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EvtBBScalar.cpp
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//--------------------------------------------------------------------------
//
// Environment:
// This software is part of the EvtGen package developed jointly
// for the BaBar and CLEO collaborations. If you use all or part
// of it, please give an appropriate acknowledgement.
//
// Copyright Information: See EvtGen/COPYRIGHT
// Copyright (C) 2003 Caltech
//
// Module: EvtGen/EvtBBScalar
//
// Description:Implementation of the decay B- -> lambda p_bar pi according to
// hep-ph/0204185, hep-ph/0211240
// This model is intended to be applicable to all decays of the type B-> baryon baryon scalar
//
// Modification history:
//
// Jan Strube March 24, 2006 Module created
//
//------------------------------------------------------------------------
#include "EvtGenBase/EvtPatches.hh"
#include "EvtGenModels/EvtBBScalar.hh"
#include "EvtGenBase/EvtGammaMatrix.hh"
#include "EvtGenBase/EvtDiracSpinor.hh"
#include "EvtGenBase/EvtSpinType.hh"
#include "EvtGenBase/EvtTensor4C.hh"
#include <cmath>
using namespace std;
const float pi = 3.14159;
const EvtComplex EvtBBScalar::I = EvtComplex(0, 1);
const EvtComplex EvtBBScalar::V_ub = EvtComplex(3.67e-3*cos(60/180*pi), 3.67e-3*cos(60/180*pi));
const EvtComplex EvtBBScalar::V_us_star = EvtComplex(0.22, 0);
const EvtComplex EvtBBScalar::a1 = EvtComplex(1.05, 0);
const EvtComplex EvtBBScalar::V_tb = EvtComplex(0.99915, 0);
const EvtComplex EvtBBScalar::V_ts_star = EvtComplex(-0.04029-0.000813*cos(60/180*pi), -0.000813*cos(60/180*pi));
const EvtComplex EvtBBScalar::a4 = EvtComplex(-387.3e-4, -121e-4);
const EvtComplex EvtBBScalar::a6 = EvtComplex(-555.3e-4, -121e-4);
const double EvtBBScalar::x[] = {420.96, -10485.50, 100639.97, -433916.61, 613780.15};
const double EvtBBScalar::y[] = {292.62, -735.73};
const double EvtBBScalar::m_s = 0.120;
const double EvtBBScalar::m_u = 0.029 * 0.120;
const double EvtBBScalar::m_b = 4.88;
EvtBBScalar::EvtBBScalar()
: EvtDecayAmp()
, _massRatio(0)
, _baryonMassSum(0)
{
FormFactor dummy;
dummy.value = 0.36;
dummy.sigma1 = 0.43;
dummy.sigma2 = 0.0;
dummy.mV = 5.42;
_f1Map.insert(make_pair(string("K"), dummy));
dummy.sigma1 = 0.70;
dummy.sigma2 = 0.27;
_f0Map.insert(make_pair(string("K"), dummy));
dummy.value = 0.29;
dummy.sigma1 = 0.48;
dummy.sigma2 = 0.0;
dummy.mV = 5.32;
_f1Map.insert(make_pair(string("pi"), dummy));
dummy.sigma1 = 0.76;
dummy.sigma2 = 0.28;
_f0Map.insert(make_pair(string("pi"), dummy));
}
std::string EvtBBScalar::getName(){
return "B_TO_2BARYON_SCALAR";
}
EvtDecayBase* EvtBBScalar::clone(){
return new EvtBBScalar;
}
void EvtBBScalar::setKnownBaryonTypes(const EvtId& baryon) {
int baryonId = EvtPDL::getStdHep(baryon);
if (EvtPDL::getStdHep(EvtPDL::getId("Lambda0")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-Lambda0")) == baryonId ) {
_baryonCombination.set(Lambda);
} else if (EvtPDL::getStdHep(EvtPDL::getId("p+")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-p-")) == baryonId ) {
_baryonCombination.set(Proton);
} else if (EvtPDL::getStdHep(EvtPDL::getId("n0")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-n0")) == baryonId) {
_baryonCombination.set(Neutron);
} else if (EvtPDL::getStdHep(EvtPDL::getId("Sigma0")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-Sigma0")) == baryonId ) {
_baryonCombination.set(Sigma0);
} else if (EvtPDL::getStdHep(EvtPDL::getId("Sigma-")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-Sigma+")) == baryonId ) {
_baryonCombination.set(Sigma_minus);
} else if (EvtPDL::getStdHep(EvtPDL::getId("Xi0")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-Xi0")) == baryonId) {
_baryonCombination.set(Xi0);
} else if (EvtPDL::getStdHep(EvtPDL::getId("Xi-")) == baryonId
or EvtPDL::getStdHep(EvtPDL::getId("anti-Xi+")) == baryonId) {
_baryonCombination.set(Xi_minus);
} else {
report(ERROR, "EvtGen")
<< "EvtBBScalar::init: Don't know what to do with this type as the first or second baryon\n";
exit(2);
}
}
double EvtBBScalar::baryonF1F2(double t) const {
// check for known form factors for combination of baryons
if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
return -sqrt(1.5) * G_p(t);
} else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
return -sqrt(0.5) * (G_p(t) + 2* G_n(t));
} else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
return -G_p(t) - 2* G_n(t);
} else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
return G_p(t) - G_n(t);
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
return sqrt(0.5) * (G_p(t) - G_n(t));
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
return sqrt(1.5) * (G_p(t) + G_n(t));
} else {
report(ERROR, "EvtGen")
<< "EvtBBScalar::baryonF1F2: Don't know what to do with this type as the first or second baryon\n";
exit(2);
}
}
double EvtBBScalar::formFactorFit(double t, const vector<double>& params) const {
static const double gamma = 2.148;
static const double Lambda_0 = 0.3;
double result = 0;
for (size_t i=0; i<params.size(); ++i) {
result += params[i]/pow(t, static_cast<int>(i+1));
}
return result * pow(log(t/pow(Lambda_0, 2)), -gamma);
}
double EvtBBScalar::G_p(double t) const {
const vector<double> v_x(x, x+5);
return formFactorFit(t, v_x);
}
double EvtBBScalar::G_n(double t) const {
const vector<double> v_y(y, y+2);
return -formFactorFit(t, v_y);
}
double EvtBBScalar::baryon_gA(double t) const {
// check for known form factors for combination of baryons
if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
return -1/sqrt(6.) * (D_A(t) + 3*F_A(t));
} else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
return 1/sqrt(2.) * (D_A(t) - F_A(t));
} else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
return D_A(t) - F_A(t);
} else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
return D_A(t) + F_A(t);
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
return 1/sqrt(2.) * (D_A(t) + F_A(t));
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
return -1 / sqrt(6.) * (D_A(t) - 3*F_A(t));
} else {
report(ERROR, "EvtGen")
<< "EvtBBScalar::baryon_gA: Don't know what to do with this type as the first or second baryon\n";
exit(2);
}
}
double EvtBBScalar::baryon_gP(double t) const {
// check for known form factors for combination of baryons
if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
return -1/sqrt(6.) * (D_P(t) + 3*F_P(t));
} else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
return 1/sqrt(2.) * (D_P(t) - F_P(t));
} else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
return D_P(t) - F_P(t);
} else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
return D_P(t) + F_P(t);
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
return 1/sqrt(2.) * (D_P(t) + F_P(t));
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
return -1 / sqrt(6.) * (D_P(t) - 3*F_P(t));
} else {
report(ERROR, "EvtGen")
<< "EvtBBScalar::baryon_gP: Don't know what to do with this type as the first or second baryon\n";
exit(2);
}
}
double EvtBBScalar::baryon_fS(double t) const {
// check for known form factors for combination of baryons
if (_baryonCombination.test(Lambda) and _baryonCombination.test(Proton)) {
return -1/sqrt(6.) * (D_S(t) + 3*F_S(t));
} else if (_baryonCombination.test(Sigma0) and _baryonCombination.test(Proton)) {
return 1/sqrt(2.) * (D_S(t) - F_S(t));
} else if (_baryonCombination.test(Sigma_minus) and _baryonCombination.test(Neutron)) {
return D_S(t) - F_S(t);
} else if (_baryonCombination.test(Xi0) and _baryonCombination.test(Sigma_minus)) {
return D_S(t) + F_S(t);
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Sigma0)) {
return 1/sqrt(2.) * (D_S(t) + F_S(t));
} else if (_baryonCombination.test(Xi_minus) and _baryonCombination.test(Lambda)) {
return -1 / sqrt(6.) * (D_S(t) - 3*F_S(t));
} else {
report(ERROR, "EvtGen")
<< "EvtBBScalar::baryon_fS: Don't know what to do with this type as the first or second baryon\n";
exit(2);
}
}
double EvtBBScalar::D_A(double t) const {
const double d_tilde[] = {x[0]-1.5*y[0], -478};
const vector<double> v_d_tilde(d_tilde, d_tilde+2);
return formFactorFit(t, v_d_tilde);
}
double EvtBBScalar::F_A(double t) const {
const double f_tilde[] = {2./3*x[0]+0.5*y[0], -478};
const vector<double> v_f_tilde(f_tilde, f_tilde+2);
return formFactorFit(t, v_f_tilde);
}
double EvtBBScalar::D_P(double t) const {
const double d_bar[] = {1.5*y[0]* _massRatio, /*-952*/0};
const vector<double> v_d_bar(d_bar, d_bar+2);
return formFactorFit(t, v_d_bar);
}
double EvtBBScalar::F_P(double t) const {
const double f_bar[] = {(x[0]-0.5*y[0]) * _massRatio, /*-952*/0};
const vector<double> v_f_bar(f_bar, f_bar+2);
return formFactorFit(t, v_f_bar);
}
double EvtBBScalar::D_S(double t) const {
return -1.5 * _massRatio * G_n(t);
}
double EvtBBScalar::F_S(double t) const {
return (G_p(t) + 0.5*G_n(t)) * _massRatio;
}
double EvtBBScalar::baryon_hA(double t) const {
return (1/_massRatio*baryon_gP(t)-baryon_gA(t))*pow(_baryonMassSum, 2)/t;
}
void EvtBBScalar::init() {
// no arguments, daughter lambda p_bar pi
// charge conservation is checked by base class
checkNArg(0);
checkNDaug(3);
checkSpinParent(EvtSpinType::SCALAR);
checkSpinDaughter(0, EvtSpinType::DIRAC);
checkSpinDaughter(1, EvtSpinType::DIRAC);
checkSpinDaughter(2, EvtSpinType::SCALAR);
EvtId baryon1 = getDaug(0);
EvtId baryon2 = getDaug(1);
EvtId scalar = getDaug(2);
int scalarId = EvtPDL::getStdHep(scalar);
// Different form factors for the B-pi or B-K transition.
if ( scalarId == EvtPDL::getStdHep(EvtPDL::getId("pi+"))
or scalarId == EvtPDL::getStdHep(EvtPDL::getId("pi-"))
or scalarId == EvtPDL::getStdHep(EvtPDL::getId("pi0"))) {
_scalarType = "pi";
} else if (scalarId == EvtPDL::getStdHep(EvtPDL::getId("K+"))
or scalarId == EvtPDL::getStdHep(EvtPDL::getId("K-"))
or scalarId == EvtPDL::getStdHep(EvtPDL::getId("K0"))
or scalarId == EvtPDL::getStdHep(EvtPDL::getId("anti-K0"))) {
_scalarType = "K";
} else {
report(ERROR, "EvtGen")
<< "EvtBBScalar::init: Can only deal with Kaons or pions as the third particle\n"
<< "\tFound: " << scalarId << endl;
exit(2);
}
// check for known particles
setKnownBaryonTypes(baryon1);
setKnownBaryonTypes(baryon2);
double mass1 = EvtPDL::getMass(baryon1);
double mass2 = EvtPDL::getMass(baryon2);
// This whole model deals only with baryons that differ in s-u
if (mass1 > mass2)
_massRatio = (mass1-mass2) / (m_s-m_u);
else
_massRatio = (mass2-mass1) / (m_s-m_u);
_baryonMassSum = mass1 + mass2;
}
// initialize phasespace and calculate the amplitude
void EvtBBScalar::decay(EvtParticle* p) {
p->initializePhaseSpace(getNDaug(), getDaugs());
EvtVector4R B_Momentum = p->getP4Lab();
EvtDiracParticle* theLambda = dynamic_cast<EvtDiracParticle*>(p->getDaug(0));
EvtDiracParticle* theAntiP = dynamic_cast<EvtDiracParticle*>(p->getDaug(1));
EvtScalarParticle* theScalar = dynamic_cast<EvtScalarParticle*>(p->getDaug(2));
EvtVector4R scalarMomentum = theScalar->getP4Lab();
// The amplitude consists of three matrix elements. These will be calculated one by one here.
// loop over all possible spin states
for (int i=0; i<2; ++i) {
EvtDiracSpinor lambdaPol = theLambda->spParent(i);
for (int j=0; j<2; ++j) {
EvtDiracSpinor antiP_Pol = theAntiP->spParent(j);
EvtVector4C theAmplitudePartA = amp_A(B_Momentum, scalarMomentum);
EvtComplex amplitude;
for (int index=0; index<4; ++index) {
amplitude += theAmplitudePartA.get(index)
* ( const_B*amp_B(theLambda, lambdaPol, theAntiP, antiP_Pol, index)
+ const_C*amp_C(theLambda, lambdaPol, theAntiP, antiP_Pol, index) );
}
vertex(i, j, amplitude);
}
}
}
void EvtBBScalar::initProbMax()
{
// setProbMax(1);
setProbMax(0.2); // found by trial and error
}
// Form factor f1 for B-pi transition
double EvtBBScalar::B_pi_f1(double t) const
{
FormFactor f = _f1Map[_scalarType];
double mv2 = f.mV*f.mV;
return f.value / ((1-t/mv2) * (1-f.sigma1*t/mv2+f.sigma2*t*t/mv2/mv2));
}
// Form factor f0 for B-pi transition
double EvtBBScalar::B_pi_f0(double t) const
{
FormFactor f = _f0Map[_scalarType];
double mv2 = f.mV*f.mV;
return f.value / (1 - f.sigma1*t/mv2 + f.sigma2*t*t/mv2/mv2);
}
// constants of the B and C parts of the amplitude
const EvtComplex EvtBBScalar::const_B = V_ub*V_us_star*a1 - V_tb*V_ts_star*a4;
const EvtComplex EvtBBScalar::const_C = 2*a6*V_tb*V_ts_star;
// part A of the amplitude, see hep-ph/0204185
const EvtVector4C
EvtBBScalar::amp_A(const EvtVector4R& p4B, const EvtVector4R& p4Scalar)
{
double mB2 = p4B.mass2();
double mScalar2 = p4Scalar.mass2();
double t = (p4B-p4Scalar).mass2();
return ((p4B+p4Scalar) - (mB2-mScalar2)/t * (p4B-p4Scalar)) * B_pi_f1(t)
+ (mB2-mScalar2)/t * (p4B-p4Scalar) * B_pi_f0(t);
}
// part B of the amplitude, Vector and Axial Vector parts
const EvtComplex
EvtBBScalar::amp_B(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
, const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
, int index)
{
return amp_B_vectorPart(baryon1, b1Pol, baryon2, b2Pol, index)
- amp_B_axialPart(baryon1, b1Pol, baryon2, b2Pol, index);
}
const EvtComplex
EvtBBScalar::amp_B_vectorPart(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
, const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
, int index)
{
double t = (baryon1->getP4Lab() + baryon2->getP4Lab()).mass2();
EvtGammaMatrix gamma;
for (int i=0; i<4; ++i) {
gamma += EvtTensor4C::g().get(index, i) * EvtGammaMatrix::g(i);
}
// The F2 contribution that is written out in the paper is neglected here.
// see hep-ph/0204185
EvtDiracSpinor A = EvtComplex(baryonF1F2(t))*b2Pol ;
EvtDiracSpinor Adjb1Pol = b1Pol.adjoint() ;
EvtDiracSpinor gammaA = gamma * A ;
return Adjb1Pol * gammaA ;
// return b1Pol.adjoint()*(gamma*(EvtComplex(baryonF1F2(t))*b2Pol));
}
const EvtComplex
EvtBBScalar::amp_B_axialPart(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
, const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
, int index)
{
EvtGammaMatrix gamma;
for (int i=0; i<4; ++i) {
gamma += EvtTensor4C::g().get(index, i) * EvtGammaMatrix::g(i);
}
double t = (baryon1->getP4Lab() + baryon2->getP4Lab()).mass2();
double mSum = baryon1->mass() + baryon2->mass();
EvtVector4C momentum_upper = (baryon1->getP4Lab()+baryon2->getP4Lab());
EvtVector4C momentum;
for (int mu=0; mu<0; ++mu) {
EvtComplex dummy;
for (int i=0; i<4; ++i) {
dummy += EvtTensor4C::g().get(index, i)*momentum_upper.get(i);
}
momentum.set(mu, dummy);
}
return b1Pol.adjoint() * (((baryon_gA(t) * gamma +
EvtGammaMatrix::id()*baryon_hA(t)/mSum*momentum.get(index))
* EvtGammaMatrix::g5()) * b2Pol);
}
// part C of the amplitude, Scalar and Pseudoscalar parts
const EvtComplex
EvtBBScalar::amp_C(const EvtDiracParticle* baryon1, const EvtDiracSpinor& b1Pol
, const EvtDiracParticle* baryon2, const EvtDiracSpinor& b2Pol
, int index)
{
EvtVector4C baryonSumP4_upper = baryon1->getP4Lab() + baryon2->getP4Lab();
EvtVector4C baryonSumP4;
for (int mu=0; mu<4; ++mu) {
EvtComplex dummy;
for (int i=0; i<4; ++i) {
dummy += EvtTensor4C::g().get(mu, i) * baryonSumP4_upper.get(i);
}
baryonSumP4.set(mu, dummy);
}
double t = (baryon1->getP4Lab() + baryon2->getP4Lab()).mass2();
return baryonSumP4.get(index)/(m_b-m_u)*(amp_C_scalarPart(b1Pol, b2Pol, t) + amp_C_pseudoscalarPart(b1Pol, b2Pol, t));
}
const EvtComplex
EvtBBScalar::amp_C_scalarPart(const EvtDiracSpinor& b1Pol, const EvtDiracSpinor& b2Pol, double t)
{
return baryon_fS(t) * b1Pol.adjoint()*b2Pol;
}
const EvtComplex
EvtBBScalar::amp_C_pseudoscalarPart(const EvtDiracSpinor& b1Pol, const EvtDiracSpinor& b2Pol, double t)
{
return baryon_gP(t) * b1Pol.adjoint()*(EvtGammaMatrix::g5()*b2Pol);
}

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