// the amplitudes for K-> 2pi // the physical amplitudes are the Feynman Diagram amplitude // for K->pi pi and // -i_ times the Feynman diagram amplitude for K-> 3 pi // uses the output from KPPall_iso.6.frm // last version used for the publication // oneloopintegrals and IRoneloopintegrals can both be used here #include #include #include #include "IRoneloopintegrals.h" #include "amplitudes.iso.2pi.h" #include "amplitudes.iso.h" typedef std::complex dcomplex; namespace photoncutoffs{ extern double eg3pi,egfpi,egcoulomb; } const double pi=4.*atan(1.); const double pi16 = 1./(16.*pi*pi); //inline double prop(double msq, double qsq){ // return 1./(qsq-msq); //} // is in amplitudes.iso.6b.cc double Ab(double mko2, double mkp2, double mu2); //double Ab(double mko2, double mkp2, double mu2){ // return Ab(mko2,mu2)-Ab(mkp2,mu2); //} dcomplex Ap2KSpm(){ using namespace inputpars; double mpp2r = mpp*mpp, mko2r = mko*mko; double spe3 = spe/sqrt(3.); double Ap2KSpmiso = 0.; Ap2KSpmiso += + G8 * ( 2*mpp2r - 2*mko2r ); Ap2KSpmiso += + G27 * ( 4./3.*mpp2r - 4./3.*mko2r ); Ap2KSpmiso += + GE * ( 2 ); return dcomplex(Ap2KSpmiso/(pow(fpip,2)*fkp)); } dcomplex Ap2KSoo(){ using namespace inputpars; double mpo2r = mpo*mpo, mko2r = mko*mko; double spe3 = spe/sqrt(3.); double Ap2KSooiso = 0.; Ap2KSooiso += + G8*spe3 * ( - 4*mpo2r + 4*mko2r ); Ap2KSooiso += + G8 * ( 2*mpo2r - 2*mko2r ); Ap2KSooiso += + G27*spe3 * ( 4*mpo2r - 4*mko2r ); Ap2KSooiso += + G27 * ( - 2*mpo2r + 2*mko2r ); return dcomplex(Ap2KSooiso/(pow(fpip,2)*fkp)); } dcomplex Ap2KPpo(){ using namespace inputpars; double mpo2r = mpo*mpo, mpp2r = mpp*mpp, mkp2r = mkp*mkp; double spe3 = spe/sqrt(3.); double Ap2KPpoiso = 0.; Ap2KPpoiso += + G8*spe3 * ( - mpp2r + 3*mpo2r - 2*mkp2r ); Ap2KPpoiso += + G8 * ( mpp2r - mpo2r ); Ap2KPpoiso += + G27*spe3 * ( mpp2r + 2*mpo2r - 3*mkp2r ); Ap2KPpoiso += + G27 * ( 7./3.*mpp2r - 2./3.*mpo2r - 5./3.*mkp2r ); Ap2KPpoiso += + GE * ( 1 ); return dcomplex(Ap2KPpoiso/(pow(fpip,2)*fkp)); } dcomplex Ap4KSoo(){ using namespace inputpars; double mpp2 = mpp*mpp, mpo2 = mpo*mpo, mkp2 = mkp*mkp, mko2 = mko*mko, me2 = me*me, mu2 = mu*mu; double mp2 = mpo2,mk2=mko2; double spe3 = spe/sqrt(3.); dcomplex Ap4KSooiso = 0.; Ap4KSooiso = + G8*L5r*spe3 * ( - 64*mp2*mk2 + 32*pow(mp2,2) + 32*pow(mk2,2) ); Ap4KSooiso += + G8*L7r*spe3 * ( 768*mp2*mk2 - 384*pow(mp2,2) - 384*pow(mk2,2) ); Ap4KSooiso += + G8*L8r*spe3 * ( 256*mp2*mk2 - 128*pow(mp2,2) - 128*pow(mk2,2) ); Ap4KSooiso += + G8*spe3 * ( 56*mp2*mk2*N5r + 96*mp2*mk2*N6r + 96 *mp2*mk2*N7r - 40*mp2*mk2*N8r - 8*mp2*mk2*N9r - 112*mp2*mk2* N10r - 64*mp2*mk2*N11r - 144*mp2*mk2*N12r - 192*mp2*mk2*N13r - 48*pow(mp2,2)*N5r - 48*pow(mp2,2)*N6r - 64*pow(mp2,2)*N7r + 8*pow(mp2,2)*N8r + 80*pow(mp2,2)*N10r + 64*pow(mp2,2)*N11r + 80*pow(mp2,2)*N12r + 96*pow(mp2,2)*N13r - 8*pow(mk2,2)*N5r - 48*pow(mk2,2)*N6r - 32*pow(mk2,2)*N7r + 32*pow(mk2,2)*N8r + 8*pow(mk2,2)*N9r + 32*pow(mk2,2)*N10r + 64*pow(mk2,2)*N12r + 96*pow(mk2,2)*N13r ); Ap4KSooiso += + G8 * ( 2*mp2*Z5r - 4./3.*mp2*Z6r + 4./3.*mp2*Z7r - 2*mp2*Z8r - 2*mp2*Z9r - 4./3.*mp2*Z10r + 4./3.*mp2*Z11r + 4. /3.*mp2*Z12r + 4*mp2*K3r - 2*mp2*K4r + 8./3.*mp2*K5r + 8./3.* mp2*K6r - 4./3.*mp2*K9r - 4./3.*mp2*K10r + 12*mp2*K12r - 2*mk2 *Z5r + 4./3.*mk2*Z6r - 4./3.*mk2*Z7r + 2*mk2*Z8r + 2*mk2*Z9r + 4./3.*mk2*Z10r - 4./3.*mk2*Z11r - 4./3.*mk2*Z12r - 8*mk2* K3r + 4*mk2*K4r - 4./3.*mk2*K5r - 4./3.*mk2*K6r - 12*mk2*K12r - 4*mpo2*mko2*N5r - 24*mpo2*mko2*N7r + 4*mpo2*mko2*N8r + 4* mpo2*mko2*N9r + 8*mpo2*mko2*N10r + 16*mpo2*mko2*N11r + 8*mpo2* mko2*N12r + 8*pow(mpo2,2)*N5r + 16*pow(mpo2,2)*N7r + 4*pow( mpo2,2)*N8r - 8*pow(mpo2,2)*N10r - 16*pow(mpo2,2)*N11r - 8* pow(mpo2,2)*N12r - 4*pow(mko2,2)*N5r + 8*pow(mko2,2)*N7r - 8* pow(mko2,2)*N8r - 4*pow(mko2,2)*N9r ); Ap4KSooiso += + G27*L5r*spe3 * ( 64*mp2*mk2 - 32*pow(mp2,2) - 32 *pow(mk2,2) ); Ap4KSooiso += + G27*L7r*spe3 * ( - 768*mp2*mk2 + 384*pow(mp2,2) + 384*pow(mk2,2) ); Ap4KSooiso += + G27*L8r*spe3 * ( - 256*mp2*mk2 + 128*pow(mp2,2) + 128*pow(mk2,2) ); Ap4KSooiso += + G27*spe3 * ( 208./3.*mp2*mk2*D1r + 16*mp2*mk2* D2r - 12*mp2*mk2*D4r - 4*mp2*mk2*D5r - 28./3.*mp2*mk2*D6r + 40 *mp2*mk2*D7r - 112./3.*pow(mp2,2)*D1r - 16*pow(mp2,2)*D2r + 16 *pow(mp2,2)*D4r + 16./3.*pow(mp2,2)*D6r - 8*pow(mp2,2)*D7r - 32*pow(mk2,2)*D1r - 4*pow(mk2,2)*D4r + 4*pow(mk2,2)*D5r + 4* pow(mk2,2)*D6r - 32*pow(mk2,2)*D7r ); Ap4KSooiso += + G27 * ( - 4*mp2*K3r + 2*mp2*K4r - 8./3.*mp2*K5r - 8./3.*mp2*K6r + 4./3.*mp2*K9r + 4./3.*mp2*K10r - 12*mp2* K12r + 8*mk2*K3r - 4*mk2*K4r + 4./3.*mk2*K5r + 4./3.*mk2*K6r + 12*mk2*K12r + 8./3.*mpo2*mko2*D1r - 8*mpo2*mko2*D2r + 6* mpo2*mko2*D4r + 2*mpo2*mko2*D5r - 14./3.*mpo2*mko2*D6r - 4* mpo2*mko2*D7r - 8./3.*pow(mpo2,2)*D1r + 8*pow(mpo2,2)*D2r - 8* pow(mpo2,2)*D4r + 8./3.*pow(mpo2,2)*D6r - 4*pow(mpo2,2)*D7r + 2*pow(mko2,2)*D4r - 2*pow(mko2,2)*D5r + 2*pow(mko2,2)*D6r + 8* pow(mko2,2)*D7r ); Ap4KSooiso += + Ab(mp2,mu2)*ZE*G8 * ( 8./3. ); Ap4KSooiso += + Ab(mp2,mu2)*ZE*G27 * ( 46./9. ); Ap4KSooiso += + Ab(mp2,mu2)*G8*spe3 * ( - 17*mp2 + 22*mk2 ); Ap4KSooiso += + Ab(mp2,mu2)*G27*spe3 * ( 61./3.*mp2 - 91./3.*mk2 ); Ap4KSooiso += + Ab(mp2,mu2)*GE * ( - 1 ); Ap4KSooiso += + Ab(mk2,mk2,mu2)*G8 * ( - 1./3.*mp2 - 2./3.*mk2 ); Ap4KSooiso += + Ab(mk2,mk2,mu2)*G27 * ( 1./3.*mp2 + 2./3.*mk2 ); Ap4KSooiso += + Ab(mk2,mu2)*ZE*G8 * ( - 8./3. ); Ap4KSooiso += + Ab(mk2,mu2)*ZE*G27 * ( - 46./9. ); Ap4KSooiso += + Ab(mk2,mu2)*G8*spe3 * ( - 2*mp2 - mk2 ); Ap4KSooiso += + Ab(mk2,mu2)*G27*spe3 * ( 88./9.*mp2 - 16./9.*mk2 ); Ap4KSooiso += + Ab(mk2,mu2)*GE * ( 1 ); Ap4KSooiso += + Ab(mpp2,mu2)*G8 * ( - 7./3.*mpp2 + 4./3.*mpo2 + 1./2.*mko2 ); Ap4KSooiso += + Ab(mpp2,mu2)*G27 * ( - 29./9.*mpp2 - 67./9.* mpo2 + 7*mko2 ); Ap4KSooiso += + Ab(mpo2,mu2)*G8 * ( 5./2.*mpo2 - 4*mko2 ); Ap4KSooiso += + Ab(mpo2,mu2)*G27 * ( - 5./2.*mpo2 + 4*mko2 ); Ap4KSooiso += + Ab(mkp2,mu2)*G8 * ( mpp2 + 7./6.*mpo2 + 4./3.* mkp2 - 3*mko2 ); Ap4KSooiso += + Ab(mkp2,mu2)*G27 * ( 7./3.*mpp2 - 17./6.*mpo2 + 8./9.*mkp2 + 59./18.*mko2 ); Ap4KSooiso += + Ab(mko2,mu2)*G8 * ( 8./3.*mpo2 + 1./12.*mko2 - 1. /2.*me2 ); Ap4KSooiso += + Ab(mko2,mu2)*G27 * ( - 8./3.*mpo2 - 1./12.*mko2 + 1./2.*me2 ); Ap4KSooiso += + Ab(me2,mu2)*G8*spe3 * ( 7./9.*mp2 - 25./9.*mk2 ) ; Ap4KSooiso += + Ab(me2,mu2)*G8 * ( - 2./9.*mpo2 - 49./36.*mko2 + 5./6.*me2 ); Ap4KSooiso += + Ab(me2,mu2)*G27*spe3 * ( - 7./9.*mp2 + 25./9.* mk2 ); Ap4KSooiso += + Ab(me2,mu2)*G27 * ( 2./9.*mpo2 + 49./36.*mko2 - 5./6.*me2 ); Ap4KSooiso += + Bb(mp2,mp2,mk2,mu2)*ZE*G8 * ( 8./3.*mp2 - 8./3.* mk2 ); Ap4KSooiso += + Bb(mp2,mp2,mk2,mu2)*ZE*G27 * ( 16./9.*mp2 - 16./ 9.*mk2 ); Ap4KSooiso += + Bb(mp2,mp2,mk2,mu2)*G8*spe3 * ( 2*mp2*mk2 - 2* pow(mp2,2) ); Ap4KSooiso += + Bb(mp2,mp2,mk2,mu2)*G27*spe3 * ( - 2*mp2*mk2 + 2*pow(mp2,2) ); Ap4KSooiso += + Bb(mp2,mp2,mk2,mu2)*GE * ( - 2*mp2 + 2*mk2 ); Ap4KSooiso += + Bb(mp2,mk2,mp2,mu2)*ZE*G27 * ( - 10./3.*mp2 + 10./3.*mk2 ); Ap4KSooiso += + Bb(mp2,mk2,mp2,mu2)*G8*spe3 * ( - 12*mp2*mk2 + 5*pow(mk2,2) ); Ap4KSooiso += + Bb(mp2,mk2,mp2,mu2)*G27*spe3 * ( 16./3.*mp2*mk2 - 10./3.*pow(mk2,2) ); Ap4KSooiso += + Bb(mp2,mk2,mp2,mu2)*GE * ( mk2 ); Ap4KSooiso += + Bb(mp2,me2,mk2,mu2)*G8*spe3 * ( - 16./3.*mp2* mk2 + 8./3.*pow(mp2,2) + 8./3.*pow(mk2,2) ); Ap4KSooiso += + Bb(mp2,me2,mk2,mu2)*G27*spe3 * ( 16./3.*mp2*mk2 - 8./3.*pow(mp2,2) - 8./3.*pow(mk2,2) ); Ap4KSooiso += + Bb(mk2,mk2,mk2,mu2)*GE * ( - 1./2.*mk2 ); Ap4KSooiso += + Bb(mk2,me2,mp2,mu2)*G8*spe3 * ( 16./9.*mp2*mk2 - 8./9.*pow(mp2,2) - 26./9.*pow(mk2,2) ); Ap4KSooiso += + Bb(mk2,me2,mp2,mu2)*G27*spe3 * ( - 16./9.*mp2* mk2 + 8./9.*pow(mp2,2) + 26./9.*pow(mk2,2) ); Ap4KSooiso += + Bb(mpp2,mpp2,mko2,mu2)*G8 * ( - 2./3.*mpp2*mpo2 + 10./3.*mpp2*mko2 - 4./3.*pow(mpp2,2) + 2./3.*mpo2*mko2 - 2* pow(mko2,2) ); Ap4KSooiso += + Bb(mpp2,mpp2,mko2,mu2)*G27 * ( - 4./9.*mpp2* mpo2 + 20./9.*mpp2*mko2 - 8./9.*pow(mpp2,2) + 4./9.*mpo2*mko2 - 4./3.*pow(mko2,2) ); Ap4KSooiso += + Bb(mpp2,mkp2,mpo2,mu2)*G8 * ( - 2*mpp2*mpo2 + 3. /2.*mpp2*mko2 + pow(mpp2,2) - 1./2.*mpo2*mko2 + pow(mpo2,2) - 1./2.*mkp2*mko2 ); Ap4KSooiso += + Bb(mpp2,mkp2,mpo2,mu2)*G27 * ( - 3*mpp2*mpo2 - 5./3.*mpp2*mkp2 + 8./3.*mpp2*mko2 + 7./3.*pow(mpp2,2) + 5./3.* mpo2*mkp2 - 1./3.*mpo2*mko2 + 2./3.*pow(mpo2,2) - 2*mkp2*mko2 ); Ap4KSooiso += + Bb(mpo2,mpo2,mko2,mu2)*G8 * ( - mpo2*mko2 + pow(mpo2,2) ); Ap4KSooiso += + Bb(mpo2,mpo2,mko2,mu2)*G27 * ( mpo2*mko2 - pow( mpo2,2) ); Ap4KSooiso += + Bb(mpo2,mko2,mpo2,mu2)*G8 * ( 2*mpo2*mko2 - 3./2. *pow(mko2,2) ); Ap4KSooiso += + Bb(mpo2,mko2,mpo2,mu2)*G27 * ( - 2*mpo2*mko2 + 3./2.*pow(mko2,2) ); Ap4KSooiso += + Bb(mkp2,mkp2,mko2,mu2)*G8 * ( - 7./6.*mkp2*mko2 + 1./3.*pow(mkp2,2) + 5./6.*pow(mko2,2) ); Ap4KSooiso += + Bb(mkp2,mkp2,mko2,mu2)*G27 * ( - 7./9.*mkp2* mko2 + 2./9.*pow(mkp2,2) + 5./9.*pow(mko2,2) ); Ap4KSooiso += + Bb(mko2,me2,mpo2,mu2)*G8 * ( - 7./36.*mpo2*mko2 + 1./18.*pow(mpo2,2) + 7./4.*mko2*me2 - 31./36.*pow(mko2,2) - 1./2.*pow(me2,2) ); Ap4KSooiso += + Bb(mko2,me2,mpo2,mu2)*G27 * ( 7./36.*mpo2*mko2 - 1./18.*pow(mpo2,2) - 7./4.*mko2*me2 + 31./36.*pow(mko2,2) + 1./2.*pow(me2,2) ); Ap4KSooiso += + Bb(me2,me2,mk2,mu2)*G8*spe3 * ( 2./9.*mp2*mk2 - 2./9.*pow(mp2,2) ); Ap4KSooiso += + Bb(me2,me2,mk2,mu2)*G27*spe3 * ( - 2./9.*mp2* mk2 + 2./9.*pow(mp2,2) ); Ap4KSooiso += + Bb(me2,me2,mko2,mu2)*G8 * ( 1./3.*mpo2*mko2 - 1./ 3.*mpo2*me2 ); Ap4KSooiso += + Bb(me2,me2,mko2,mu2)*G27 * ( - 1./3.*mpo2*mko2 + 1./3.*mpo2*me2 ); Ap4KSooiso += + B1b(mp2,mk2,mp2,mu2)*G8*spe3 * ( 4*mp2*mk2 + 10* pow(mk2,2) ); Ap4KSooiso += + B1b(mp2,mk2,mp2,mu2)*G27*spe3 * ( 6*mp2*mk2 - 10 *pow(mk2,2) ); Ap4KSooiso += + B1b(mp2,mk2,mp2,mu2)*GE * ( - mk2 ); Ap4KSooiso += + B1b(mk2,me2,mp2,mu2)*G8*spe3 * ( 4*pow(mk2,2) ); Ap4KSooiso += + B1b(mk2,me2,mp2,mu2)*G27*spe3 * ( - 4*pow( mk2,2) ); Ap4KSooiso += + B1b(mpp2,mkp2,mpo2,mu2)*G8 * ( - mpp2*mko2 ); Ap4KSooiso += + B1b(mpp2,mkp2,mpo2,mu2)*G27 * ( - 7./3.*mpp2* mko2 + 5./3.*mkp2*mko2 ); Ap4KSooiso += + B1b(mpo2,mko2,mpo2,mu2)*G8 * ( - pow(mko2,2) ); Ap4KSooiso += + B1b(mpo2,mko2,mpo2,mu2)*G27 * ( pow(mko2,2) ); Ap4KSooiso += + B1b(mko2,me2,mpo2,mu2)*G8 * ( - 3./2.*mko2*me2 + pow(mko2,2) ); Ap4KSooiso += + B1b(mko2,me2,mpo2,mu2)*G27 * ( 3./2.*mko2*me2 - pow(mko2,2) ); return Ap4KSooiso/(pow(fpip,4)*fkp); } dcomplex Ap4KSpm(){ using namespace inputpars; double mpp2 = mpp*mpp, mpo2 = mpo*mpo, mkp2 = mkp*mkp, mko2 = mko*mko, me2 = me*me, mu2 = mu*mu; double mp2 = mpp2,mk2=mko2; double spe3 = spe/sqrt(3.); dcomplex Ap4KSpmiso = 0.; Ap4KSpmiso = + ZE*G8 * ( - 16*mp2*N5r - 32*mp2*N7r - 8*mp2*N8r + 32*mp2*N10r + 64*mp2*N11r + 32*mp2*N12r + 8*mk2*N5r + 16*mk2*N7r + 8*mk2* N8r + 8*mk2*N9r - 16*mk2*N10r - 32*mk2*N11r - 16*mk2*N12r ); Ap4KSpmiso += + ZE*G27 * ( 32./3.*mp2*D1r + 64./3.*mp2*D2r - 32./ 3.*mp2*D4r - 16./3.*mp2*D6r - 16./3.*mp2*D7r - 16./3.*mk2*D1r - 32./3.*mk2*D2r + 8*mk2*D4r - 8./3.*mk2*D5r + 4*mk2*D6r + 16. /3.*mk2*D7r ); Ap4KSpmiso += + G8*L5r*spe3 * ( - 64*mp2*mk2 + 32*pow(mp2,2) + 32*pow(mk2,2) ); Ap4KSpmiso += + G8*spe3 * ( 32*mp2*mk2*N5r + 96*mp2*mk2*N7r - 32 *mp2*mk2*N8r - 64*mp2*mk2*N10r - 64*mp2*mk2*N11r - 32*pow( mp2,2)*N5r - 64*pow(mp2,2)*N7r + 16*pow(mp2,2)*N8r + 64*pow( mp2,2)*N10r + 64*pow(mp2,2)*N11r - 32*pow(mk2,2)*N7r + 16*pow( mk2,2)*N8r ); Ap4KSpmiso += + G8 * ( 8*mp2*Z1r + 4*mp2*Z2r + 8./3.*mp2*Z3r - 8 *mp2*Z4r + 2*mp2*Z5r - 4./3.*mp2*Z6r + 4./3.*mp2*Z7r + 4./3.* mp2*K5r + 4./3.*mp2*K6r + 12*mp2*K12r + 4*mk2*Z1r + 8*mk2*Z2r - 8./3.*mk2*Z3r + 8*mk2*Z4r - 2*mk2*Z5r - 2./3.*mk2*Z6r - 4./ 3.*mk2*Z7r - 4./3.*mk2*K5r - 4./3.*mk2*K6r - 12*mk2*K12r - 4* mpp2*mko2*N5r - 24*mpp2*mko2*N7r + 4*mpp2*mko2*N8r + 4*mpp2* mko2*N9r + 8*mpp2*mko2*N10r + 16*mpp2*mko2*N11r + 8*mpp2*mko2* N12r + 8*pow(mpp2,2)*N5r + 16*pow(mpp2,2)*N7r + 4*pow(mpp2,2)* N8r - 8*pow(mpp2,2)*N10r - 16*pow(mpp2,2)*N11r - 8*pow(mpp2,2) *N12r - 4*pow(mko2,2)*N5r + 8*pow(mko2,2)*N7r - 8*pow(mko2,2)* N8r - 4*pow(mko2,2)*N9r ); Ap4KSpmiso += + G27*L5r*spe3 * ( - 128./3.*mp2*mk2 + 64./3.* pow(mp2,2) + 64./3.*pow(mk2,2) ); Ap4KSpmiso += + G27*spe3 * ( 224./3.*mp2*mk2*D1r - 8*mp2*mk2*D6r - 64./3.*mp2*mk2*D7r - 64./3.*pow(mp2,2)*D1r + 32./3.*pow( mp2,2)*D7r - 160./3.*pow(mk2,2)*D1r + 8*pow(mk2,2)*D6r + 32./3. *pow(mk2,2)*D7r ); Ap4KSpmiso += + G27 * ( 8./9.*mp2*K5r + 8./9.*mp2*K6r + 8*mp2* K12r - 8./9.*mk2*K5r - 8./9.*mk2*K6r - 8*mk2*K12r + 8./3.*mpp2 *mko2*D1r + 16./3.*mpp2*mko2*D2r - 4*mpp2*mko2*D4r - 4./3.* mpp2*mko2*D5r - 14./3.*mpp2*mko2*D6r + 8./3.*mpp2*mko2*D7r - 8. /3.*pow(mpp2,2)*D1r - 16./3.*pow(mpp2,2)*D2r + 16./3.*pow( mpp2,2)*D4r + 8./3.*pow(mpp2,2)*D6r + 8./3.*pow(mpp2,2)*D7r - 4./3.*pow(mko2,2)*D4r + 4./3.*pow(mko2,2)*D5r + 2*pow(mko2,2)* D6r - 16./3.*pow(mko2,2)*D7r ); Ap4KSpmiso += + Ab(mp2,mu2)*ZE*G8 * ( 26./3. ); Ap4KSpmiso += + Ab(mp2,mu2)*ZE*G27 * ( 19./3. ); Ap4KSpmiso += + Ab(mp2,mu2)*G8*spe3 * ( - 3./2.*mk2 ); Ap4KSpmiso += + Ab(mp2,mu2)*G27*spe3 * ( 5*mp2 + 7./3.*mk2 ); Ap4KSpmiso += + Ab(mp2,mu2)*GE * ( 7 ); Ap4KSpmiso += + Ab(mk2,mu2)*ZE*G8 * ( - 16./3. ); Ap4KSpmiso += + Ab(mk2,mu2)*ZE*G27 * ( - 32./9. ); Ap4KSpmiso += + Ab(mk2,mu2)*G8*spe3 * ( - 4*mp2 + 4*mk2 ); Ap4KSpmiso += + Ab(mk2,mu2)*G27*spe3 * ( - 8./3.*mp2 + 8./3.* mk2 ); Ap4KSpmiso += + Ab(mk2,mu2)*GE * ( 5 ); Ap4KSpmiso += + Ab(mpp2,mu2)*G8 * ( mpp2 - 5./2.*mko2 ); Ap4KSpmiso += + Ab(mpp2,mu2)*G27 * ( 22./3.*mpp2 - 10./3.*mko2 ) ; Ap4KSpmiso += + Ab(mpo2,mu2)*G8 * ( 5./3.*mpp2 - 7./6.*mpo2 - 3./ 4.*mko2 ); Ap4KSpmiso += + Ab(mpo2,mu2)*G27 * ( 5./6.*mpp2 - 4./3.*mpo2 - 41./12.*mko2 ); Ap4KSpmiso += + Ab(mkp2,mu2)*G8 * ( 11./6.*mpp2 + 1./2.*mpo2 + 4. /3.*mkp2 - 19./6.*mko2 - 1./2.*me2 ); Ap4KSpmiso += + Ab(mkp2,mu2)*G27 * ( 11./9.*mpp2 + 1./3.*mpo2 + 8./9.*mkp2 - 53./18.*mko2 - 1./3.*me2 ); Ap4KSpmiso += + Ab(mko2,mu2)*G8 * ( 5./2.*mpp2 ); Ap4KSpmiso += + Ab(mko2,mu2)*G27 * ( 5./3.*mpp2 ); Ap4KSpmiso += + Ab(me2,mu2)*ZE*G8 * ( 16./9. ); Ap4KSpmiso += + Ab(me2,mu2)*ZE*G27 * ( 1 ); Ap4KSpmiso += + Ab(me2,mu2)*G8*spe3 * ( 4./9.*mp2 + 19./18.*mk2 ); Ap4KSpmiso += + Ab(me2,mu2)*G8 * ( - 2./9.*mpp2 - 2./3.*mkp2 - 25./36.*mko2 + 5./6.*me2 ); Ap4KSpmiso += + Ab(me2,mu2)*G27*spe3 * ( - mp2 - 19./3.*mk2 ); Ap4KSpmiso += + Ab(me2,mu2)*G27 * ( 1./2.*mpp2 - mkp2 - 5./12.* mko2 ); Ap4KSpmiso += + Bb(mp2,mp2,mk2,mu2)*ZE*G8 * ( 26./3.*mp2 - 26./3. *mk2 ); Ap4KSpmiso += + Bb(mp2,mp2,mk2,mu2)*ZE*G27 * ( 14./3.*mp2 - 14./ 3.*mk2 ); Ap4KSpmiso += + Bb(mp2,mp2,mk2,mu2)*G8*spe3 * ( - 4*mp2*mk2 + 2 *pow(mp2,2) + 2*pow(mk2,2) ); Ap4KSpmiso += + Bb(mp2,mp2,mk2,mu2)*G27*spe3 * ( 4*mp2*mk2 - 2* pow(mp2,2) - 2*pow(mk2,2) ); Ap4KSpmiso += + Bb(mp2,mp2,mk2,mu2)*GE * ( mk2 ); Ap4KSpmiso += + Bb(mp2,mk2,mp2,mu2)*ZE*G27 * ( - 5./3.*mp2 + 5./ 3.*mk2 ); Ap4KSpmiso += + Bb(mp2,mk2,mp2,mu2)*G8*spe3 * ( 1./2.*pow(mk2,2) ); Ap4KSpmiso += + Bb(mp2,mk2,mp2,mu2)*G27*spe3 * ( 5./3.*mp2*mk2 + 1./3.*pow(mk2,2) ); Ap4KSpmiso += + Bb(mp2,mk2,mp2,mu2)*GE * ( 1./2.*mk2 ); Ap4KSpmiso += + Bb(mp2,me2,mk2,mu2)*G8*spe3 * ( - 14./3.*mp2* mk2 + 8./3.*pow(mp2,2) + 2*pow(mk2,2) ); Ap4KSpmiso += + Bb(mp2,me2,mk2,mu2)*G27*spe3 * ( 14./3.*mp2*mk2 - 8./3.*pow(mp2,2) - 2*pow(mk2,2) ); Ap4KSpmiso += + Bb(mk2,mk2,mk2,mu2)*GE * ( - 1./2.*mk2 ); Ap4KSpmiso += + Bb(mk2,me2,mp2,mu2)*ZE*G8 * ( 10./9.*mp2 - 10./9. *mk2 ); Ap4KSpmiso += + Bb(mk2,me2,mp2,mu2)*ZE*G27 * ( - 5./27.*mp2 + 5. /27.*mk2 ); Ap4KSpmiso += + Bb(mk2,me2,mp2,mu2)*G8*spe3 * ( - 38./9.*mp2* mk2 + 16./9.*pow(mp2,2) + 53./18.*pow(mk2,2) ); Ap4KSpmiso += + Bb(mk2,me2,mp2,mu2)*G27*spe3 * ( 19./27.*mp2*mk2 - 8./27.*pow(mp2,2) + 43./27.*pow(mk2,2) ); Ap4KSpmiso += + Bb(mk2,me2,mp2,mu2)*GE * ( - mk2 ); Ap4KSpmiso += + Bb(mpp2,mpp2,mko2,mu2)*G8 * ( mpp2*mko2 - pow( mko2,2) ); Ap4KSpmiso += + Bb(mpp2,mpp2,mko2,mu2)*G27 * ( 2./3.*mpp2*mko2 - 2./3.*pow(mko2,2) ); Ap4KSpmiso += + Bb(mpp2,mko2,mpp2,mu2)*G8 * ( 2*mpp2*mko2 - 3./2. *pow(mko2,2) ); Ap4KSpmiso += + Bb(mpp2,mko2,mpp2,mu2)*G27 * ( 4./3.*mpp2*mko2 - pow(mko2,2) ); Ap4KSpmiso += + Bb(mpo2,mpo2,mko2,mu2)*G8 * ( - 1./3.*mpp2*mpo2 + 1./3.*mpp2*mko2 + 5./3.*mpo2*mko2 - 2./3.*pow(mpo2,2) - pow(mko2,2) ); Ap4KSpmiso += + Bb(mpo2,mpo2,mko2,mu2)*G27 * ( 1./3.*mpp2*mpo2 - 1./3.*mpp2*mko2 - 5./3.*mpo2*mko2 + 2./3.*pow(mpo2,2) + pow(mko2,2) ); Ap4KSpmiso += + Bb(mpo2,mkp2,mpp2,mu2)*G8 * ( - mpp2*mpo2 - 1./ 4.*mpp2*mko2 + 1./2.*pow(mpp2,2) + 3./4.*mpo2*mko2 + 1./2.* pow(mpo2,2) - 1./4.*mkp2*mko2 ); Ap4KSpmiso += + Bb(mpo2,mkp2,mpp2,mu2)*G27 * ( - 3./2.*mpp2* mpo2 - 5./6.*mpp2*mkp2 - 7./12.*mpp2*mko2 + 7./6.*pow(mpp2,2) + 5./6.*mpo2*mkp2 + 11./12.*mpo2*mko2 + 1./3.*pow(mpo2,2) + 1. /4.*mkp2*mko2 ); Ap4KSpmiso += + Bb(mkp2,mkp2,mko2,mu2)*G8 * ( - 7./6.*mkp2*mko2 + 1./3.*pow(mkp2,2) + 5./6.*pow(mko2,2) ); Ap4KSpmiso += + Bb(mkp2,mkp2,mko2,mu2)*G27 * ( - 7./9.*mkp2* mko2 + 2./9.*pow(mkp2,2) + 5./9.*pow(mko2,2) ); Ap4KSpmiso += + Bb(mkp2,me2,mpp2,mu2)*G8 * ( - 2./9.*mpp2*mkp2 + 1./36.*mpp2*mko2 + 1./18.*pow(mpp2,2) - 7./36.*mkp2*mko2 + 4./3.*mkp2*me2 - 2./3.*pow(mkp2,2) + 5./12.*mko2*me2 - 1./2.* pow(me2,2) ); Ap4KSpmiso += + Bb(mkp2,me2,mpp2,mu2)*G27 * ( 1./2.*mpp2*mkp2 - 1./36.*mpp2*mko2 - 5./18.*mpp2*me2 - 1./18.*pow(mpp2,2) - 11./ 12.*mkp2*mko2 + 7./6.*mkp2*me2 - pow(mkp2,2) + 25./36.*mko2* me2 - 1./3.*pow(me2,2) ); Ap4KSpmiso += + Bb(me2,me2,mk2,mu2)*ZE*G8 * ( - 2./9.*mp2 + 2./ 9.*mk2 ); Ap4KSpmiso += + Bb(me2,me2,mk2,mu2)*ZE*G27 * ( 2./9.*mp2 - 2./9. *mk2 ); Ap4KSpmiso += + Bb(me2,me2,mk2,mu2)*G8*spe3 * ( 2./9.*mp2*mk2 - 2./9.*pow(mp2,2) ); Ap4KSpmiso += + Bb(me2,me2,mk2,mu2)*G27*spe3 * ( - 2./9.*mp2* mk2 + 2./9.*pow(mp2,2) ); Ap4KSpmiso += + Bb(me2,me2,mko2,mu2)*G8 * ( 1./3.*mpp2*mko2 - 1./ 3.*mpp2*me2 ); Ap4KSpmiso += + Bb(me2,me2,mko2,mu2)*G27 * ( - 1./3.*mpp2*mko2 + 1./3.*mpp2*me2 ); Ap4KSpmiso += + B1b(mp2,mk2,mp2,mu2)*G8*spe3 * ( - pow(mk2,2) ) ; Ap4KSpmiso += + B1b(mp2,mk2,mp2,mu2)*G27*spe3 * ( - 4*pow( mk2,2) ); Ap4KSpmiso += + B1b(mp2,mk2,mp2,mu2)*GE * ( 3./2.*mk2 ); Ap4KSpmiso += + B1b(mk2,me2,mp2,mu2)*G8*spe3 * ( - pow(mk2,2) ) ; Ap4KSpmiso += + B1b(mk2,me2,mp2,mu2)*G27*spe3 * ( - 4*pow( mk2,2) ); Ap4KSpmiso += + B1b(mk2,me2,mp2,mu2)*GE * ( 3./2.*mk2 ); Ap4KSpmiso += + B1b(mpp2,mko2,mpp2,mu2)*G8 * ( - pow(mko2,2) ); Ap4KSpmiso += + B1b(mpp2,mko2,mpp2,mu2)*G27 * ( - 2./3.*pow( mko2,2) ); Ap4KSpmiso += + B1b(mpo2,mkp2,mpp2,mu2)*G8 * ( - 1./2.*mpo2* mko2 ); Ap4KSpmiso += + B1b(mpo2,mkp2,mpp2,mu2)*G27 * ( - 1./3.*mpo2* mko2 - 5./6.*mkp2*mko2 ); Ap4KSpmiso += + B1b(mkp2,me2,mpp2,mu2)*G8 * ( mkp2*mko2 - 3./2.* mko2*me2 ); Ap4KSpmiso += + B1b(mkp2,me2,mpp2,mu2)*G27 * ( 3./2.*mkp2*mko2 - mko2*me2 ); return Ap4KSpmiso/(pow(fpip,4)*fkp); } dcomplex Ap4KPpo(){ using namespace inputpars; double mpp2 = mpp*mpp, mpo2 = mpo*mpo, mkp2 = mkp*mkp, mko2 = mko*mko, me2 = me*me, mu2 = mu*mu; double mp2 = (mpp2+mpo2)/2.,mk2=mkp2; double spe3 = spe/sqrt(3.); dcomplex Ap4KPpoiso = 0.; Ap4KPpoiso = + ZE*G8 * ( - 8*mp2*N10r - 4*mp2*N11r - 4*pow(mp2,2)*pow( mk2,-1)*N11r + 8*mk2*N10r + 8*mk2*N11r ); Ap4KPpoiso += + ZE*G27 * ( 16./3.*mp2*D1r - 40./3.*mp2*D2r + 20./ 3.*mp2*D5r - 40./3.*mp2*D7r - 8./3.*pow(mp2,2)*pow(mk2,-1)*D1r - 8./3.*mk2*D1r + 10./3.*mk2*D4r - 10./3.*mk2*D5r + 40./3.* mk2*D7r ); Ap4KPpoiso += + G8*L7r*spe3 * ( - 384*mp2*mk2 + 192*pow(mp2,2) + 192*pow(mk2,2) ); Ap4KPpoiso += + G8*L8r*spe3 * ( - 128*mp2*mk2 + 64*pow(mp2,2) + 64*pow(mk2,2) ); Ap4KPpoiso += + G8*spe3 * ( - 12*mp2*mk2*N5r - 48*mp2*mk2*N6r + 4*mp2*mk2*N8r + 4*mp2*mk2*N9r + 24*mp2*mk2*N10r + 72*mp2* mk2*N12r + 96*mp2*mk2*N13r + 8*pow(mp2,2)*N5r + 24*pow(mp2,2)* N6r + 4*pow(mp2,2)*N8r - 8*pow(mp2,2)*N10r - 40*pow(mp2,2)* N12r - 48*pow(mp2,2)*N13r + 4*pow(mk2,2)*N5r + 24*pow(mk2,2)* N6r - 8*pow(mk2,2)*N8r - 4*pow(mk2,2)*N9r - 16*pow(mk2,2)*N10r - 32*pow(mk2,2)*N12r - 48*pow(mk2,2)*N13r ); Ap4KPpoiso += + G8 * ( 4*mp2*Z1r + 2*mp2*Z2r + 4./3.*mp2*Z3r + mp2*Z8r + mp2*Z9r + 2./3.*mp2*Z10r + 4./3.*mp2*Z11r + 4./3.* mp2*Z12r + 2*mp2*K3r - mp2*K4r - 2./3.*mp2*K5r - 2./3.*mp2*K6r + 2./3.*mp2*K9r + 2./3.*mp2*K10r + 2*mk2*Z1r + 4*mk2*Z2r - 4./ 3.*mk2*Z3r - mk2*Z6r - mk2*Z8r - mk2*Z9r - 2./3.*mk2*Z10r - 4./ 3.*mk2*Z11r - 4./3.*mk2*Z12r + 4*mpp2*mpo2*mkp2*pow(mko2,-1)* N10r + 2*mpp2*mpo2*mkp2*pow(mko2,-1)*N11r + 2*mpp2*mpo2*N8r + 4*mpp2*mpo2*N9r + 2*mpp2*pow(mpo2,2)*pow(mko2,-1)*N11r + 4* mpp2*mkp2*N5r + 4*mpp2*mkp2*N8r - 4*mpp2*pow(mkp2,2)*pow( mko2,-1)*N10r - 4*mpp2*pow(mkp2,2)*pow(mko2,-1)*N11r - 4*mpo2* mkp2*N5r - 4*mpo2*mkp2*N8r + 4*mpo2*pow(mkp2,2)*pow(mko2,-1)* N10r + 4*mpo2*pow(mkp2,2)*pow(mko2,-1)*N11r - 4*pow(mpo2,2)* mkp2*pow(mko2,-1)*N10r - 2*pow(mpo2,2)*mkp2*pow(mko2,-1)*N11r - 2*pow(mpo2,2)*N8r - 4*pow(mpo2,2)*N9r - 2*pow(mpo2,3)*pow( mko2,-1)*N11r ); Ap4KPpoiso += + G27*L7r*spe3 * ( - 576*mp2*mk2 + 288*pow(mp2,2) + 288*pow(mk2,2) ); Ap4KPpoiso += + G27*L8r*spe3 * ( - 192*mp2*mk2 + 96*pow(mp2,2) + 96*pow(mk2,2) ); Ap4KPpoiso += + G27*spe3 * ( 16*mp2*mk2*D1r + 12*mp2*mk2*D2r - 9 *mp2*mk2*D4r - 3*mp2*mk2*D5r - 28./3.*mp2*mk2*D6r + 98./3.*mp2 *mk2*D7r - 16./3.*pow(mp2,2)*D1r - 12*pow(mp2,2)*D2r + 12*pow( mp2,2)*D4r + 4*pow(mp2,2)*D6r - 22./3.*pow(mp2,2)*D7r - 32./3. *pow(mk2,2)*D1r - 3*pow(mk2,2)*D4r + 3*pow(mk2,2)*D5r + 16./3. *pow(mk2,2)*D6r - 76./3.*pow(mk2,2)*D7r ); Ap4KPpoiso += + G27 * ( 19./3.*mp2*K3r - 19./6.*mp2*K4r - mp2* K5r - mp2*K6r + mp2*K9r + mp2*K10r + 10*mp2*K12r - 10./3.*mk2* K3r + 5./3.*mk2*K4r - 10*mk2*K12r - 8./3.*mpp2*mpo2*mkp2*pow( mko2,-1)*D1r + 19./3.*mpp2*mpo2*D4r - 3*mpp2*mpo2*D5r + 2./3.* mpp2*mpo2*D6r + 14./3.*mpp2*mpo2*D7r + 4./3.*mpp2*pow(mpo2,2)* pow(mko2,-1)*D1r + 3*mpp2*mkp2*D4r - 5./3.*mpp2*mkp2*D5r - 2./ 3.*mpp2*mkp2*D6r + 28./3.*mpp2*mkp2*D7r + 4./3.*mpp2*pow( mkp2,2)*pow(mko2,-1)*D1r + 20./3.*mpo2*mkp2*D2r - 8*mpo2*mkp2* D4r + 2./3.*mpo2*mkp2*D6r - 6*mpo2*mkp2*D7r - 4./3.*mpo2*pow( mkp2,2)*pow(mko2,-1)*D1r + 8./3.*pow(mpo2,2)*mkp2*pow(mko2,-1) *D1r - 20./3.*pow(mpo2,2)*D2r + 1./3.*pow(mpo2,2)*D4r + 3*pow( mpo2,2)*D5r - 2./3.*pow(mpo2,2)*D6r - 4./3.*pow(mpo2,2)*D7r - 4./3.*pow(mpo2,3)*pow(mko2,-1)*D1r - 5./3.*pow(mkp2,2)*D4r + 5. /3.*pow(mkp2,2)*D5r - 20./3.*pow(mkp2,2)*D7r ); Ap4KPpoiso += + Ab(mp2,mu2)*ZE*G8 * ( 2 + 3./2.*mp2*pow(mk2,-1) ); Ap4KPpoiso += + Ab(mp2,mu2)*ZE*G27 * ( - 2 + 1./6.*mp2*pow( mk2,-1) ); Ap4KPpoiso += + Ab(mp2,mu2)*G8*spe3 * ( 73./8.*mp2 - 69./8.*mk2 ); Ap4KPpoiso += + Ab(mp2,mu2)*G27*spe3 * ( 89./6.*mp2 - 97./6.*mk2 ); Ap4KPpoiso += + Ab(mp2,mu2)*GE * ( 27./8. ); Ap4KPpoiso += + Ab(mk2,mk2,mu2)*G8 * ( 1./6.*mp2 + 1./3.*mk2 ); Ap4KPpoiso += + Ab(mk2,mk2,mu2)*G27 * ( 1./4.*mp2 + 1./2.*mk2 ); Ap4KPpoiso += + Ab(mk2,mu2)*ZE*G8 * ( 4./3. ); Ap4KPpoiso += + Ab(mk2,mu2)*ZE*G27 * ( 16./3. ); Ap4KPpoiso += + Ab(mk2,mu2)*G8*spe3 * ( - 13./8.*mp2 + 5./8.* mk2 ); Ap4KPpoiso += + Ab(mk2,mu2)*G27*spe3 * ( 667./72.*mp2 - 655./72. *mk2 ); Ap4KPpoiso += + Ab(mk2,mu2)*GE * ( 9./4. ); Ap4KPpoiso += + Ab(mpp2,mu2)*G8 * ( 1./2.*mpp2*mpo2*pow(mko2,-1) - 1./12.*mpp2 - 1./2.*pow(mpp2,2)*pow(mko2,-1) - 7./6.*mpo2 + 1./2.*mkp2 + 1./4.*mko2 ); Ap4KPpoiso += + Ab(mpp2,mu2)*G27 * ( 1./3.*mpp2*mpo2*pow( mko2,-1) + 233./36.*mpp2 - 1./3.*pow(mpp2,2)*pow(mko2,-1) - 19. /18.*mpo2 - 61./12.*mkp2 + 1./6.*mko2 ); Ap4KPpoiso += + Ab(mpo2,mu2)*G8 * ( - 1./4.*mpp2*mpo2*pow( mko2,-1) + 23./24.*mpp2 + 1./6.*mpo2 + 1./4.*pow(mpo2,2)*pow( mko2,-1) - 3./8.*mkp2 - 1./4.*mko2 ); Ap4KPpoiso += + Ab(mpo2,mu2)*G27 * ( 1./4.*mpp2*mpo2*pow( mko2,-1) + 281./72.*mpp2 + 13./72.*mpo2 - 1./4.*pow(mpo2,2)* pow(mko2,-1) - 19./6.*mkp2 + 1./4.*mko2 ); Ap4KPpoiso += + Ab(mkp2,mu2)*G8 * ( 1./2.*mpp2*mkp2*pow(mko2,-1) + mpp2 - 1./2.*mpo2*mkp2*pow(mko2,-1) - 19./24.*mpo2 - 1./3.* mkp2 + 1./8.*me2 ); Ap4KPpoiso += + Ab(mkp2,mu2)*G27 * ( 1./3.*mpp2*mkp2*pow( mko2,-1) + 46./9.*mpp2 - 1./3.*mpo2*mkp2*pow(mko2,-1) - 3./2.* mpo2 - 103./36.*mkp2 + 1./12.*me2 ); Ap4KPpoiso += + Ab(mko2,mu2)*G8 * ( 17./24.*mpp2 - 19./24.*mpo2 - 1./24.*mkp2 + 1./4.*mko2 - 1./8.*me2 ); Ap4KPpoiso += + Ab(mko2,mu2)*G27 * ( 11./8.*mpp2 - 31./24.*mpo2 - 29./24.*mkp2 - 2./3.*mko2 + 1./8.*me2 ); Ap4KPpoiso += + Ab(me2,mu2)*ZE*G8 * ( - 5./3. + 1./6.*mp2*pow( mk2,-1) ); Ap4KPpoiso += + Ab(me2,mu2)*ZE*G27 * ( - 5./9. - 1./6.*mp2*pow( mk2,-1) ); Ap4KPpoiso += + Ab(me2,mu2)*G8*spe3 * ( - 1./6.*mp2 + 2./3.*mk2 ); Ap4KPpoiso += + Ab(me2,mu2)*G8 * ( 1./4.*mpp2*pow(mko2,-1)*me2 + 13./12.*mpp2 - 1./4.*mpo2*pow(mko2,-1)*me2 - 13./12.*mpo2 - 1./12.*mkp2 + 1./12.*mko2 ); Ap4KPpoiso += + Ab(me2,mu2)*G27*spe3 * ( - 103./72.*mp2 + 187./ 72.*mk2 ); Ap4KPpoiso += + Ab(me2,mu2)*G27 * ( - 1./4.*mpp2*pow(mko2,-1)* me2 + 17./12.*mpp2 + 1./4.*mpo2*pow(mko2,-1)*me2 - 23./18.* mpo2 - 49./72.*mkp2 - 1./12.*mko2 - 5./24.*me2 ); Ap4KPpoiso += + Ab(me2,mu2)*GE * ( 3./8. ); Ap4KPpoiso += + Bb(mp2,mp2,mk2,mu2)*ZE*G27 * ( 20./9.*mp2 - 20./ 9.*mk2 ); Ap4KPpoiso += + Bb(mp2,mp2,mk2,mu2)*G8*spe3 * ( - 3*mp2*mk2 + 2 *pow(mp2,2) + pow(mk2,2) ); Ap4KPpoiso += + Bb(mp2,mp2,mk2,mu2)*G27*spe3 * ( - 9./2.*mp2* mk2 + 3*pow(mp2,2) + 3./2.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mp2,mp2,mk2,mu2)*GE * ( mp2 - 1./2.*mk2 ); Ap4KPpoiso += + Bb(mp2,mk2,mp2,mu2)*ZE*G8 * ( - 2*mp2 + 2*mk2 ) ; Ap4KPpoiso += + Bb(mp2,mk2,mp2,mu2)*ZE*G27 * ( 38./9.*mp2 - 38./ 9.*mk2 ); Ap4KPpoiso += + Bb(mp2,mk2,mp2,mu2)*G8*spe3 * ( 3./8.*mp2*mk2 - 5./4.*pow(mp2,2) + 7./8.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mp2,mk2,mp2,mu2)*G27*spe3 * ( 13./12.*mp2*mk2 - 13./12.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mp2,mk2,mp2,mu2)*GE * ( 5./4.*mp2 - 7./8.*mk2 ); Ap4KPpoiso += + Bb(mp2,me2,mk2,mu2)*G8*spe3 * ( 1./3.*mp2*mk2 - 1./3.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mp2,me2,mk2,mu2)*G27*spe3 * ( - 1./18.*mp2* mk2 + 1./18.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mk2,me2,mp2,mu2)*ZE*G8 * ( - mp2 + mk2 ); Ap4KPpoiso += + Bb(mk2,me2,mp2,mu2)*ZE*G27 * ( 7./27.*mp2 - 7./ 27.*mk2 ); Ap4KPpoiso += + Bb(mk2,me2,mp2,mu2)*G8*spe3 * ( - 14./3.*mp2* mk2 + 4./3.*pow(mp2,2) + 10./3.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mk2,me2,mp2,mu2)*G27*spe3 * ( 83./216.*mp2* mk2 - 7./54.*pow(mp2,2) - 55./216.*pow(mk2,2) ); Ap4KPpoiso += + Bb(mk2,me2,mp2,mu2)*GE * ( 1./2.*mp2 - 5./8.*mk2 ); Ap4KPpoiso += + Bb(mpp2,mpo2,mkp2,mu2)*G8 * ( - 2./3.*mpp2*mpo2 - 1./2.*mpp2*mkp2 + 5./6.*pow(mpp2,2) + 1./2.*mpo2*mkp2 - 1./ 6.*pow(mpo2,2) ); Ap4KPpoiso += + Bb(mpp2,mpo2,mkp2,mu2)*G27 * ( - 11./6.*mpp2* mpo2 - 31./18.*mpp2*mkp2 + 25./9.*pow(mpp2,2) - 7./9.*mpo2* mkp2 + 13./18.*pow(mpo2,2) + 5./6.*pow(mkp2,2) ); Ap4KPpoiso += + Bb(mpp2,mkp2,mpo2,mu2)*G8 * ( 7./12.*mpp2*mpo2 - 3./4.*mpp2*mkp2 + 1./3.*pow(mpp2,2) - 5./12.*pow(mpo2,2) + 1./4.*pow(mkp2,2) ); Ap4KPpoiso += + Bb(mpp2,mkp2,mpo2,mu2)*G27 * ( 13./12.*mpp2*mpo2 - 19./18.*mpp2*mkp2 + 13./36.*pow(mpp2,2) - 25./36.*mpo2*mkp2 - 5./18.*pow(mpo2,2) + 7./12.*pow(mkp2,2) ); Ap4KPpoiso += + Bb(mpp2,mko2,mpp2,mu2)*G8 * ( - 1./2.*mpp2*mpo2 - 3./4.*mpp2*mko2 + 1./2.*pow(mpp2,2) + 1./4.*mpo2*mko2 + 1./ 4.*mkp2*mko2 + 1./4.*pow(mko2,2) ); Ap4KPpoiso += + Bb(mpp2,mko2,mpp2,mu2)*G27 * ( - 1./3.*mpp2* mpo2 - 1./2.*mpp2*mko2 + 1./3.*pow(mpp2,2) + 1./6.*mpo2*mko2 + 1./6.*mkp2*mko2 + 1./6.*pow(mko2,2) ); Ap4KPpoiso += + Bb(mpo2,mkp2,mpp2,mu2)*G8 * ( 3./8.*mpp2*mpo2 + 1./4.*mpp2*mkp2 - 1./8.*pow(mpp2,2) + 1./8.*mpo2*mkp2 - 1./2.* pow(mpo2,2) - 1./8.*pow(mkp2,2) ); Ap4KPpoiso += + Bb(mpo2,mkp2,mpp2,mu2)*G27 * ( 2./3.*mpp2*mpo2 + 19./24.*mpp2*mkp2 - 7./24.*pow(mpp2,2) - 1./8.*mpo2*mkp2 - 13./24.*pow(mpo2,2) - 1./2.*pow(mkp2,2) ); Ap4KPpoiso += + Bb(mpo2,mko2,mpo2,mu2)*G8 * ( 1./2.*mpp2*mpo2 - 1./4.*mpp2*mko2 + 3./4.*mpo2*mko2 - 1./2.*pow(mpo2,2) - 1./4.* mkp2*mko2 - 1./4.*pow(mko2,2) ); Ap4KPpoiso += + Bb(mpo2,mko2,mpo2,mu2)*G27 * ( - 1./2.*mpp2* mpo2 + 1./4.*mpp2*mko2 - 3./4.*mpo2*mko2 + 1./2.*pow(mpo2,2) + 1./4.*mkp2*mko2 + 1./4.*pow(mko2,2) ); Ap4KPpoiso += + Bb(mkp2,mko2,mkp2,mu2)*G8 * ( - 1./2.*mpp2*mkp2 + 1./2.*mpo2*mkp2 ); Ap4KPpoiso += + Bb(mkp2,mko2,mkp2,mu2)*G27 * ( - 1./3.*mpp2* mkp2 + 1./3.*mpo2*mkp2 ); Ap4KPpoiso += + Bb(mkp2,me2,mpp2,mu2)*G8 * ( - 7./72.*mpp2*mpo2 + 2./9.*mpp2*mkp2 - 5./12.*mpp2*me2 + 1./8.*pow(mpp2,2) - 5./ 72.*mpo2*mkp2 + 1./24.*mpo2*me2 + 1./4.*mkp2*me2 - 13./72.* pow(mkp2,2) + 1./8.*pow(me2,2) ); Ap4KPpoiso += + Bb(mkp2,me2,mpp2,mu2)*G27 * ( 7./72.*mpp2*mpo2 + 29./72.*mpp2*mkp2 - 5./24.*mpp2*me2 - 1./8.*pow(mpp2,2) + 5. /24.*mpo2*mkp2 - 13./72.*mpo2*me2 + 11./36.*mkp2*me2 - 7./12.* pow(mkp2,2) + 1./12.*pow(me2,2) ); Ap4KPpoiso += + Bb(mko2,me2,mpo2,mu2)*G8 * ( 1./24.*mpp2*mpo2 - 1./24.*mpp2*mko2 + 1./8.*mpp2*me2 - 1./72.*mpo2*mkp2 - 7./72.* mpo2*mko2 + 1./4.*mpo2*me2 - 5./72.*pow(mpo2,2) + 7./72.*mkp2* mko2 - 5./24.*mkp2*me2 - 1./24.*mko2*me2 + 1./12.*pow(mko2,2) - 1./8.*pow(me2,2) ); Ap4KPpoiso += + Bb(mko2,me2,mpo2,mu2)*G27 * ( - 1./24.*mpp2* mpo2 + 1./24.*mpp2*mko2 - 1./8.*mpp2*me2 + 1./72.*mpo2*mkp2 + 7./72.*mpo2*mko2 - 1./4.*mpo2*me2 + 5./72.*pow(mpo2,2) - 7./72. *mkp2*mko2 + 5./24.*mkp2*me2 + 1./24.*mko2*me2 - 1./12.*pow( mko2,2) + 1./8.*pow(me2,2) ); Ap4KPpoiso += + B1b(mp2,mk2,mp2,mu2)*G8*spe3 * ( 17./4.*mp2*mk2 + 5./4.*pow(mp2,2) - 11./2.*pow(mk2,2) ); Ap4KPpoiso += + B1b(mp2,mk2,mp2,mu2)*G27*spe3 * ( 13./4.*mp2*mk2 - 13./4.*pow(mk2,2) ); Ap4KPpoiso += + B1b(mp2,mk2,mp2,mu2)*GE * ( - 5./4.*mp2 + 5./4. *mk2 ); Ap4KPpoiso += + B1b(mk2,me2,mp2,mu2)*G8*spe3 * ( 5./2.*mp2*mk2 - 5./2.*pow(mk2,2) ); Ap4KPpoiso += + B1b(mk2,me2,mp2,mu2)*G27*spe3 * ( 5./2.*mp2*mk2 - 5./4.*pow(mp2,2) - 5./4.*pow(mk2,2) ); Ap4KPpoiso += + B1b(mk2,me2,mp2,mu2)*GE * ( - 3./4.*mp2 + 3./4. *mk2 ); Ap4KPpoiso += + B1b(mpp2,mpo2,mkp2,mu2)*G8 * ( 2*mpp2*mpo2 - pow(mpp2,2) - pow(mpo2,2) ); Ap4KPpoiso += + B1b(mpp2,mpo2,mkp2,mu2)*G27 * ( 3*mpp2*mpo2 - 7./ 3.*pow(mpp2,2) - 2./3.*pow(mpo2,2) ); Ap4KPpoiso += + B1b(mpp2,mkp2,mpo2,mu2)*G8 * ( 1./2.*mpp2*mkp2 - 1./2.*pow(mpp2,2) ); Ap4KPpoiso += + B1b(mpp2,mkp2,mpo2,mu2)*G27 * ( 2*mpp2*mkp2 - 7./ 6.*pow(mpp2,2) - 5./6.*pow(mkp2,2) ); Ap4KPpoiso += + B1b(mpp2,mko2,mpp2,mu2)*G8 * ( 1./2.*mpo2*mko2 - 1./2.*mkp2*mko2 ); Ap4KPpoiso += + B1b(mpp2,mko2,mpp2,mu2)*G27 * ( 1./3.*mpo2*mko2 - 1./3.*mkp2*mko2 ); Ap4KPpoiso += + B1b(mpo2,mkp2,mpp2,mu2)*G8 * ( - 1./4.*mpo2* mkp2 + 1./4.*pow(mpo2,2) ); Ap4KPpoiso += + B1b(mpo2,mkp2,mpp2,mu2)*G27 * ( 1./4.*mpo2*mkp2 + 1./6.*pow(mpo2,2) - 5./12.*pow(mkp2,2) ); Ap4KPpoiso += + B1b(mpo2,mko2,mpo2,mu2)*G8 * ( - 1./2.*mpp2* mko2 + 1./2.*mkp2*mko2 ); Ap4KPpoiso += + B1b(mpo2,mko2,mpo2,mu2)*G27 * ( 1./2.*mpp2*mko2 - 1./2.*mkp2*mko2 ); Ap4KPpoiso += + B1b(mkp2,mko2,mkp2,mu2)*G8 * ( mpp2*mko2 - mpo2* mko2 ); Ap4KPpoiso += + B1b(mkp2,mko2,mkp2,mu2)*G27 * ( 2./3.*mpp2*mko2 - 2./3.*mpo2*mko2 ); Ap4KPpoiso += + B1b(mkp2,me2,mpp2,mu2)*G8 * ( - 1./2.*mpo2*mkp2 + 3./4.*mpo2*me2 - 3./4.*mkp2*me2 + 1./2.*pow(mkp2,2) ); Ap4KPpoiso += + B1b(mkp2,me2,mpp2,mu2)*G27 * ( - 3./4.*mpo2* mkp2 + 1./2.*mpo2*me2 - 1./2.*mkp2*me2 + 3./4.*pow(mkp2,2) ); Ap4KPpoiso += + B1b(mko2,me2,mpo2,mu2)*G8 * ( 1./2.*mpp2*mko2 - 3./4.*mpp2*me2 - 1./2.*mkp2*mko2 + 3./4.*mkp2*me2 ); Ap4KPpoiso += + B1b(mko2,me2,mpo2,mu2)*G27 * ( - 1./2.*mpp2* mko2 + 3./4.*mpp2*me2 + 1./2.*mkp2*mko2 - 3./4.*mkp2*me2 ); return Ap4KPpoiso/(pow(fpip,4)*fkp); } dcomplex Ap4IKSoo(){ using namespace inputpars; double mpp2 = mpp*mpp, mpo2 = mpo*mpo, mkp2 = mkp*mkp, mko2 = mko*mko, me2 = me*me, mu2 = mu*mu; double mp2 = mpo2,mk2=mko2; dcomplex Ap4KSooem=dcomplex(0.); const double mg2 = 0.; Ap4KSooem = + B1b(mg2,mp2,mp2,mu2)*G8 * ( - 4*mp2 + 4*mk2 ); Ap4KSooem += + B1b(mg2,mp2,mp2,mu2)*G27 * ( 4*mp2 - 4*mk2 ); Ap4KSooem += + B1b(mg2,mk2,mk2,mu2)*G8 * ( - 2*mp2 + 2*mk2 ); Ap4KSooem += + B1b(mg2,mk2,mk2,mu2)*G27 * ( 2*mp2 - 2*mk2 ); Ap4KSooem += + dqsqBb(mg2,mp2,mp2,mu2)*G8 * ( - 8*mp2*mk2 + 8* pow(mp2,2) ); Ap4KSooem += + dqsqBb(mg2,mp2,mp2,mu2)*G27 * ( 8*mp2*mk2 - 8* pow(mp2,2) ); Ap4KSooem += + dqsqBb(mg2,mk2,mk2,mu2)*G8 * ( 4*mp2*mk2 - 4*pow( mk2,2) ); Ap4KSooem += + dqsqBb(mg2,mk2,mk2,mu2)*G27 * ( - 4*mp2*mk2 + 4* pow(mk2,2) ); Ap4KSooem += + dqsqB1b(mg2,mp2,mp2,mu2)*G8 * ( 8*mp2*mk2 - 8* pow(mp2,2) ); Ap4KSooem += + dqsqB1b(mg2,mp2,mp2,mu2)*G27 * ( - 8*mp2*mk2 + 8 *pow(mp2,2) ); Ap4KSooem += + dqsqB1b(mg2,mk2,mk2,mu2)*G8 * ( - 4*mp2*mk2 + 4* pow(mk2,2) ); Ap4KSooem += + dqsqB1b(mg2,mk2,mk2,mu2)*G27 * ( 4*mp2*mk2 - 4* pow(mk2,2) ); return Ap4KSooem*e2/(pow(fpip,2)*fkp); } dcomplex Ap4IKSpm(){ using namespace inputpars; double mpp2 = mpp*mpp, mpo2 = mpo*mpo, mkp2 = mkp*mkp, mko2 = mko*mko, me2 = me*me, mu2 = mu*mu; double mp2 = mpp2,mk2=mko2; dcomplex Ap4KSpmem=dcomplex(0.); const double mg2 = 0.; Ap4KSpmem = + Bb(mp2,mp2,mk2,mu2)*G8 * ( 2*mp2 - 4*mk2 ); Ap4KSpmem += + Bb(mp2,mp2,mk2,mu2)*G27 * ( 4./3.*mp2 - 8./3.*mk2 ); Ap4KSpmem += + Bb(mg2,mp2,mp2,mu2)*G8 * ( - 8*mp2 - 4*mk2 ); Ap4KSpmem += + Bb(mg2,mp2,mp2,mu2)*G27 * ( - 16./3.*mp2 - 8./3. *mk2 ); Ap4KSpmem += + B1b(mg2,mp2,mp2,mu2)*G8 * ( 10*mk2 ); Ap4KSpmem += + B1b(mg2,mp2,mp2,mu2)*G27 * ( 20./3.*mk2 ); Ap4KSpmem += + B1b(mg2,mk2,mk2,mu2)*G8 * ( - 2*mp2 + 2*mk2 ); Ap4KSpmem += + B1b(mg2,mk2,mk2,mu2)*G27 * ( - 4./3.*mp2 + 4./3. *mk2 ); Ap4KSpmem += + Cb(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G8 * ( - 12*mp2* mk2 + 8*pow(mp2,2) + 4*pow(mk2,2) ); Ap4KSpmem += + Cb(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G27 * ( - 8*mp2* mk2 + 16./3.*pow(mp2,2) + 8./3.*pow(mk2,2) ); Ap4KSpmem += + C11b(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G8 * ( 22*mp2* mk2 - 24*pow(mp2,2) - 4*pow(mk2,2) ); Ap4KSpmem += + C11b(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G27 * ( 44./3.* mp2*mk2 - 16*pow(mp2,2) - 8./3.*pow(mk2,2) ); Ap4KSpmem += + C21b(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G8 * ( - 8*mp2 *mk2 + 16*pow(mp2,2) + pow(mk2,2) ); Ap4KSpmem += + C21b(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G27 * ( - 16./ 3.*mp2*mk2 + 32./3.*pow(mp2,2) + 2./3.*pow(mk2,2) ); Ap4KSpmem += + C24b(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G8 * ( 16*mp2 - 4*mk2 ); Ap4KSpmem += + C24b(mg2,mp2,mp2,mp2,mk2,mp2,mu2)*G27 * ( 32./3.* mp2 - 8./3.*mk2 ); Ap4KSpmem += + dqsqBb(mg2,mp2,mp2,mu2)*G8 * ( - 16*mp2*mk2 + 16 *pow(mp2,2) ); Ap4KSpmem += + dqsqBb(mg2,mp2,mp2,mu2)*G27 * ( - 32./3.*mp2*mk2 + 32./3.*pow(mp2,2) ); Ap4KSpmem += + dqsqBb(mg2,mk2,mk2,mu2)*G8 * ( 4*mp2*mk2 - 4*pow( mk2,2) ); Ap4KSpmem += + dqsqBb(mg2,mk2,mk2,mu2)*G27 * ( 8./3.*mp2*mk2 - 8. /3.*pow(mk2,2) ); Ap4KSpmem += + dqsqB1b(mg2,mp2,mp2,mu2)*G8 * ( 16*mp2*mk2 - 16* pow(mp2,2) ); Ap4KSpmem += + dqsqB1b(mg2,mp2,mp2,mu2)*G27 * ( 32./3.*mp2*mk2 - 32./3.*pow(mp2,2) ); Ap4KSpmem += + dqsqB1b(mg2,mk2,mk2,mu2)*G8 * ( - 4*mp2*mk2 + 4* pow(mk2,2) ); Ap4KSpmem += + dqsqB1b(mg2,mk2,mk2,mu2)*G27 * ( - 8./3.*mp2*mk2 + 8./3.*pow(mk2,2) ); return Ap4KSpmem*e2/(pow(fpip,2)*fkp); } dcomplex Ap4IKPpo(){ using namespace inputpars; double mpp2 = mpp*mpp, mpo2 = mpo*mpo, mkp2 = mkp*mkp, mko2 = mko*mko, me2 = me*me, mu2 = mu*mu; double mp2 = (mpp2+mpo2)/2.,mk2=mkp2; dcomplex Ap4KPpoem=dcomplex(0.); const double mg2 = 0.; Ap4KPpoem = + Ab(mp2,mu2)*G8 * ( - 1 ); Ap4KPpoem += + Ab(mp2,mu2)*G27 * ( - 29./6. ); Ap4KPpoem += + Ab(mk2,mu2)*G8 * ( 3./2. ); Ap4KPpoem += + Ab(mk2,mu2)*G27 * ( 13./3. ); Ap4KPpoem += + Bb(mp2,mk2,mp2,mu2)*G8 * ( - 2*mp2 + mk2 ); Ap4KPpoem += + Bb(mp2,mk2,mp2,mu2)*G27 * ( 1./3.*mp2 - mk2 ); Ap4KPpoem += + Bb(mg2,mp2,mp2,mu2)*G8 * ( - 4*mp2 ); Ap4KPpoem += + Bb(mg2,mp2,mp2,mu2)*G27 * ( - 6*mp2 ); Ap4KPpoem += + Bb(mg2,mk2,mk2,mu2)*G8 * ( - 2*mk2 ); Ap4KPpoem += + Bb(mg2,mk2,mk2,mu2)*G27 * ( 10./3.*mp2 - 4./3.* mk2 ); Ap4KPpoem += + B1b(mp2,mk2,mp2,mu2)*G8 * ( 2*mp2 - 2*mk2 ); Ap4KPpoem += + B1b(mp2,mk2,mp2,mu2)*G27 * ( 4./3.*mp2 - 4./3.* mk2 ); Ap4KPpoem += + B1b(mg2,mp2,mp2,mu2)*G8 * ( 4*mp2 ); Ap4KPpoem += + B1b(mg2,mp2,mp2,mu2)*G27 * ( 13./3.*mp2 + 5*mk2 ) ; Ap4KPpoem += + B1b(mg2,mk2,mk2,mu2)*G27 * ( - 5*mp2 ); Ap4KPpoem += + Cb(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( 10./3.* mp2*mk2 - 10./3.*pow(mk2,2) ); Ap4KPpoem += + C11b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G8 * ( - 4*mp2 *mk2 ); Ap4KPpoem += + C11b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( - 23./ 3.*mp2*mk2 - 10./3.*pow(mp2,2) + 5*pow(mk2,2) ); Ap4KPpoem += + C12b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G8 * ( 4*mp2* mk2 - 2*pow(mk2,2) ); Ap4KPpoem += + C12b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( 8./3.* mp2*mk2 + 10./3.*pow(mp2,2) + 2*pow(mk2,2) ); Ap4KPpoem += + C21b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G8 * ( 2*mp2* mk2 + 4*pow(mp2,2) ); Ap4KPpoem += + C21b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( 4./3.* mp2*mk2 + 28./3.*pow(mp2,2) - 5./3.*pow(mk2,2) ); Ap4KPpoem += + C22b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G8 * ( - 6*mp2 *mk2 + 4*pow(mp2,2) + 2*pow(mk2,2) ); Ap4KPpoem += + C22b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( - 32./ 3.*mp2*mk2 + 28./3.*pow(mp2,2) + 4./3.*pow(mk2,2) ); Ap4KPpoem += + C23b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G8 * ( 4*mp2* mk2 - 8*pow(mp2,2) + pow(mk2,2) ); Ap4KPpoem += + C23b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( 28./3.* mp2*mk2 - 56./3.*pow(mp2,2) - 8./3.*pow(mk2,2) ); Ap4KPpoem += + C24b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G8 * ( 4*mp2 + 2*mk2 ); Ap4KPpoem += + C24b(mg2,mp2,mk2,mp2,mp2,mk2,mu2)*G27 * ( 28./3.* mp2 - 16./3.*mk2 ); Ap4KPpoem += + dqsqBb(mg2,mp2,mp2,mu2)*G27 * ( - 10*mp2*mk2 + 10*pow(mp2,2) ); Ap4KPpoem += + dqsqBb(mg2,mk2,mk2,mu2)*G27 * ( 20./3.*mp2*mk2 - 20./3.*pow(mk2,2) ); Ap4KPpoem += + dqsqB1b(mg2,mp2,mp2,mu2)*G27 * ( 10*mp2*mk2 - 10* pow(mp2,2) ); Ap4KPpoem += + dqsqB1b(mg2,mk2,mk2,mu2)*G27 * ( - 20./3.*mp2* mk2 + 20./3.*pow(mk2,2) ); return Ap4KPpoem*e2/(pow(fpip,2)*fkp); } dcomplex Ap4KSooIR(double eg3pi,double egfpi){ using namespace inputpars; double mp2 = mpo*mpo, mk2 = mko*mko; double Ap2KSooiso = 0.; Ap2KSooiso = (G8-G27) * ( 2*mp2 - 2*mk2 )/(pow(fpip,2)*fkp); return -Ap2KSooiso*e2*3.*pi16*log(egfpi*egfpi/ffcut_.delta); } dcomplex Ap4KSpmIR(double eg3pi,double egfpi){ using namespace inputpars; double mp2 = mpp*mpp, mk2 = mko*mko; dcomplex Ap4IR = dcomplex(0.),Ap2KSpm = dcomplex(0.); Ap2KSpm = dcomplex((G8+2./3.*G27) * ( 2*mp2 - 2*mk2 )/(pow(fpip,2)*fkp)); Ap4IR = -Ap2KSpm*e2*3.*pi16*log(egfpi*egfpi/ffcut_.delta); Ap4IR += -Ap2KSpm*e2/2.*log(eg3pi*eg3pi/ffcut_.delta)* (4.*pi16-(mk2-2.*mp2)*CbREAL(ffcut_.delta,mp2,mp2,mk2)); return Ap4IR; } dcomplex Ap4KPpoIR(double eg3pi,double egfpi){ using namespace inputpars; double mp2 = (mpp*mpp+mpo*mpo)/2., mk2 = mkp*mkp; dcomplex Ap4IR = dcomplex(0.),Ap2KPpo=dcomplex(0.); Ap2KPpo = + G27*(5./3.*mp2 - 5./3.*mk2)/(pow(fpip,2)*fkp); Ap4IR = -Ap2KPpo*e2*3.*pi16*log(egfpi*egfpi/ffcut_.delta); Ap4IR += -Ap2KPpo*e2/2.*log(eg3pi*eg3pi/ffcut_.delta)* (4.*pi16-(-mk2)*CbREAL(ffcut_.delta,mp2,mk2,mp2)); return Ap4IR; } dcomplex AKSpmg(double s1, double s2, double s3){ using namespace photoncutoffs; using namespace inputpars; double mp2 = mpp*mpp, mk2 = mko*mko; double egamma = (mk2-s3)/(2.*mko); double t0 = (s3-mk2)/2.; double t1 = (s2-mp2)/2.; double t2 = (s1-mp2)/2.; double low1,low2,low3; double A2KSpmg = e2*pow((G8+2./3.*G27)*(mk2-mp2)/(pow(fpip,2)*fkp),2); double result; low1 = 1./t1-1./t2; low2 = -1./t1-1./t2; low3 = -low2; //low's theorem // low1 = 0.; // low2 = -2./t1; // low3 = 2./t2; result = -mk2*low1*low1-mp2*low2*low2-mp2*low3*low3 -(s1-mk2-mp2)*low1*low2-(s2-mk2-mp2)*low1*low3 -(s3-2.*mp2)*low2*low3; if(egamma < eg3pi){ return dcomplex(0.); // low1 = 0.; // low2 = -2./t1; // low3 = 2./t2; // result += (-mk2*low1*low1-mp2*low2*low2-mp2*low3*low3 // -(s1-mk2-mp2)*low1*low2-(s2-mk2-mp2)*low1*low3 // -(s3-2.*mp2)*low2*low3); } return dcomplex(sqrt(result*A2KSpmg)); //if (result<0.) return dcomplex(0.,sqrt(-result*A2KSpmg)); } dcomplex AKPpog(double s1, double s2, double s3){ using namespace photoncutoffs; using namespace inputpars; double mp2 = (mpp*mpp+mpo*mpo)/2., mk2 = mkp*mkp; double egamma = (mk2-s3)/(2.*mkp); double t0 = (s3-mk2)/2.; double t1 = (s2-mp2)/2.; double t2 = (s1-mp2)/2.; double low1,low2,low3; double A2KPpog= e2*pow(G27*(mk2-mp2)*5./6./(pow(fpip,2)*fkp),2); double result; low1 = 1./t1+1./t0; low2 = -low1; low3 = 1./t1-1./t0; // Low's theorem // low1 = 2./t0; // low2 = -2./t1; // low3 = 0.; result = -mk2*low1*low1-mp2*low2*low2-mp2*low3*low3 -(s1-mk2-mp2)*low1*low2-(s2-mk2-mp2)*low1*low3 -(s3-2.*mp2)*low2*low3; if(egamma < eg3pi){ return dcomplex(0.); } // std::cout << egamma <<' '<=0.) return dcomplex(sqrt(result*A2KPpog)); if (result<0.) return dcomplex(0.,sqrt(-result*A2KPpog)); } dcomplex Ap2KSpmold(){ using namespace inputpars; double mp2 = mpp*mpp, mk2 = mko*mko; double Ap2KSpmiso = 0.; Ap2KSpmiso += + G8 * ( 2*mp2 - 2*mk2 ); Ap2KSpmiso += + G27 * ( 4./3.*mp2 - 4./3.*mk2 ); return dcomplex(Ap2KSpmiso/(pow(fpip,2)*fkp)); } dcomplex Ap2KPpoold(){ using namespace inputpars; double mp2 = (mpo*mpo+mpp*mpp)/2., mk2 = mkp*mkp; double Ap2KPpoiso = 0.; Ap2KPpoiso += + G27 * ( 5./3.*mp2 - 5./3.*mk2 ); return dcomplex(Ap2KPpoiso/(pow(fpip,2)*fkp)); }