epsilon.h

// -*- C++ -*-
//
// epsilon.h is a part of ThePEG - Toolkit for HEP Event Generation
// Copyright (C) 2003-2019 Peter Richardson, Leif Lonnblad
//
// ThePEG is licenced under version 3 of the GPL, see COPYING for details.
// Please respect the MCnet academic guidelines, see GUIDELINES for details.
//
#ifndef ThePEG_epsilon_H
#define ThePEG_epsilon_H
//
// This is the declaration of the epsilon class.

#include "ThePEG/Vectors/LorentzVector.h"

namespace ThePEG {
namespace Helicity {

  template <typename A, typename B, typename C>
  auto epsilon(const LorentzVector<A> & a,
               const LorentzVector<B> & b,
               const LorentzVector<C> & c) 
  -> LorentzVector<decltype(a.x()*b.y()*c.z())>
  {
    auto diffxy = a.x() * b.y()  -  a.y() * b.x();
    auto diffxz = a.x() * b.z()  -  a.z() * b.x();
    auto diffxt = a.x() * b.t()  -  a.t() * b.x();
    auto diffyz = a.y() * b.z()  -  a.z() * b.y();
    auto diffyt = a.y() * b.t()  -  a.t() * b.y();
    auto diffzt = a.z() * b.t()  -  a.t() * b.z();

    using ResultType = LorentzVector<decltype(a.x()*b.x()*c.x())>;    
    ResultType result;
    result.setX( c.z() * diffyt  - c.t() * diffyz  - c.y() * diffzt); 
    result.setY( c.t() * diffxz  - c.z() * diffxt  + c.x() * diffzt);
    result.setZ(-c.t() * diffxy  + c.y() * diffxt  - c.x() * diffyt);
    result.setT(-c.z() * diffxy  + c.y() * diffxz  - c.x() * diffyz);
    
    return result;
  }


}
}

#endif /* ThePEG_epsilon_H */