TUtil.h

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#include "TConstant.h"
#include "TLorentzVector.h"
#include <complex>
 
typedef std::complex<double> complex_t;
 
inline complex_t operator+( const double& x, const complex_t& y ) { return y + x; }
 
inline complex_t operator-( const double& x, const complex_t& y ) { return -( y - x ); }
 
namespace rb {
  inline double Gamma( const double Q2, const double M2, const double G, const double mkpp2,
                       const double mkmp2 ) {
    const double mkmp22  = mkmp2 * mkmp2;
    double       beta2_q = ( Q2 * Q2 - 2 * Q2 * mkpp2 + mkmp22 ) / pow( Q2 - mkpp2, 2 );
    double       beta2_M = ( M2 * M2 - 2 * M2 * mkpp2 + mkmp22 ) / pow( M2 - mkpp2, 2 );
    double       beta2   = beta2_q / beta2_M;
    double       beta    = sqrt( beta2 );
    return G * M2 / Q2 * beta2 * beta;
  }
 
  inline complex_t R( double Q2, double M2, double G, double Mp2, double Mm2 ) {
    if ( Q2 < Mp2 ) return 0;
    const complex_t I( 0, 1 );
    double          Q    = sqrt( Q2 );
    complex_t       prop = M2 / ( Q2 - M2 + I * ( Gamma( Q2, M2, G, Mp2, Mm2 ) * Q ) );
    return prop;
  }
 
  inline TLorentzVector PseudoScalars3( const TLorentzVector& qp, const TLorentzVector& qm,
                                        const TLorentzVector& q0 ) {
    // The hadronic current
    // here for 3pi J_\mu=\epsilon_{a b g \mu}q+_{a}q-_{b}q0_{g}
 
    double Jx = qp.Y() * qm.Z() * q0.T() - qp.Y() * qm.T() * q0.Z() +
                qp.T() * qm.Y() * q0.Z() - qp.T() * qm.Z() * q0.Y() +
                qp.Z() * qm.T() * q0.Y() - qp.Z() * qm.Y() * q0.T();
 
    double Jy = qp.X() * qm.Z() * q0.T() - qp.X() * qm.T() * q0.Z() +
                qp.T() * qm.X() * q0.Z() - qp.T() * qm.Z() * q0.X() +
                qp.Z() * qm.T() * q0.X() - qp.Z() * qm.X() * q0.T();
 
    double Jz = qp.Y() * qm.X() * q0.T() - qp.Y() * qm.T() * q0.X() +
                qp.T() * qm.Y() * q0.X() - qp.T() * qm.X() * q0.Y() +
                qp.X() * qm.T() * q0.Y() - qp.X() * qm.Y() * q0.T();
 
    double Jt = qp.Y() * qm.Z() * q0.X() - qp.Y() * qm.X() * q0.Z() +
                qp.X() * qm.Y() * q0.Z() - qp.X() * qm.Z() * q0.Y() +
                qp.Z() * qm.X() * q0.Y() - qp.Z() * qm.Y() * q0.X();
 
    TLorentzVector J( Jx, Jy, Jz, Jt );
    return J;
  }
 
} // namespace rb