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ISGWFormFactor.cc
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// -*- C++ -*-
//
// ISGWFormFactor.cc is a part of Herwig++ - A multi-purpose Monte Carlo event generator
// Copyright (C) 2002-2007 The Herwig Collaboration
//
// Herwig++ is licenced under version 2 of the GPL, see COPYING for details.
// Please respect the MCnet academic guidelines, see GUIDELINES for details.
//
//
// This is the implementation of the non-inlined, non-templated member
// functions of the ISGWFormFactor class.
//
#include "ISGWFormFactor.h"
#include "ThePEG/Interface/ClassDocumentation.h"
#include "ThePEG/Interface/Parameter.h"
#include "ThePEG/Persistency/PersistentOStream.h"
#include "ThePEG/Persistency/PersistentIStream.h"
using namespace Herwig;
using namespace ThePEG;
ISGWFormFactor::ISGWFormFactor() {
// default values of the parameters
// fudge factor
_kappa=0.7;
// quark masses
_mdown =0.33*GeV;
_mup =0.33*GeV;
_mstrange=0.55*GeV;
_mcharm =1.82*GeV;
_mbottom =5.12*GeV;
// beta values
_betaSud = 0.31*GeV;
_betaSus = 0.34*GeV;
_betaSuc = 0.39*GeV;
_betaSub = 0.41*GeV;
_betaPud = 0.27*GeV;
_betaPus = 0.30*GeV;
_betaPuc = 0.34*GeV;
// the mixing for eta/eta'
_thetaeta=-Constants::pi/18.;
// B_u decays to d ubar
addFormFactor(-521,-211 ,0,-2, 5, 1);
addFormFactor(-521,-213 ,1,-2, 5, 1);
addFormFactor(-521,-215 ,2,-2, 5, 1);
addFormFactor(-521,-10213,1,-2, 5, 1);
addFormFactor(-521,-20213,1,-2, 5, 1);
addFormFactor(-521,-10211,0,-2, 5, 1);
// B_u to uu (I=0)
addFormFactor(-521, 221 ,0,-2, 5, 2);
addFormFactor(-521, 331 ,0,-2, 5, 2);
addFormFactor(-521, 223 ,1,-2, 5, 2);
addFormFactor(-521, 225 ,2,-2, 5, 2);
addFormFactor(-521, 10223,1,-2, 5, 2);
addFormFactor(-521, 20223,1,-2, 5, 2);
addFormFactor(-521, 10221,0,-2, 5, 2);
// B_u to uu (I=1)
addFormFactor(-521, 111 ,0,-2, 5, 2);
addFormFactor(-521, 113 ,1,-2, 5, 2);
addFormFactor(-521, 115 ,2,-2, 5, 2);
addFormFactor(-521, 10113,1,-2, 5, 2);
addFormFactor(-521, 20113,1,-2, 5, 2);
addFormFactor(-521, 10111,0,-2, 5, 2);
// B_u decays to d ubar
addFormFactor(-521,-321 ,0,-2, 5, 3);
addFormFactor(-521,-323 ,1,-2, 5, 3);
addFormFactor(-521,-325 ,2,-2, 5, 3);
addFormFactor(-521,-10323,1,-2, 5, 3);
addFormFactor(-521,-20323,1,-2, 5, 3);
addFormFactor(-521,-10321,0,-2, 5, 3);
// B_u decays to c ubar
addFormFactor(-521, 421 ,0,-2, 5, 4);
addFormFactor(-521, 423 ,1,-2, 5, 4);
addFormFactor(-521, 425 ,2,-2, 5, 4);
addFormFactor(-521, 10423,1,-2, 5, 4);
addFormFactor(-521, 20423,1,-2, 5, 4);
addFormFactor(-521, 10421,0,-2, 5, 4);
// B_d to d dbar (I=0)
addFormFactor(-511, 221 ,0, 1,-5,-1);
addFormFactor(-511, 331 ,0, 1,-5,-1);
addFormFactor(-511, 223 ,1, 1,-5,-1);
addFormFactor(-511, 225 ,2, 1,-5,-1);
addFormFactor(-511, 10223,1, 1,-5,-1);
addFormFactor(-511, 20223,1, 1,-5,-1);
addFormFactor(-511, 10221,0, 1,-5,-1);
// B_d to d dbar (I=1)
addFormFactor(-511, 111 ,0, 1,-5,-1);
addFormFactor(-511, 113 ,1, 1,-5,-1);
addFormFactor(-511, 115 ,2, 1,-5,-1);
addFormFactor(-511, 10113,1, 1,-5,-1);
addFormFactor(-511, 20113,1, 1,-5,-1);
addFormFactor(-511, 10111,0, 1,-5,-1);
// B_d to u dbar
addFormFactor(-511, 211 ,0, 1,-5,-2);
addFormFactor(-511, 213 ,1, 1,-5,-2);
addFormFactor(-511, 215 ,2, 1,-5,-2);
addFormFactor(-511, 10213,1, 1,-5,-2);
addFormFactor(-511, 20213,1, 1,-5,-2);
addFormFactor(-511, 10211,0, 1,-5,-2);
// B_d to s dbar
addFormFactor(-511, 311 ,0, 1,-5,-3);
addFormFactor(-511, 313 ,1, 1,-5,-3);
addFormFactor(-511, 315 ,2, 1,-5,-3);
addFormFactor(-511, 10313,1, 1,-5,-3);
addFormFactor(-511, 20313,1, 1,-5,-3);
addFormFactor(-511, 10311,0, 1,-5,-3);
// B_d decays to c dbar
addFormFactor(-511, 411 ,0, 1,-5,-4);
addFormFactor(-511, 413 ,1, 1,-5,-4);
addFormFactor(-511, 415 ,2, 1,-5,-4);
addFormFactor(-511, 10413,1, 1,-5,-4);
addFormFactor(-511, 20413,1, 1,-5,-4);
addFormFactor(-511, 10411,0, 1,-5,-4);
// D0 to d ubar
addFormFactor( 421,-211 ,0,-2, 4, 1);
addFormFactor( 421,-213 ,1,-2, 4, 1);
addFormFactor( 421,-215 ,2,-2, 4, 1);
addFormFactor( 421,-10213,1,-2, 4, 1);
addFormFactor( 421,-20213,1,-2, 4, 1);
addFormFactor( 421,-10211,0,-2, 4, 1);
// D0 to d ubar (I=1)
addFormFactor( 421, 111 ,0,-2, 4, 2);
addFormFactor( 421, 113 ,1,-2, 4, 2);
addFormFactor( 421, 115 ,2,-2, 4, 2);
addFormFactor( 421, 10113,1,-2, 4, 2);
addFormFactor( 421, 20113,1,-2, 4, 2);
addFormFactor( 421, 10111,0,-2, 4, 2);
// D0 to d ubar (I=0)
addFormFactor( 421, 221 ,0,-2, 4, 2);
addFormFactor( 421, 331 ,0,-2, 4, 2);
addFormFactor( 421, 223 ,1,-2, 4, 2);
addFormFactor( 421, 225 ,2,-2, 4, 2);
addFormFactor( 421, 10223,1,-2, 4, 2);
addFormFactor( 421, 20223,1,-2, 4, 2);
addFormFactor( 421, 10221,0,-2, 4, 2);
// D0 to s ubar
addFormFactor( 421,-321 ,0,-2, 4, 3);
addFormFactor( 421,-323 ,1,-2, 4, 3);
addFormFactor( 421,-325 ,2,-2, 4, 3);
addFormFactor( 421,-10323,1,-2, 4, 3);
addFormFactor( 421,-20323,1,-2, 4, 3);
addFormFactor( 421,-10321,0,-2, 4, 3);
// D+ to d dbar I=0
addFormFactor( 411, 221 ,0,-1, 4, 1);
addFormFactor( 411, 331 ,0,-1, 4, 1);
addFormFactor( 411, 223 ,1,-1, 4, 1);
addFormFactor( 411, 225 ,2,-1, 4, 1);
addFormFactor( 411, 10223,1,-1, 4, 1);
addFormFactor( 411, 20223,1,-1, 4, 1);
addFormFactor( 411, 10221,0,-1, 4, 1);
// D+ to d dbar I=1
addFormFactor( 411, 111 ,0,-1, 4, 1);
addFormFactor( 411, 113 ,1,-1, 4, 1);
addFormFactor( 411, 115 ,2,-1, 4, 1);
addFormFactor( 411, 10113,1,-1, 4, 1);
addFormFactor( 411, 20113,1,-1, 4, 1);
addFormFactor( 411, 10111,0,-1, 4, 1);
// D+ to u dbar
addFormFactor( 411, 211 ,0,-1, 4, 2);
addFormFactor( 411, 213 ,1,-1, 4, 2);
addFormFactor( 411, 215 ,2,-1, 4, 2);
addFormFactor( 411, 10213,1,-1, 4, 2);
addFormFactor( 411, 20213,1,-1, 4, 2);
addFormFactor( 411, 10211,0,-1, 4, 2);
// D+ to s dbar
addFormFactor( 411,-311 ,0,-1, 4, 3);
addFormFactor( 411,-313 ,1,-1, 4, 3);
addFormFactor( 411,-315 ,2,-1, 4, 3);
addFormFactor( 411,-10313,1,-1, 4, 3);
addFormFactor( 411,-20313,1,-1, 4, 3);
addFormFactor( 411,-10311,0,-1, 4, 3);
// set the initial number of modes
initialModes(numberOfFactors());
}
void ISGWFormFactor::doinit() throw(InitException) {
ScalarFormFactor::doinit();
// set up the quark masses
_mquark.resize(5);
_mquark[0]=_mdown;
_mquark[1]=_mup;
_mquark[2]=_mstrange;
_mquark[3]=_mcharm;
_mquark[4]=_mbottom;
// and the beta values
_betaS.resize(5,vector<Energy>(5));
_betaP.resize(5,vector<Energy>(5));
_betaS[0][0] = _betaSud;_betaP[0][0] = _betaPud;
_betaS[1][0] = _betaSud;_betaP[1][0] = _betaPud;
_betaS[2][0] = _betaSus;_betaP[2][0] = _betaPus;
_betaS[3][0] = _betaSuc;_betaP[3][0] = _betaPuc;
_betaS[4][0] = _betaSub;_betaP[4][0] = 0.*MeV ;
_betaS[0][1] = _betaSud;_betaP[0][1] = _betaPud;
_betaS[1][1] = _betaSud;_betaP[1][1] = _betaPud;
_betaS[2][1] = _betaSus;_betaP[2][1] = _betaPus;
_betaS[3][1] = _betaSuc;_betaP[3][1] = _betaPuc;
_betaS[4][1] = _betaSub;_betaP[4][1] = 0.*MeV ;
_betaS[0][2] = _betaSus;_betaP[0][2] = _betaPus;
_betaS[1][2] = _betaSus;_betaP[1][2] = _betaPus;
_betaS[2][2] = 0.*MeV ;_betaP[2][2] = 0.*MeV ;
_betaS[3][2] = 0.*MeV ;_betaP[3][2] = 0.*MeV ;
_betaS[4][2] = 0.*MeV ;_betaP[4][2] = 0.*MeV ;
_betaS[0][3] = _betaSuc;_betaP[0][3] = _betaPuc;
_betaS[1][3] = _betaSuc;_betaP[1][3] = _betaPuc;
_betaS[2][3] = 0.*MeV ;_betaP[2][3] = 0.*MeV ;
_betaS[3][3] = 0.*MeV ;_betaP[3][3] = 0.*MeV ;
_betaS[4][3] = 0.*MeV ;_betaP[4][3] = 0.*MeV ;
_betaS[0][4] = 0.*MeV ;_betaP[0][4] = 0.*MeV ;
_betaS[1][4] = 0.*MeV ;_betaP[1][4] = 0.*MeV ;
_betaS[2][4] = 0.*MeV ;_betaP[2][4] = 0.*MeV ;
_betaS[3][4] = 0.*MeV ;_betaP[3][4] = 0.*MeV ;
_betaS[4][4] = 0.*MeV ;_betaP[4][4] = 0.*MeV ;
}
void ISGWFormFactor::persistentOutput(PersistentOStream & os) const {
os << _kappa << ounit(_mdown,GeV) << ounit(_mup,GeV) << ounit(_mstrange,GeV)
<< ounit(_mcharm,GeV) << ounit(_mbottom,GeV) << ounit(_betaSud,GeV)
<< ounit(_betaSus,GeV) << ounit(_betaSuc,GeV) << ounit(_betaSub,GeV)
<< ounit(_betaPud,GeV) << ounit(_betaPus,GeV) << ounit(_betaPuc,GeV)
<< _thetaeta << ounit(_mquark,GeV) << ounit(_betaS,GeV) << ounit(_betaP,GeV);
}
void ISGWFormFactor::persistentInput(PersistentIStream & is, int) {
is >> _kappa >> iunit(_mdown,GeV) >> iunit(_mup,GeV) >> iunit(_mstrange,GeV)
>> iunit(_mcharm,GeV) >> iunit(_mbottom,GeV) >> iunit(_betaSud,GeV)
>> iunit(_betaSus,GeV) >> iunit(_betaSuc,GeV) >> iunit(_betaSub,GeV)
>> iunit(_betaPud,GeV) >> iunit(_betaPus,GeV) >> iunit(_betaPuc,GeV)
>> _thetaeta >> iunit(_mquark,GeV) >> iunit(_betaS,GeV) >> iunit(_betaP,GeV);
}
ClassDescription<ISGWFormFactor> ISGWFormFactor::initISGWFormFactor;
// Definition of the static class description member.
void ISGWFormFactor::Init() {
static ClassDocumentation<ISGWFormFactor> documentation
("The ISGWFormFactor class implements the ISGW model of"
"Phys. Rev. D39, 799 (1989) for the scalar meson form-factors.",
"The form factor model of ISGW \\cite{Isgur:1988gb} together with the"
"form factors for the term which are supressed by the lepton mass from"
"\\cite{Scora:1989ys,Isgur:1990jf}",
"\\bibitem{Isgur:1988gb} N.~Isgur, D.~Scora, B.~Grinstein and M.~B.~Wise,\n"
"Phys.\\ Rev.\\ D {\\bf 39} (1989) 799.\n"
"%%CITATION = PHRVA,D39,799;%%\n"
"\\bibitem{Scora:1989ys} D.~Scora and N.~Isgur, \n"
"Phys.\\ Rev.\\ D {\\bf 40} (1989) 1491.\n"
"%%CITATION = PHRVA,D40,1491;%%\n"
"\\bibitem{Isgur:1990jf} N.~Isgur and M.~B.~Wise,\n"
"Phys.\\ Rev.\\ D {\\bf 43} (1991) 819.\n"
"%%CITATION = PHRVA,D43,819;%%\n");
static Parameter<ISGWFormFactor,double> interfaceKappa
("Kappa",
"The relavistic compensation factor of the ISGW model",
&ISGWFormFactor::_kappa, 0.7, 0.0, 1.0,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceDownMass
("DownMass",
"The mass of the down quark in the ISGW model (this is a consituent mass)",
&ISGWFormFactor::_mdown, GeV, 0.33*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceUpMass
("UpMass",
"The mass of the up quark in the ISGW model (this is a consituent mass)",
&ISGWFormFactor::_mup, GeV, 0.33*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceStrangeMass
("StrangeMass",
"The mass of the strange quark in the ISGW model (this is a consituent mass)",
&ISGWFormFactor::_mstrange, GeV, 0.55*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceCharmMass
("CharmMass",
"The mass of the charm quark in the ISGW model (this is a consituent mass)",
&ISGWFormFactor::_mcharm, GeV, 1.82*GeV, 0.0*GeV, 3.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBottomMass
("BottomMass",
"The mass of the bottom quark in the ISGW model (this is a consituent mass)",
&ISGWFormFactor::_mbottom, GeV, 5.12*GeV, 3.0*GeV, 10.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaSud
("BetaSud",
"The variational parameter for s-wave ud mesons",
&ISGWFormFactor::_betaSud, GeV, 0.31*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaSus
("BetaSus",
"The variational parameter for s-wave us mesons",
&ISGWFormFactor::_betaSus, GeV, 0.34*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaSuc
("BetaSuc",
"The variational parameter for s-wave uc mesons",
&ISGWFormFactor::_betaSuc, GeV, 0.39*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaSub
("BetaSub",
"The variational parameter for s-wave ub mesons",
&ISGWFormFactor::_betaSub, GeV, 0.41*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaPud
("BetaPud",
"The variational parameter for p-wave ud mesons",
&ISGWFormFactor::_betaPud, GeV, 0.27*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaPus
("BetaPus",
"The variational parameter for p-wave us mesons",
&ISGWFormFactor::_betaPus, GeV, 0.30*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,Energy> interfaceBetaPuc
("BetaPuc",
"The variational parameter for p-wave uc mesons",
&ISGWFormFactor::_betaPuc, GeV, 0.34*GeV, 0.0*GeV, 1.0*GeV,
false, false, true);
static Parameter<ISGWFormFactor,double> interfaceThetaEtaEtaPrime
("ThetaEtaEtaPrime",
"The eta-eta' mixing angle",
&ISGWFormFactor::_thetaeta, -Constants::pi/18., -Constants::pi, Constants::pi,
false, false, true);
}
// form-factor for scalar to scalar
void ISGWFormFactor::ScalarScalarFormFactor(Energy2 q2, unsigned int iloc,int id0,
int id1,Energy mY,Energy mX,
Complex & f0,Complex & fp) const {
Complex d1(0.),d2(0.);
formFactor(q2,iloc,id0,id1,mY,mX,f0,fp,d1,d2);
}
// form-factor for scalar to vector
void ISGWFormFactor::ScalarVectorFormFactor(Energy2 q2, unsigned int iloc, int id0,
int id1,Energy mY, Energy mX,
Complex & A0,Complex & A1,
Complex & A2,Complex & V) const {
formFactor(q2,iloc,id0,id1,mY,mX,A0,A1,A2,V);
}
// form-factor for scalar to tensor
void ISGWFormFactor::ScalarTensorFormFactor(Energy2 q2, unsigned int iloc, int id0,
int id1, Energy mY, Energy mX,
complex<InvEnergy2> & h,Complex & k,
complex<InvEnergy2> & bp,
complex<InvEnergy2> & bm) const {
Complex f1,f2,f3,f4;
formFactor(q2,iloc,id0,id1,mY,mX,f1,f2,f3,f4);
Energy msum(mX+mY);
h = f1/sqr(msum);
k = f2;
bp = f3/sqr(msum);
bm = f4/sqr(msum);
}
// member which does the work
void ISGWFormFactor::formFactor(Energy2 q2, unsigned int iloc, int, int id1,
Energy mY,Energy mX, Complex & f1,Complex & f2,
Complex & f3, Complex & f4) const {
useMe();
// work out the flavour of the heavy quarks etc
int jspin,spect,inquark,outquark;
formFactorInfo(iloc,jspin,spect,inquark,outquark);
int ifl0(abs(inquark)),ifl1(abs(outquark)),ifls(abs(spect));
// determine the multiplet
int ispin(abs(id1)/1000);
// masses of the quarks
Energy mQ(_mquark[ifl0-1]),mq(_mquark[ifl1-1]),ms(_mquark[ifls-1]);
Energy mtildeX(mq+ms),mtildeY(mQ+ms);
// wavefunction parameters for the mesons
Energy betaX(0.*MeV),betaY(_betaS[ifl0-1][ifls-1]);
// spin-0 outgoing mesons
if(ispin==0&&jspin<2) {
betaX=_betaS[ifl1-1][ifls-1];
}
else {
betaX=_betaP[ifl1-1][ifls-1];
}
// compute the F_n function we will need
Energy2 beta2XY(0.5*(betaX*betaX+betaY*betaY)),tm((mY-mX)*(mY-mX));
double betar(betaX*betaY/beta2XY),kappa2(_kappa*_kappa),
slope((tm-q2)/(kappa2*beta2XY));
Energy mup(mq*mQ/(mQ+mq)),mum(mq*mQ/(mQ-mq));
double fn(sqrt(mtildeX/mtildeY)*betar*sqrt(betar)*
exp(-0.25*ms*ms/(mtildeX*mtildeY)*slope));
// now we can compute the form-factors
// for scalars
if(jspin==0) {
Complex fp,fm;
// 1 1S0
if(ispin==0) {
double yratio(ms/mtildeX*betaY*betaY/beta2XY);
fp = fn*(1.+0.5*mQ/mum-0.25*mQ*mq/mup/mum*yratio);
fm = fn*(1.-(mtildeX+mtildeY)*(0.5/mq-0.25/mup*yratio));
}
// 1 3P0
else if(ispin<100) {
// extra power of beta factors
fn*=betar;
fp = fn*ms*mQ*mq/sqrt(6.)/betaY/mtildeX/mum;
fm =-fn*ms/betaY/sqrt(6.)*(mtildeX+mtildeY)/mtildeX;
}
// 2 1S0
else {
throw Exception() << "ISGWFormFactor::formFactor"
<< " 2S not implemented" << Exception::abortnow;
}
// convert to the standard form
f1 = Complex(q2/(mY*mY-mX*mX)*fm)+fp;
f2 = fp;
}
// for vectors
else if(jspin==1) {
complex<Energy> f;
complex<InvEnergy> g,ap,am;
Energy2 betaX2(betaX*betaX),betaY2(betaY*betaY);
// 1 3S1
if(ispin==0) {
f = 2.*mtildeY*fn;
g = 0.5*fn*(1./mq-0.5/mum*ms/mtildeX*betaY2/beta2XY);
ap =-0.5*fn/mtildeX*(1.+ms/mQ*(betaY2-betaX2)/(betaX2+betaY2)
-0.25*ms*ms/mum/mtildeY*betaX2*betaX2/beta2XY/beta2XY);
am = 0.5*fn/mtildeX*(1.+ms/mQ+ms*ms/mq/mQ*betaX2/beta2XY*
(1.-0.25*(mtildeX+mtildeY)/mtildeY*betaX2/beta2XY));
}
// 1 3P1
else if(ispin==20) {
fn*=betar;
f =-fn*mtildeY*betaY*(1./mum+0.5*ms/mtildeY*beta2XY*slope/betaY2*
(1./mq-0.5/mum*ms/mtildeX*betaY2/beta2XY));
g = 0.5*fn*ms/mtildeX/betaY;
ap = 0.25*fn*ms*mQ/mtildeY/betaY/mum*(1.-0.5*ms*mq/mtildeX/mum*betaY2/beta2XY);
am = -0.25*fn*ms*(mtildeX+mtildeY)/mq/betaY/mtildeY*
(1.-0.5*ms*mq/mtildeX/mum*betaY2/beta2XY);
}
// 1 1P1
else if(ispin==10) {
fn*=betar;
double ort(1./sqrt(2.));
f = fn*ort*mtildeY*betaY/mup;
g = 0.25*fn*mtildeY*betaY*ort/mq/mQ/mtildeX;
Energy msum(mtildeX+mtildeY);
ap = fn*ms*ort/betaY/mtildeY*(1.+0.5*mQ/mum
-0.25*mq*mQ*ms/mum/mup/mtildeX*betaY2/beta2XY);
am = fn*ms*ort/betaY/mtildeY*(1.-0.5/mq*msum
+0.25*ms*betaY2/mup/beta2XY*msum/mtildeX);
}
// 2 1S0
else {
throw Exception() << "ISGWFormFactor::formFactor"
<< " 2S not implemented" << Exception::abortnow;
}
// convert to the standard notation
Energy msum(mX+mY),mdiff(mY-mX);
Complex ii(0.,1.);
f2 = -ii*f/msum;
f3 = +ii*ap*msum;
f1 = -ii*0.5/mX*(am*q2+ii*msum*f2-ii*mdiff*f3);
f4 = ii*g*msum;
}
// for tensors
else if(jspin==2) {
Energy msum(mX+mY);
fn *=betar/sqrt(2.);
double betaXb2(betaX*betaX/beta2XY);
// 1 3P2
if(ispin==0) {
f1 = 0.5*fn*ms/mtildeY/betaY*(1./mq
-0.5*ms/mtildeX/mum*betaY*betaY/beta2XY)*sqr(msum);
f2 = 2.*fn*ms/betaY;
f3 =-0.5*fn*ms/mtildeX/mQ/betaY*
(1.-0.5*ms*mQ/mup/mtildeY*betaXb2
+0.25*ms*mQ/mtildeY/mum*betaXb2*(1.-0.5*ms*betaXb2/mtildeY))*
sqr(msum);
f4 = 0.5*fn*ms/mtildeX/mQ/betaY*
(1.-0.5*ms*mQ/mup/mtildeY*betaXb2+
0.25*ms*betaXb2/mq*(mtildeX+mtildeY)/mtildeY*(1.-0.5*ms*betaXb2/mtildeY))*
sqr(msum);
}
}
else {
throw Exception() << "ISGWFormFactor::FormFactor spin = " << jspin
<< " but spins higher than 2 not implemented"
<< Exception::runerror;
}
// special for mixing
double fact(1.);
if(id1==ParticleID::eta) {
if(ifl1==3&&ifls==3) fact = -2.*cos(_thetaeta)/sqrt(6.) - sin(_thetaeta)/sqrt(3.);
else fact = cos(_thetaeta)/sqrt(6.) - sin(_thetaeta)/sqrt(3.);
}
else if(id1==ParticleID::etaprime) {
if(ifl1==3&&ifls==3) fact = -2.*sin(_thetaeta)/sqrt(6.) + cos(_thetaeta)/sqrt(3.);
else fact = sin(_thetaeta)/sqrt(6.) + cos(_thetaeta)/sqrt(3.);
}
else if(ifl1==ifls&&ifl1<3) {
if(abs(ifl1)==1&&int(id1/10)%100==1) fact = -sqrt(0.5);
else fact = sqrt(0.5);
}
f1*=fact;
f2*=fact;
f3*=fact;
f4*=fact;
}
void ISGWFormFactor::dataBaseOutput(ofstream & output,bool header,bool create) const {
if(header) output << "update decayers set parameters=\"";
if(create) output << "create Herwig::ISGWFormFactor " << name() << "\n";
output << "set " << name() << ":Kappa " << _kappa << "\n";
output << "set " << name() << ":DownMass " << _mdown/GeV << "\n";
output << "set " << name() << ":UpMass " << _mup/GeV << "\n";
output << "set " << name() << ":StrangeMass " << _mstrange/GeV << "\n";
output << "set " << name() << ":CharmMass " << _mcharm/GeV << "\n";
output << "set " << name() << ":BottomMass " << _mbottom/GeV << "\n";
output << "set " << name() << ":BetaSud " << _betaSud/GeV << "\n";
output << "set " << name() << ":BetaSus " << _betaSus/GeV << "\n";
output << "set " << name() << ":BetaSuc " << _betaSuc/GeV << "\n";
output << "set " << name() << ":BetaSub " << _betaSub/GeV << "\n";
output << "set " << name() << ":BetaPud " << _betaPud/GeV << "\n";
output << "set " << name() << ":BetaPus " << _betaPus/GeV << "\n";
output << "set " << name() << ":BetaPuc " << _betaPuc/GeV << "\n";
output << "set " << name() << ":ThetaEtaEtaPrime " << _thetaeta << "\n";
ScalarFormFactor::dataBaseOutput(output,false,false);
if(header) output << "\n\" where BINARY ThePEGName=\"" << fullName() << "\";" << endl;
}

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