LauGounarisSakuraiRes.cc

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// Copyright University of Warwick 2006 - 2014.
// 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 "LauGounarisSakuraiRes.hh"

ClassImp(LauGounarisSakuraiRes)


LauGounarisSakuraiRes::LauGounarisSakuraiRes(LauResonanceInfo* resInfo, const Int_t resPairAmpInt, const LauDaughters* daughters) :
        LauAbsResonance(resInfo, resPairAmpInt, daughters),
        q0_(0.0),
        p0_(0.0),
        pstar0_(0.0),
        erm0_(0.0),
        resMass_(0.0),
        resMassSq_(0.0),
        resWidth_(0.0),
        resRadius_(0.0),
        parRadius_(0.0),
        mDaugSum_(0.0),
        mDaugSumSq_(0.0),
        mDaugDiff_(0.0),
        mDaugDiffSq_(0.0),
        mParentSq_(0.0),
        mBachSq_(0.0),
        h0_(0.0),
        dhdm0_(0.0),
        d_(0.0),
        FR0_(1.0),
        FP0_(1.0)
{
}

LauGounarisSakuraiRes::~LauGounarisSakuraiRes()
{
}

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

        resMass_ = this->getMass();
        resWidth_ = this->getWidth();
        resRadius_ = this->getResRadius();
        parRadius_ = this->getParRadius();

        Double_t massDaug1 = this->getMassDaug1();
        Double_t massDaug2 = this->getMassDaug2();
        Double_t massBachelor = this->getMassBachelor();
        Double_t massParent = this->getMassParent();

        // Check that the spin is 1
        Int_t resSpin = this->getSpin();
        if (resSpin != 1) {
                std::cerr << "WARNING in LauGounarisSakuraiRes::initialise : Resonance spin is != 1. This lineshape is for the rho(770), setting the spin to 1." << std::endl;
                this->changeResonance( -1.0, -1.0, 1 );
                resSpin = this->getSpin();
        }

        // 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;

        // Decay momentum of either daughter in the resonance rest frame
        // when resonance mass = rest-mass value, m_0 (PDG value)
        Double_t term1 = resMassSq_ - mDaugSumSq_;
        Double_t term2 = resMassSq_ - mDaugDiffSq_;
        Double_t term12 = term1*term2;
        if (term12 > 0.0) {
                q0_ = TMath::Sqrt(term12)/(2.0*resMass_);
        } 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_ - resMassSq_ - mBachSq_)/(2.0*resMass_);
        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_ - resMassSq_)/(2.0*massParent);
        Double_t termStarBach = eStarBach*eStarBach - mBachSq_;
        if ( eStarBach<0.0 || termStarBach<0.0 ) {
                pstar0_ = 0.0;
        } else {
                pstar0_ = TMath::Sqrt( termStarBach );
        }

        // Covariant factor when resonance mass = rest-mass value, m_0 (PDF value)
        erm0_ = (mParentSq_ + resMassSq_ - mBachSq_)/(2.0*massParent*resMass_);
        this->calcCovFactor( erm0_ );

        // Calculate the Blatt-Weisskopf form factor for the case when m = m_0
        FR0_ = 1.0;
        FP0_ = 1.0;
        if ( resSpin > 0 ) {
                const LauBlattWeisskopfFactor* resBWFactor = this->getResBWFactor();
                const LauBlattWeisskopfFactor* parBWFactor = this->getParBWFactor();
                FR0_ = (resBWFactor!=0) ? resBWFactor->calcFormFactor(q0_) : 1.0;
                switch ( parBWFactor->getRestFrame() ) {
                        case LauBlattWeisskopfFactor::ResonanceFrame:
                                FP0_ = (parBWFactor!=0) ? parBWFactor->calcFormFactor(p0_) : 1.0;
                                break;
                        case LauBlattWeisskopfFactor::ParentFrame:
                                FP0_ = (parBWFactor!=0) ? parBWFactor->calcFormFactor(pstar0_) : 1.0;
                                break;
                        case LauBlattWeisskopfFactor::Covariant:
                                {
                                Double_t covFactor = this->getCovFactor();
                                if ( resSpin > 2 ) {
                                        covFactor = TMath::Power( covFactor, 1.0/resSpin );
                                } else if ( resSpin == 2 ) {
                                        covFactor = TMath::Sqrt( covFactor );
                                }
                                FP0_ = (parBWFactor!=0) ? parBWFactor->calcFormFactor(pstar0_*covFactor) : 1.0;
                                break;
                                }
                }
        }

        // Calculate the extra things needed by the G-S shape
        h0_ = 2.0*LauConstants::invPi * q0_/resMass_ * TMath::Log((resMass_ + 2.0*q0_)/(2.0*LauConstants::mPi));
        dhdm0_ = h0_ * (1.0/(8.0*q0_*q0_) - 1.0/(2.0*resMassSq_)) + 1.0/(LauConstants::twoPi*resMassSq_);
        d_ = 3.0*LauConstants::invPi * LauConstants::mPi*LauConstants::mPi/(q0_*q0_)
                * TMath::Log((resMass_ + 2.0*q0_)/(2.0*LauConstants::mPi))
                + resMass_/(LauConstants::twoPi*q0_)
                - LauConstants::mPi*LauConstants::mPi*resMass_/(LauConstants::pi*q0_*q0_*q0_);
}

LauComplex LauGounarisSakuraiRes::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 LauGounarisSakuraiRes::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(...)

        const Double_t resMass = this->getMass();
        const Double_t resWidth = this->getWidth();
        const Double_t resRadius = this->getResRadius();
        const Double_t parRadius = this->getParRadius();

        // If the mass is floating and its value has changed we need to
        // recalculate everything that assumes that value
        // Similarly for the BW radii
        if ( ( (!this->fixMass()) && resMass != resMass_ ) ||
             ( (!this->fixResRadius()) && resRadius != resRadius_ ) ||
             ( (!this->fixParRadius()) && parRadius != parRadius_ ) ) {
                this->initialise();
        }

        const Int_t resSpin = this->getSpin();
        const Double_t q = this->getQ();
        const Double_t p = this->getP();
        const Double_t pstar = this->getPstar();

        Double_t fFactorR(1.0);
        Double_t fFactorB(1.0);
        if ( resSpin > 0 ) {
                const LauBlattWeisskopfFactor* resBWFactor = this->getResBWFactor();
                const LauBlattWeisskopfFactor* parBWFactor = this->getParBWFactor();
                fFactorR = (resBWFactor!=0) ? resBWFactor->calcFormFactor(q) : 1.0;
                switch ( parBWFactor->getRestFrame() ) {
                        case LauBlattWeisskopfFactor::ResonanceFrame:
                                fFactorB = (parBWFactor!=0) ? parBWFactor->calcFormFactor(p) : 1.0;
                                break;
                        case LauBlattWeisskopfFactor::ParentFrame:
                                fFactorB = (parBWFactor!=0) ? parBWFactor->calcFormFactor(pstar) : 1.0;
                                break;
                        case LauBlattWeisskopfFactor::Covariant:
                                {
                                Double_t covFactor = this->getCovFactor();
                                if ( resSpin > 2 ) {
                                        covFactor = TMath::Power( covFactor, 1.0/resSpin );
                                } else if ( resSpin == 2 ) {
                                        covFactor = TMath::Sqrt( covFactor );
                                }
                                fFactorB = (parBWFactor!=0) ? parBWFactor->calcFormFactor(pstar*covFactor) : 1.0;
                                break;
                                }
                }
        }
        const Double_t fFactorRRatio = fFactorR/FR0_;
        const Double_t fFactorBRatio = fFactorB/FP0_;

        const Double_t qRatio = q/q0_;
        const Double_t qTerm = qRatio*qRatio*qRatio;

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

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

        const Double_t h = 2.0*LauConstants::invPi * q/mass * TMath::Log((mass + 2.0*q)/(2.0*LauConstants::mPi));
        const Double_t f = resWidth * resMassSq_/(q0_*q0_*q0_) * (q*q * (h - h0_) + massSqTerm * q0_*q0_ * dhdm0_);

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

        // Scale by the denominator factor, as well as the spin term and Blatt-Weisskopf factors
        Double_t numerFactor = spinTerm*(1.0 + d_ * resWidth/resMass);
        if (!this->ignoreBarrierScaling()) {
                numerFactor *= fFactorRRatio*fFactorBRatio;
        }
        const Double_t denomFactor = (massSqTerm + f)*(massSqTerm + f) + resMassSq_*totWidth*totWidth;
        resAmplitude.rescale(numerFactor/denomFactor);

        return resAmplitude;
}

const std::vector<LauParameter*>& LauGounarisSakuraiRes::getFloatingParameters()
{
        this->clearFloatingParameters();

        if ( ! this->fixMass() ) {
                this->addFloatingParameter( this->getMassPar() );
        }
        if ( ! this->fixWidth() ) {
                this->addFloatingParameter( this->getWidthPar() );
        }
        if ( ! this->fixResRadius() ) {
                this->addFloatingParameter( this->getResBWFactor()->getRadiusParameter() );
        }
        if ( ! this->fixParRadius() ) {
                this->addFloatingParameter( this->getParBWFactor()->getRadiusParameter() );
        }

        return this->getParameters();
}