ROM2,ROG2,BETA2 COMMON / PARMAS / AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST C REAL*4 AMTAU,AMNUTA,AMEL,AMNUE,AMMU,AMNUMU * ,AMPIZ,AMPI,AMRO,GAMRO,AMA1,GAMA1 * ,AMK,AMKZ,AMKST,GAMKST COMMON / DECPAR / GFERMI,GV,GA,CCABIB,SCABIB,GAMEL REAL*4 GFERMI,GV,GA,CCABIB,SCABIB,GAMEL REAL PIM1(4),PIM2(4),PIM3(4),PIM4(4),PAA(4) COMPLEX HADCUR(4),FORM1,FORM2,FORM3,FPIKM COMPLEX BWIGN,FRHO4 COMPLEX BWIGEPS,BWIGA1 COMPLEX HCOMP1(4),HCOMP2(4),HCOMP3(4),HCOMP4(4) COMPLEX T243,T213,T143,T123,T341,T342 COMPLEX T124,T134,T214,T234,T314,T324 COMPLEX S2413,S2314,S1423,S1324,S34 COMPLEX S2431,S3421 COMPLEX BRACK1,BRACK2,BRACK3,BRACK4A,BRACK4B,BRACK4 REAL QMP1,QMP2,QMP3,QMP4 REAL PS43,PS41,PS42,PS34,PS14,PS13,PS24,PS23 REAL PS21,PS31 REAL PD243,PD241,PD213,PD143,PD142 REAL PD123,PD341,PD342,PD413,PD423 REAL PD124,PD134,PD214,PD234,PD314,PD324 REAL QP1,QP2,QP3,QP4 REAL PA(4),PB(4) REAL AA(4,4),PP(4,4) DATA PI /3.141592653589793238462643/ DATA FPI /93.3E-3/ DATA INIT /0/ BWIGN(A,XM,XG)=1.0/CMPLX(A-XM**2,XM*XG) C IF (INIT.EQ.0) THEN CALL CURINI CALL CURINF INIT = 1 ENDIF C C --- MASSES AND CONSTANTS G1=12.924 G2=1475.98 * GOMEGA G =G1*G2 ELPHA=-.1 AMROP=1.7 GAMROP=0.26 AMOM=.782 GAMOM=0.0085 ARFLAT=1.0 AROMEG=1.0 C FRO=0.266*AMRO**2 COEF1=2.0*SQRT(3.0)/FPI**2*ARFLAT COEF2=FRO*G*AROMEG C --- INITIALIZATION OF FOUR VECTORS DO 7 K=1,4 DO 8 L=1,4 8 AA(K,L)=0.0 HADCUR(K)=CMPLX(0.0) PAA(K)=PIM1(K)+PIM2(K)+PIM3(K)+PIM4(K) PP(1,K)=PIM1(K) PP(2,K)=PIM2(K) PP(3,K)=PIM3(K) 7 PP(4,K)=PIM4(K) C IF (MNUM.EQ.1) THEN C =================================================================== C PI- PI- P0 PI+ CASE ==== C =================================================================== QQ=PAA(4)**2-PAA(3)**2-PAA(2)**2-PAA(1)**2 C FIRST DEFINITION OF SCALAR PRODUCTS OF MOMENTUM VECTORS C DEFINE (Q-PI)**2 AS QPI: QMP1=(PIM2(4)+PIM3(4)+PIM4(4))**2-(PIM2(3)+PIM3(3)+PIM4(3))**2 % -(PIM2(2)+PIM3(2)+PIM4(2))**2-(PIM2(1)+PIM3(1)+PIM4(1))**2 QMP2=(PIM1(4)+PIM3(4)+PIM4(4))**2-(PIM1(3)+PIM3(3)+PIM4(3))**2 % -(PIM1(2)+PIM3(2)+PIM4(2))**2-(PIM1(1)+PIM3(1)+PIM4(1))**2 QMP3=(PIM1(4)+PIM2(4)+PIM4(4))**2-(PIM1(3)+PIM2(3)+PIM4(3))**2 % -(PIM1(2)+PIM2(2)+PIM4(2))**2-(PIM1(1)+PIM2(1)+PIM4(1))**2 QMP4=(PIM1(4)+PIM2(4)+PIM3(4))**2-(PIM1(3)+PIM2(3)+PIM3(3))**2 % -(PIM1(2)+PIM2(2)+PIM3(2))**2-(PIM1(1)+PIM2(1)+PIM3(1))**2 C DEFINE (PI+PK)**2 AS PSIK: PS43=(PIM4(4)+PIM3(4))**2-(PIM4(3)+PIM3(3))**2 % -(PIM4(2)+PIM3(2))**2-(PIM4(1)+PIM3(1))**2 PS41=(PIM4(4)+PIM1(4))**2-(PIM4(3)+PIM1(3))**2 % -(PIM4(2)+PIM1(2))**2-(PIM4(1)+PIM1(1))**2 PS42=(PIM4(4)+PIM2(4))**2-(PIM4(3)+PIM2(3))**2 % -(PIM4(2)+PIM2(2))**2-(PIM4(1)+PIM2(1))**2 PS34=PS43 PS14=PS41 PS13=(PIM1(4)+PIM3(4))**2-(PIM1(3)+PIM3(3))**2 % -(PIM1(2)+PIM3(2))**2-(PIM1(1)+PIM3(1))**2 PS24=PS42 PS23=(PIM2(4)+PIM3(4))**2-(PIM2(3)+PIM3(3))**2 % -(PIM2(2)+PIM3(2))**2-(PIM2(1)+PIM3(1))**2 PD243=PIM2(4)*(PIM4(4)-PIM3(4))-PIM2(3)*(PIM4(3)-PIM3(3)) % -PIM2(2)*(PIM4(2)-PIM3(2))-PIM2(1)*(PIM4(1)-PIM3(1)) PD241=PIM2(4)*(PIM4(4)-PIM1(4))-PIM2(3)*(PIM4(3)-PIM1(3)) % -PIM2(2)*(PIM4(2)-PIM1(2))-PIM2(1)*(PIM4(1)-PIM1(1)) PD213=PIM2(4)*(PIM1(4)-PIM3(4))-PIM2(3)*(PIM1(3)-PIM3(3)) % -PIM2(2)*(PIM1(2)-PIM3(2))-PIM2(1)*(PIM1(1)-PIM3(1)) PD143=PIM1(4)*(PIM4(4)-PIM3(4))-PIM1(3)*(PIM4(3)-PIM3(3)) % -PIM1(2)*(PIM4(2)-PIM3(2))-PIM1(1)*(PIM4(1)-PIM3(1)) PD142=PIM1(4)*(PIM4(4)-PIM2(4))-PIM1(3)*(PIM4(3)-PIM2(3)) % -PIM1(2)*(PIM4(2)-PIM2(2))-PIM1(1)*(PIM4(1)-PIM2(1)) PD123=PIM1(4)*(PIM2(4)-PIM3(4))-PIM1(3)*(PIM2(3)-PIM3(3)) % -PIM1(2)*(PIM2(2)-PIM3(2))-PIM1(1)*(PIM2(1)-PIM3(1)) PD341=PIM3(4)*(PIM4(4)-PIM1(4))-PIM3(3)*(PIM4(3)-PIM1(3)) % -PIM3(2)*(PIM4(2)-PIM1(2))-PIM3(1)*(PIM4(1)-PIM1(1)) PD342=PIM3(4)*(PIM4(4)-PIM2(4))-PIM3(3)*(PIM4(3)-PIM2(3)) % -PIM3(2)*(PIM4(2)-PIM2(2))-PIM3(1)*(PIM4(1)-PIM2(1)) PD413=PIM4(4)*(PIM1(4)-PIM3(4))-PIM4(3)*(PIM1(3)-PIM3(3)) % -PIM4(2)*(PIM1(2)-PIM3(2))-PIM4(1)*(PIM1(1)-PIM3(1)) PD423=PIM4(4)*(PIM2(4)-PIM3(4))-PIM4(3)*(PIM2(3)-PIM3(3)) % -PIM4(2)*(PIM2(2)-PIM3(2))-PIM4(1)*(PIM2(1)-PIM3(1)) C DEFINE Q*PI = QPI: QP1=PIM1(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM1(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM1(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM1(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) QP2=PIM2(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM2(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM2(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM2(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) QP3=PIM3(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM3(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM3(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM3(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) QP4=PIM4(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM4(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM4(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM4(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) C DEFINE T(PI;PJ,PK)= TIJK: T243=BWIGA1(QMP2)*FPIKM(SQRT(PS43),AMPI,AMPI)*GAMMA1 T213=BWIGA1(QMP2)*FPIKM(SQRT(PS13),AMPI,AMPI)*GAMMA1 T143=BWIGA1(QMP1)*FPIKM(SQRT(PS43),AMPI,AMPI)*GAMMA1 T123=BWIGA1(QMP1)*FPIKM(SQRT(PS23),AMPI,AMPI)*GAMMA1 T341=BWIGA1(QMP3)*FPIKM(SQRT(PS41),AMPI,AMPI)*GAMMA1 T342=BWIGA1(QMP3)*FPIKM(SQRT(PS42),AMPI,AMPI)*GAMMA1 C DEFINE S(I,J;K,L)= SIJKL: S2413=FRHO4(SQRT(PS24),AMPI,AMPI)*GAMMA2 S2314=FRHO4(SQRT(PS23),AMPI,AMPI)*BWIGEPS(PS14)*GAMMA2 S1423=FRHO4(SQRT(PS14),AMPI,AMPI)*GAMMA2 S1324=FRHO4(SQRT(PS13),AMPI,AMPI)*BWIGEPS(PS24)*GAMMA2 S34=FRHO4(SQRT(PS34),AMPI,AMPI)*GAMMA2 C DEFINITION OF AMPLITUDE, FIRST THE [] BRACKETS: BRACK1=2.*T143+2.*T243+T123+T213 % +T341*(PD241/QMP3-1.)+T342*(PD142/QMP3-1.) % +3./4.*(S1423+S2413-S2314-S1324)-3.*S34 BRACK2=2.*T143*PD243/QMP1+3.*T213 % +T123*(2.*PD423/QMP1+1.)+T341*(PD241/QMP3+3.) % +T342*(PD142/QMP3+1.) % -3./4.*(S2314+3.*S1324+3.*S1423+S2413) BRACK3=2.*T243*PD143/QMP2+3.*T123 % +T213*(2.*PD413/QMP2+1.)+T341*(PD241/QMP3+1.) % +T342*(PD142/QMP3+3.) % -3./4.*(3.*S2314+S1324+S1423+3.*S2413) BRACK4A=2.*T143*(PD243/QQ*(QP1/QMP1+1.)+PD143/QQ) % +2.*T243*(PD143/QQ*(QP2/QMP2+1.)+PD243/QQ) % +T123+T213 % +2.*T123*(PD423/QQ*(QP1/QMP1+1.)+PD123/QQ) % +2.*T213*(PD413/QQ*(QP2/QMP2+1.)+PD213/QQ) % +T341*(PD241/QMP3+1.-2.*PD241/QQ*(QP3/QMP3+1.) % -2.*PD341/QQ) % +T342*(PD142/QMP3+1.-2.*PD142/QQ*(QP3/QMP3+1.) % -2.*PD342/QQ) BRACK4B=-3./4.*(S2314*(2.*(QP2-QP3)/QQ+1.) % +S1324*(2.*(QP1-QP3)/QQ+1.) % +S1423*(2.*(QP1-QP4)/QQ+1.) % +S2413*(2.*(QP2-QP4)/QQ+1.) % +4.*S34*(QP4-QP3)/QQ) BRACK4=BRACK4A+BRACK4B DO 208 K=1,4 HCOMP1(K)=(PIM3(K)-PIM4(K))*BRACK1 HCOMP2(K)=PIM1(K)*BRACK2 HCOMP3(K)=PIM2(K)*BRACK3 HCOMP4(K)=(PIM1(K)+PIM2(K)+PIM3(K)+PIM4(K))*BRACK4 208 CONTINUE DO 209 I=1,4 HADCUR(I)=HCOMP1(I)-HCOMP2(I)-HCOMP3(I)+HCOMP4(I) HADCUR(I)=-COEF1*FRHO4(SQRT(QQ),AMPI,AMPI)*HADCUR(I) 209 CONTINUE C --- END OF THE NON OMEGA CURRENT (3 POSSIBILITIES) 201 CONTINUE C C C --- THERE ARE TWO POSSIBILITIES FOR OMEGA CURRENT C --- PA PB ARE CORRESPONDING FIRST AND SECOND PI-S DO 301 KK=1,2 DO 302 I=1,4 PA(I)=PP(KK,I) PB(I)=PP(3-KK,I) 302 CONTINUE C --- LORENTZ INVARIANTS QQA=0.0 SS23=0.0 SS24=0.0 SS34=0.0 QP1P2=0.0 QP1P3=0.0 QP1P4=0.0 P1P2 =0.0 P1P3 =0.0 P1P4 =0.0 DO 303 K=1,4 SIGN=-1.0 IF (K.EQ.4) SIGN= 1.0 QQA=QQA+SIGN*(PAA(K)-PA(K))**2 SS23=SS23+SIGN*(PB(K) +PIM3(K))**2 SS24=SS24+SIGN*(PB(K) +PIM4(K))**2 SS34=SS34+SIGN*(PIM3(K)+PIM4(K))**2 QP1P2=QP1P2+SIGN*(PAA(K)-PA(K))*PB(K) QP1P3=QP1P3+SIGN*(PAA(K)-PA(K))*PIM3(K) QP1P4=QP1P4+SIGN*(PAA(K)-PA(K))*PIM4(K) P1P2=P1P2+SIGN*PA(K)*PB(K) P1P3=P1P3+SIGN*PA(K)*PIM3(K) P1P4=P1P4+SIGN*PA(K)*PIM4(K) 303 CONTINUE C FORM2=COEF2*(BWIGN(QQ,AMRO,GAMRO)+ELPHA*BWIGN(QQ,AMROP,GAMROP)) C FORM3=BWIGN(QQA,AMOM,GAMOM)*(BWIGN(SS23,AMRO,GAMRO)+ C $ BWIGN(SS24,AMRO,GAMRO)+BWIGN(SS34,AMRO,GAMRO)) FORM3=BWIGN(QQA,AMOM,GAMOM) C DO 304 K=1,4 HADCUR(K)=HADCUR(K)+FORM2*FORM3*( $ PB (K)*(QP1P3*P1P4-QP1P4*P1P3) $ +PIM3(K)*(QP1P4*P1P2-QP1P2*P1P4) $ +PIM4(K)*(QP1P2*P1P3-QP1P3*P1P2) ) 304 CONTINUE 301 CONTINUE C ELSE C =================================================================== C PI0 PI0 P0 PI- CASE ==== C =================================================================== QQ=PAA(4)**2-PAA(3)**2-PAA(2)**2-PAA(1)**2 C FIRST DEFINITION OF SCALAR PRODUCTS OF MOMENTUM VECTORS C DEFINE (Q-PI)**2 AS QPI: QMP1=(PIM2(4)+PIM3(4)+PIM4(4))**2-(PIM2(3)+PIM3(3)+PIM4(3))**2 % -(PIM2(2)+PIM3(2)+PIM4(2))**2-(PIM2(1)+PIM3(1)+PIM4(1))**2 QMP2=(PIM1(4)+PIM3(4)+PIM4(4))**2-(PIM1(3)+PIM3(3)+PIM4(3))**2 % -(PIM1(2)+PIM3(2)+PIM4(2))**2-(PIM1(1)+PIM3(1)+PIM4(1))**2 QMP3=(PIM1(4)+PIM2(4)+PIM4(4))**2-(PIM1(3)+PIM2(3)+PIM4(3))**2 % -(PIM1(2)+PIM2(2)+PIM4(2))**2-(PIM1(1)+PIM2(1)+PIM4(1))**2 QMP4=(PIM1(4)+PIM2(4)+PIM3(4))**2-(PIM1(3)+PIM2(3)+PIM3(3))**2 % -(PIM1(2)+PIM2(2)+PIM3(2))**2-(PIM1(1)+PIM2(1)+PIM3(1))**2 C DEFINE (PI+PK)**2 AS PSIK: PS14=(PIM1(4)+PIM4(4))**2-(PIM1(3)+PIM4(3))**2 % -(PIM1(2)+PIM4(2))**2-(PIM1(1)+PIM4(1))**2 PS21=(PIM2(4)+PIM1(4))**2-(PIM2(3)+PIM1(3))**2 % -(PIM2(2)+PIM1(2))**2-(PIM2(1)+PIM1(1))**2 PS23=(PIM2(4)+PIM3(4))**2-(PIM2(3)+PIM3(3))**2 % -(PIM2(2)+PIM3(2))**2-(PIM2(1)+PIM3(1))**2 PS24=(PIM2(4)+PIM4(4))**2-(PIM2(3)+PIM4(3))**2 % -(PIM2(2)+PIM4(2))**2-(PIM2(1)+PIM4(1))**2 PS31=(PIM3(4)+PIM1(4))**2-(PIM3(3)+PIM1(3))**2 % -(PIM3(2)+PIM1(2))**2-(PIM3(1)+PIM1(1))**2 PS34=(PIM3(4)+PIM4(4))**2-(PIM3(3)+PIM4(3))**2 % -(PIM3(2)+PIM4(2))**2-(PIM3(1)+PIM4(1))**2 PD324=PIM3(4)*(PIM2(4)-PIM4(4))-PIM3(3)*(PIM2(3)-PIM4(3)) % -PIM3(2)*(PIM2(2)-PIM4(2))-PIM3(1)*(PIM2(1)-PIM4(1)) PD314=PIM3(4)*(PIM1(4)-PIM4(4))-PIM3(3)*(PIM1(3)-PIM4(3)) % -PIM3(2)*(PIM1(2)-PIM4(2))-PIM3(1)*(PIM1(1)-PIM4(1)) PD234=PIM2(4)*(PIM3(4)-PIM4(4))-PIM2(3)*(PIM3(3)-PIM4(3)) % -PIM2(2)*(PIM3(2)-PIM4(2))-PIM2(1)*(PIM3(1)-PIM4(1)) PD214=PIM2(4)*(PIM1(4)-PIM4(4))-PIM2(3)*(PIM1(3)-PIM4(3)) % -PIM2(2)*(PIM1(2)-PIM4(2))-PIM2(1)*(PIM1(1)-PIM4(1)) PD134=PIM1(4)*(PIM3(4)-PIM4(4))-PIM1(3)*(PIM3(3)-PIM4(3)) % -PIM1(2)*(PIM3(2)-PIM4(2))-PIM1(1)*(PIM3(1)-PIM4(1)) PD124=PIM1(4)*(PIM2(4)-PIM4(4))-PIM1(3)*(PIM2(3)-PIM4(3)) % -PIM1(2)*(PIM2(2)-PIM4(2))-PIM1(1)*(PIM2(1)-PIM4(1)) C DEFINE Q*PI = QPI: QP1=PIM1(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM1(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM1(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM1(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) QP2=PIM2(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM2(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM2(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM2(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) QP3=PIM3(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM3(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM3(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM3(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) QP4=PIM4(4)*(PIM1(4)+PIM2(4)+PIM3(4)+PIM4(4)) % -PIM4(3)*(PIM1(3)+PIM2(3)+PIM3(3)+PIM4(3)) % -PIM4(2)*(PIM1(2)+PIM2(2)+PIM3(2)+PIM4(2)) % -PIM4(1)*(PIM1(1)+PIM2(1)+PIM3(1)+PIM4(1)) C DEFINE T(PI;PJ,PK)= TIJK: T324=BWIGA1(QMP3)*FPIKM(SQRT(PS24),AMPI,AMPI)*GAMMA1 T314=BWIGA1(QMP3)*FPIKM(SQRT(PS14),AMPI,AMPI)*GAMMA1 T234=BWIGA1(QMP2)*FPIKM(SQRT(PS34),AMPI,AMPI)*GAMMA1 T214=BWIGA1(QMP2)*FPIKM(SQRT(PS14),AMPI,AMPI)*GAMMA1 T134=BWIGA1(QMP1)*FPIKM(SQRT(PS34),AMPI,AMPI)*GAMMA1 T124=BWIGA1(QMP1)*FPIKM(SQRT(PS24),AMPI,AMPI)*GAMMA1 C DEFINE S(I,J;K,L)= SIJKL: S1423=FRHO4(SQRT(PS14),AMPI,AMPI)*BWIGEPS(PS23)*GAMMA2 S2431=FRHO4(SQRT(PS24),AMPI,AMPI)*BWIGEPS(PS31)*GAMMA2 S3421=FRHO4(SQRT(PS34),AMPI,AMPI)*BWIGEPS(PS21)*GAMMA2 C DEFINITION OF AMPLITUDE, FIRST THE [] BRACKETS: BRACK1=T234+T324+2.*T314+T134+2.*T214+T124 % +T134*PD234/QMP1+T124*PD324/QMP1 % -3./2.*(S3421+S2431+2.*S1423) BRACK2=T234*(1.+2.*PD134/QMP2)+3.*T324+3.*T124 % +T134*(1.-PD234/QMP1)+2.*T214*PD314/QMP2 % -T124*PD324/QMP1 % -3./2.*(S3421+3.*S2431) BRACK3=T324*(1.+2.*PD124/QMP3)+3.*T234+3.*T134 % +T124*(1.-PD324/QMP1)+2.*T314*PD214/QMP3 % -T134*PD234/QMP1 % -3./2.*(3.*S3421+S2431) BRACK4A=2.*T234*(1./2.+PD134/QQ*(QP2/QMP2+1.)+PD234/QQ) % +2.*T324*(1./2.+PD124/QQ*(QP3/QMP3+1.)+PD324/QQ) % +2.*T134*(1./2.+PD234/QQ*(QP1/QMP1+1.) % -1./2.*PD234/QMP1+PD134/QQ) % +2.*T124*(1./2.+PD324/QQ*(QP1/QMP1+1.) % -1./2.*PD324/QMP1+PD124/QQ) % +2.*T214*(PD314/QQ*(QP2/QMP2+1.)+PD214/QQ) % +2.*T314*(PD214/QQ*(QP3/QMP3+1.)+PD314/QQ) BRACK4B=-3./2.*(S3421*(2.*(QP3-QP4)/QQ+1.) % +S2431*(2.*(QP2-QP4)/QQ+1.) % +S1423*2.*(QP1-QP4)/QQ) BRACK4=BRACK4A+BRACK4B DO 308 K=1,4 HCOMP1(K)=(PIM1(K)-PIM4(K))*BRACK1 HCOMP2(K)=PIM2(K)*BRACK2 HCOMP3(K)=PIM3(K)*BRACK3 HCOMP4(K)=(PIM1(K)+PIM2(K)+PIM3(K)+PIM4(K))*BRACK4 308 CONTINUE DO 309 I=1,4 HADCUR(I)=HCOMP1(I)+HCOMP2(I)+HCOMP3(I)-HCOMP4(I) HADCUR(I)=COEF1*FRHO4(SQRT(QQ),AMPI,AMPI)*HADCUR(I) 309 CONTINUE 101 CONTINUE ENDIF C M. Finkemeier et al. END END