LauRelBreitWignerRes.cc

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// Copyright University of Warwick 2004 - 2013.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

// Authors:
// Thomas Latham
// John Back
// Paul Harrison

#include <iostream>

#include "LauConstants.hh"
#include "LauRelBreitWignerRes.hh"

ClassImp(LauRelBreitWignerRes)


LauRelBreitWignerRes::LauRelBreitWignerRes(TString resName, Double_t resMass, Double_t resWidth, Int_t resSpin,
                Int_t resCharge, Int_t resPairAmpInt, const LauDaughters* daughters) :
        LauAbsResonance(resName, resMass, resWidth, resSpin, resCharge, resPairAmpInt, daughters),
        q0_(0.0),
        p0_(0.0),
        pstar0_(0.0),
        resMassSq_(0.0),
        mDaugSum_(0.0),
        mDaugSumSq_(0.0),
        mDaugDiff_(0.0),
        mDaugDiffSq_(0.0),
        mParentSq_(0.0),
        mBachSq_(0.0),
        resR_(4.0),
        parR_(4.0),
        resRSq_(16.0),
        parRSq_(16.0),
        FR0_(1.0),
        FB0_(1.0),
        barrierType_(LauAbsResonance::BWPrimeBarrier)
{
}

LauRelBreitWignerRes::~LauRelBreitWignerRes()
{
}

void LauRelBreitWignerRes::initialise()
{
        // Set-up various constants. This must be called again if the mass/width/spin
        // of a resonance changes...  

        Int_t resSpin = this->getSpin();
        Double_t resMass = this->getMass();
        Double_t massDaug1 = this->getMassDaug1();
        Double_t massDaug2 = this->getMassDaug2();
        Double_t massBachelor = this->getMassBachelor();
        Double_t massParent = this->getMassParent();

        // Create the mass squares, sums, differences etc.
        resMassSq_ = resMass*resMass;
        mDaugSum_  = massDaug1 + massDaug2;
        mDaugSumSq_ = mDaugSum_*mDaugSum_;
        mDaugDiff_ = massDaug1 - massDaug2;
        mDaugDiffSq_ = mDaugDiff_*mDaugDiff_;
        mParentSq_ = massParent*massParent;
        mBachSq_ = massBachelor*massBachelor;

        // Create an effective resonance pole mass to protect against resonances
        // that are below threshold
        Double_t effResMass = resMass;
        if (resMassSq_ - mDaugSumSq_ < 0.0 ){
                Double_t minMass = mDaugSum_;
                Double_t maxMass = massParent - massBachelor;
                Double_t tanhTerm = std::tanh( (resMass - ((minMass + maxMass)/2))/(maxMass-minMass));
                effResMass = minMass + (maxMass-minMass)*(1+tanhTerm)/2;
        }
        Double_t effResMassSq = effResMass*effResMass;

        // Decay momentum of either daughter in the resonance rest frame
        // when resonance mass = rest-mass value, m_0 (PDG value)
        Double_t term1 = effResMassSq - mDaugSumSq_;
        Double_t term2 = effResMassSq - mDaugDiffSq_;
        Double_t term12 = term1*term2;
        if (term12 > 0.0) {
                q0_ = TMath::Sqrt(term12)/(2.0*effResMass);
        } else {
                q0_ = 0.0;
        }

        // Momentum of the bachelor particle in the resonance rest frame
        // when resonance mass = rest-mass value, m_0 (PDG value)
        Double_t eBach = (mParentSq_ - effResMassSq - mBachSq_)/(2.0*effResMass);
        Double_t termBach = eBach*eBach - mBachSq_;
        if ( eBach<0.0 || termBach<0.0 ) {
                p0_ = 0.0;
        } else {
                p0_ = TMath::Sqrt( termBach );
        }

        // Momentum of the bachelor particle in the parent rest frame
        // when resonance mass = rest-mass value, m_0 (PDG value)
        Double_t eStarBach = (mParentSq_ + mBachSq_ - effResMassSq)/(2.0*massParent);
        Double_t termStarBach = eStarBach*eStarBach - mBachSq_;
        if ( eStarBach<0.0 || termStarBach<0.0 ) {
                pstar0_ = 0.0;
        } else {
                pstar0_ = TMath::Sqrt( termStarBach );
        }

        // Blatt-Weisskopf barrier factor constant: z = q^2*radius^2
        // Calculate the Blatt-Weisskopf form factor for the case when m = m_0
        this->setBarrierRadii(resR_, parR_, barrierType_);

        if (resSpin > 3) {
                std::cerr << "WARNING in LauRelBreitWignerRes::initialise : Resonances spin is > 3.  Blatt-Weisskopf form factors will be set to 1.0" << std::endl;
        }
}

void LauRelBreitWignerRes::setBarrierRadii(Double_t resRadius, Double_t parRadius, LauAbsResonance::BarrierType type)
{
        // Reset the Blatt-Weisskopf barrier radius for the resonance and its parent
        resR_ = resRadius;
        parR_ = parRadius;

        resRSq_ = resRadius*resRadius;
        parRSq_ = parRadius*parRadius;

        barrierType_ = type;
        
        // Recalculate the Blatt-Weisskopf form factor for the case when m = m_0
        Double_t zR0 = q0_*q0_*resRSq_;
        Double_t zB0 = p0_*p0_*parRSq_;
        if ( ( type == LauAbsResonance::BWPrimeBarrier ) || ( type == LauAbsResonance::ExpBarrier ) ) {
                FR0_ = (resR_==0.0) ? 1.0 : this->calcFFactor(zR0);
                FB0_ = (parR_==0.0) ? 1.0 : this->calcFFactor(zB0);
        }
}

Double_t LauRelBreitWignerRes::calcFFactor(Double_t z)
{
        // Calculate the requested form factor for the resonance, given the z value
        Double_t fFactor(1.0);

        // For scalars the form factor is always unity
        // TODO: and we currently don't have formulae for spin > 3
        Int_t resSpin = this->getSpin();
        if ( (resSpin == 0) || (resSpin>3) ) {
                return fFactor;
        }

        if ( barrierType_ == LauAbsResonance::BWBarrier ) {
                if (resSpin == 1) {
                        fFactor = TMath::Sqrt(2.0*z/(z + 1.0));
                } else if (resSpin == 2) {
                        fFactor = TMath::Sqrt(13.0*z*z/(z*z + 3.0*z + 9.0));
                } else if (resSpin == 3) {
                        fFactor = TMath::Sqrt(277.0*z*z*z/(z*z*z + 6.0*z*z + 45.0*z + 225.0));
                }
        } else if ( barrierType_ == LauAbsResonance::BWPrimeBarrier ) {
                if (resSpin == 1) {
                        fFactor = TMath::Sqrt(1.0/(z + 1.0));
                } else if (resSpin == 2) {
                        fFactor = TMath::Sqrt(1.0/(z*z + 3.0*z + 9.0));
                } else if (resSpin == 3) {
                        fFactor = TMath::Sqrt(1.0/(z*z*z + 6.0*z*z + 45.0*z + 225.0));
                }
        } else if ( barrierType_ == LauAbsResonance::ExpBarrier ) {
                if (resSpin == 1) {
                        fFactor = TMath::Exp( -TMath::Sqrt(z) );
                } else if (resSpin == 2) {
                        fFactor = TMath::Exp( -z );
                } else if (resSpin == 3) {
                        fFactor = TMath::Exp( -TMath::Sqrt(z*z*z) );
                }
        }

        return fFactor;

}

LauComplex LauRelBreitWignerRes::resAmp(Double_t mass, Double_t spinTerm)
{
        // This function returns the complex dynamical amplitude for a Breit-Wigner resonance,
        // given the invariant mass and cos(helicity) values.

        LauComplex resAmplitude(0.0, 0.0);

        if (mass < 1e-10) {
                std::cerr << "WARNING in LauRelBreitWignerRes::amplitude : mass < 1e-10." << std::endl;
                return LauComplex(0.0, 0.0);
        } else if (q0_ < 1e-30) {
                return LauComplex(0.0, 0.0);
        }

        // Calculate the width of the resonance (as a function of mass)
        // First, calculate the various form factors.
        // NB
        // q is the momentum of either daughter in the resonance rest-frame,
        // p is the momentum of the bachelor in the resonance rest-frame,
        // pstar is the momentum of the bachelor in the parent rest-frame.
        // These quantities have been calculate in LauAbsResonance::amplitude(...)

        Int_t resSpin = this->getSpin();
        Double_t resMass = this->getMass();
        Double_t resWidth = this->getWidth();
        Double_t q = this->getQ();
        Double_t p = this->getP();
        //Double_t pstar = this->getPstar();

        Double_t zR = q*q*resRSq_;
        Double_t zB = p*p*parRSq_;
        Double_t fFactorR = (resR_==0.0) ? 1.0 : this->calcFFactor(zR);
        Double_t fFactorB = (parR_==0.0) ? 1.0 : this->calcFFactor(zB);
        Double_t fFactorRRatio = fFactorR/FR0_;
        Double_t fFactorBRatio = fFactorB/FB0_;

        Double_t qRatio = q/q0_;
        Double_t qTerm(0.0);
        if (resSpin == 0) {
                qTerm = qRatio;
        } else if (resSpin == 1) {
                qTerm = qRatio*qRatio*qRatio;
        } else if (resSpin == 2) {
                qTerm = TMath::Power(qRatio, 5.0);
        } else {
                qTerm = TMath::Power(qRatio, 2*resSpin + 1);  
        }

        Double_t totWidth = resWidth*qTerm*(resMass/mass)*fFactorRRatio*fFactorRRatio;

        Double_t massSq = mass*mass;
        Double_t massSqTerm = resMassSq_ - massSq;

        // Compute the complex amplitude
        resAmplitude = LauComplex(massSqTerm, resMass*totWidth);

        // Scale by the denominator factor, as well as the spin term and Blatt-Weisskopf factors
        resAmplitude.rescale((fFactorRRatio*fFactorBRatio*spinTerm)/(massSqTerm*massSqTerm + resMassSq_*totWidth*totWidth));

        return resAmplitude;
}