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 // -*- C++ -*-
 //
 // EtaPiGammaGammaDecayer.h is a part of Herwig - A multi-purpose Monte Carlo event generator
 // Copyright (C) 2002-2019 The Herwig Collaboration
 //
 // Herwig is licenced under version 3 of the GPL, see COPYING for details.
 // Please respect the MCnet academic guidelines, see GUIDELINES for details.
 //
 #ifndef HERWIG_EtaPiGammaGammaDecayer_H
 #define HERWIG_EtaPiGammaGammaDecayer_H
 // This is the declaration of the EtaPiGammaGammaDecayer class.
 
 #include "Herwig/Decay/DecayIntegrator.h"
 #include "Herwig/Decay/PhaseSpaceMode.h"
 #include "ThePEG/StandardModel/StandardModelBase.h"
 #include "Herwig/Utilities/Kinematics.h"
 #include "ThePEG/Helicity/LorentzPolarizationVector.h"
 
 namespace Herwig {
 using namespace ThePEG;
 
 /** \ingroup Decay
  *
  * The <code>EtaPiGammaGammaDecayer</code> class implements a VMD model
  * matrix element for \f$\eta,\eta'\to \pi^0 \gamma \gamma\f$ taken from
  * hep-ph/0112150.
  *
  *  The matrix element is given by
  *  \f[ \mathcal{M} = 
  *    D(s,t,u)\left[ \epsilon_1\cdot\epsilon_2 q_1\cdot q_2
  *                  -\epsilon_1\cdot q_2\epsilon_2\cdot q_1\right]
  *   -E(s,t,u)\left[-\epsilon_1\cdot\epsilon_2p\cdot q_1p\cdot q_2
  *                  -\epsilon_1\cdot p\epsilon_2\cdot p q_1\cdot q_2
  *                  +\epsilon_1\cdot q_2 \epsilon_2\cdot  p  p\cdot q_1
  *                  +\epsilon_1\cdot  p  \epsilon_2\cdot q_1 p\cdot q_2
  *\right],
  *  \f]
  *  where \f$q_{1,2}\f$ are the momenta of the photons, \f$\epsilon_{1,2}\f$ are
  *  the polarization vectors of the photons, \f$p\f$ is the momentum of the decaying
  *  meson and
  * \f[D(s,t,u) = \frac{2\sqrt{3}}{9}g^2_{\omega\rho\pi}
  *              \left(\frac{2eF^2_{\pi}g}{m^2_V}\right)^2\times\left(\frac{F_\pi}{F_8}\cos\theta\mp\sqrt{2}\frac{F_\pi}{F_0}\sin\theta\right)\times\left[\frac{p\cdot q_2-m^2_\eta}{m^2_V-t}+\frac{p\cdot q_1-m^2_\eta}{m^2_V-u}\right]\f]
  * \f[E(s,t,u) =-\frac{2\sqrt{3}}{9}g^2_{\omega\rho\pi}\left(\frac{2eF^2_{\pi}g}{m^2_V}\right)^2\times\left(\frac{F_\pi}{F_8}\cos\theta\mp\sqrt{2}\frac{F_\pi}{F_0}\sin\theta\right)\times\left[\frac1{m^2_V-t}+\frac1{m^2_V-u}\right].\f]
  *  the \f$-\f$ sign corresponds to the \f$\eta\f$ decay and the \f$+\f$ to the \f$\eta'\f$ decay.
  *  Here
  * - \f$g_{\omega\rho\pi}\f$ is the coupling of the
  *               \f$\omega\f$ to the \f$\rho\f$ and a pion.
  * - \f$e\f$ is the electric charge.
  * - \f$F_{\pi}\f$ is the pion decay constant.
  * - \f$g\f$ is the conversion factor for a \f$\rho\f$ into a photon.
  * - \f$m_V\f$ is the mass of the vector meson, in this case we use the \f$\rho\f$.
  * - \f$F_0\f$ is the singlet decay constant.
  * - \f$F_8\f$ is the octet decay constant.
  * - \f$\theta\f$ is the octet-singlet mixing angle
  * - \f$m_\eta\f$ is the mass of the decay meson.
  *
  *  In practice we use a slightly modified form by including a running width term to 
  * include the \f$\eta'\f$ decay as well as the \f$\eta\f$ decay.
  *
  * @see DecayIntegrator
  * 
  */
 class EtaPiGammaGammaDecayer: public DecayIntegrator {
 
 public:
 
   /**
    * Default constructor.
    */
   EtaPiGammaGammaDecayer();
   
   /**
    * Which of the possible decays is required
    * @param cc Is this mode the charge conjugate
    * @param parent The decaying particle
    * @param children The decay products
    */
   virtual int modeNumber(bool & cc, tcPDPtr parent, 
              const tPDVector & children) const;
   
   /**
    * Return the matrix element squared for a given mode and phase-space channel.
    * @param ichan The channel we are calculating the matrix element for. 
    * @param part The decaying Particle.
    * @param outgoing The particles produced in the decay
    * @param momenta  The momenta of the particles produced in the decay
    * @param meopt Option for the calculation of the matrix element
    * @return The matrix element squared for the phase-space configuration.
    */
   double me2(const int ichan,const Particle & part,
          const tPDVector & outgoing,
          const vector<Lorentz5Momentum> & momenta,
          MEOption meopt) const;
 
   /**
    *   Construct the SpinInfos for the particles produced in the decay
    */
   virtual void constructSpinInfo(const Particle & part,
                  ParticleVector outgoing) const;
 
   /**
    * Method to return an object to calculate the 3 body partial width.
    * @param dm The DecayMode
    * @return A pointer to a WidthCalculatorBase object capable of calculating the width
    */
   virtual WidthCalculatorBasePtr threeBodyMEIntegrator(const DecayMode & dm) const;
 
   /**
    * The matrix element to be integrated for the three-body decays as a function
    * of the invariant masses of pairs of the outgoing particles.
    * @param imode The mode for which the matrix element is needed.
    * @param q2 The scale, \e i.e. the mass squared of the decaying particle.
    * @param s3 The invariant mass squared of particles 1 and 2, \f$s_3=m^2_{12}\f$.
    * @param s2 The invariant mass squared of particles 1 and 3, \f$s_2=m^2_{13}\f$.
    * @param s1 The invariant mass squared of particles 2 and 3, \f$s_1=m^2_{23}\f$.
    * @param m1 The mass of the first  outgoing particle.
    * @param m2 The mass of the second outgoing particle.
    * @param m3 The mass of the third  outgoing particle.
    * @return The matrix element
    */
   virtual double threeBodyMatrixElement(const int imode, const Energy2 q2,
                     const  Energy2 s3, const Energy2 s2,
                     const Energy2 s1, const Energy m1,
                     const Energy m2,const Energy m3) const;
 
   /**
    * Output the setup information for the particle database
    * @param os The stream to output the information to
    * @param header Whether or not to output the information for MySQL
    */
   virtual void dataBaseOutput(ofstream & os,bool header) const;
 
 public:
 
   /** @name Functions used by the persistent I/O system. */
   //@{
   /**
    * Function used to write out object persistently.
    * @param os the persistent output stream written to.
    */
   void persistentOutput(PersistentOStream & os) const;
 
   /**
    * Function used to read in object persistently.
    * @param is the persistent input stream read from.
    * @param version the version number of the object when written.
    */
   void persistentInput(PersistentIStream & is, int version);
   //@}
 
   /**
    * Standard Init function used to initialize the interfaces.
    */
   static void Init();
 
 protected:
 
   /** @name Clone Methods. */
   //@{
   /**
    * Make a simple clone of this object.
    * @return a pointer to the new object.
    */
   virtual IBPtr clone() const {return new_ptr(*this);}
 
   /** Make a clone of this object, possibly modifying the cloned object
    * to make it sane.
    * @return a pointer to the new object.
    */
   virtual IBPtr fullclone() const {return new_ptr(*this);}
   //@}
   
 protected:
   
   /** @name Standard Interfaced functions. */
   //@{
   /**
    * Initialize this object after the setup phase before saving and
    * EventGenerator to disk.
    * @throws InitException if object could not be initialized properly.
    */
   virtual void doinit();
 
   /**
    * Initialize this object to the begining of the run phase.
    */
   virtual void doinitrun();
   //@}
 
 private:
 
   /**
    * Private and non-existent assignment operator.
    */
   EtaPiGammaGammaDecayer & operator=(const EtaPiGammaGammaDecayer &) = delete;
 
 private:
 
   /**
    * The coupling \f$g_{\omega\rho\pi}\f$ of the \f$\rho\f$ to \f$\omega\f$ and
    * a \f$\pi\f$.
    */
   InvEnergy _grhoomega;
 
   /**
    * The pion decay constant, \f$F_{\pi}\f$
    */
   Energy _fpi;
 
   /**
    * The mass of the \f$\rho\f$.
    */
   Energy _rhomass;
 
   /**
    * The width of the \f$\rho\f$. 
    */
   Energy _rhowidth;
 
   /**
    * The coupling for the conversion of a rho to a photon, \f$g\f$
    */
   double _grho;
 
   /**
    * The mass of the pion
    */
   Energy _mpi;
 
   /**
    * Constant for the running \f$\rho\f$ width calculation.
    */
   double _rhoconst;
 
   /**
    * Use local values of the \f$\rho\f$ mass and width.
    */
   bool _localparameters;
 
   /**
    * Ratios of the decay constants \f$F_8/F_\pi\f$.
    */
   double _ratiofpif8;
 
   /**
    * Ratios of the decay constants \f$F_0/F_\pi\f$.
    */
   double _ratiofpif0;
 
   /**
    * the mixing angle, \f$\theta\f$.
    */
   double _theta;
 
   /**
    * the maximum weights for the \f$\eta\f$ decay.
    */
   double _etamax;
 
   /**
    * the maximum weights for the \f$\eta'\f$ decay.
    */
   double _etapmax;
 
   /**
    * The prefactor for the \f$D(s,t,u)\f$ function.
    */
   vector<InvEnergy2> _dconst;
 
   /**
    * The prefactor for the \f$E(s,t,u)\f$ function.
    */
   vector<InvEnergy2> _econst;
 
   /**
    *  Spin density matrix
    */
   mutable RhoDMatrix _rho;
 
   /**
    *  Polarization vectors for the photons
    */
   mutable vector<Helicity::LorentzPolarizationVector> _vectors[2];
 };
 
 }
 
 
 #endif /* HERWIG_EtaPiGammaGammaDecayer_H */

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