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 // -*- C++ -*-
 //
 // ThreePionCLEOCurrent.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 THEPEG_ThreePionCLEOCurrent_H
 #define THEPEG_ThreePionCLEOCurrent_H
 //
 // This is the declaration of the ThreePionCLEOCurrent class.
 //
 #include "WeakCurrent.h"
 #include "Herwig/Utilities/Interpolator.h"
 #include "Herwig/Utilities/Kinematics.h"
 #include "ThePEG/StandardModel/StandardModelBase.h"
 
 namespace Herwig {
 using namespace ThePEG;
 
 /** \ingroup Decay
  *
  *  The <code>ThreePionCLEOCurrent</code> class implements
  *  the decay of the weak current to three pions
  *  using the currents from CLEO Phys. Rev. D 61,012002. This is
  *  a model including two \f$\rho\f$ mesons in both \f$s\f$ and \f$p\f$ wave,
  *  a \f$\sigma\f$, the \f$f_2\f$ and \f$f_0(1370)\f$.
  *
  * The form factors for the \f$a_1^+ \to \pi^0 \pi^0 \pi^+\f$ mode are
  *
  * \f[F_1=\sum_k\left\{g^P_{\rho_k}B_{\rho_k}^P(s_1)
  *          -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_2)
  *                        \left((s_3-m_{\pi^+}^2)-(s_1-m_{\pi^0}^2)\right)\right\}
  *     +\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right)     
  * +\frac{g_{f_2}}{18s_3}(q^2-m_{\pi^+}^2+s_3)(4m_{\pi^0}^2-s_3)B^D_{f_2}(s_3)
  *\f]
  *
  * \f[F_2=\sum_k\left\{-\frac13g^P_{\rho_k}B_{\rho_k}^P(s_2)
  *         -g^D_{\rho_k}B_{\rho_k}^P(s_1)
  *                       \left((s_3-m_{\pi^+}^2)-(s_2-m_{\pi^0}^2)\right)\right\}
  *     +\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3)\right)
  * +\frac1{18s_3}g_{f_2}(q^2-m_{\pi^+}^2+s_3)(4m_{\pi^0}^2-s_3)B^D_{f_2}(s_3)
  *\f]
  *
  * \f[F_3=\sum_k g^D_{\rho_k}\left\{ 
  *     -\frac13B_{\rho_k}^P(s_1)\left((s_3-m_{\pi^+}^2)-(s_2-m_{\pi^0}^2)\right)
  *     +\frac13B_{\rho_k}^P(s_2)\left((s_3-m_{\pi^+}^2)-(s_1-m_{\pi^0}^2)\right)\right\}
  *  -\frac{g_{f_2}}2(s_1-s_2)B^D_{f_2}(s_3)\f]
  *  The form factors for  \f$a_1^+\to \pi^+ \pi^+ \pi^-\f$ mode
  *
  * \f[F_1=\sum_k\left\{-g^P_{\rho_k}B_{\rho_k}^P(s_1)
  *                       -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_2)(s_1-s_3)\right\}
  *    -\frac23\left(g_\sigma B^S_\sigma(s_2)+g_{f_0} B^S_{f_0}(s_2)\right) 
  *    +g_{f_2}\left(\frac12(s_3-s_2)B^D_{f_2}(s_1)
  *    -\frac1{18s_2}(4m_{\pi^+}^2-s_2)(q^2+s_2-m_{\pi^+}^2)B^D_{f_2}(s_2)\right)\f]
  *
  * \f[F_2=\sum_k\left\{-g^P_{\rho_k}B_{\rho_k}^P(s_2)
  *                       -\frac{g^D_{\rho_k}}3B_{\rho_k}^P(s_1)(s_2-s_3)\right\}
  *    -\frac23\left(g_\sigma B^S_\sigma(s_1)+g_{f_0} B^S_{f_0}(s_1)\right)
  *    +g_{f_2}\left(\frac12(s_3-s_1)B^D_{f_2}(s_2)
  *    -\frac1{18s_1}(4m_{\pi^+}^2-s_1)(q^2+s_1-m_{\pi^+}^2)B^D_{f_2}(s_1)\right)\f]
  *
  * \f[F_3=\sum_k
  *     -g^D_{\rho_k}\left( \frac13(s_2-s_3)B_{\rho_k}^P(s_1)
  *                        -\frac13(s_1-s_3)B_{\rho_k}^P(s_2)\right)
  *   -\frac23\left(g_\sigma B^S_\sigma(s_1)+g_{f_0}B^S_{f_0}(s_1)\right)
  *   +\frac23\left(g_\sigma B^S_\sigma(s_2)+g_{f_0}B^S_{f_0}(s_2)\right)\f]
  *\f[
  *   +g_{f_2}\left(-\frac1{18s_1}(4m_{\pi^+}^2-s_1)(q^2+s_1-m_{\pi^+}^2)B^D_{f_2}(s_1)
  *            +\frac1{18s_2}(4m_{\pi^+}^2-s_2)(q^2+s_2-m_{\pi^+}^2)B^D_{f_2}(s_2)\right)\f]
  *
  * where
  *
  * - \f$g_{f_2}\f$ is the coupling of the \f$f_2\f$ to the \f$a_1\f$
  * - \f$g_{f_0}\f$ is the coupling of the \f$f_0(1370)\f$ to the \f$a_1\f$
  * - \f$g_{\sigma}\f$ is the coupling of the \f$\sigma\f$ to the \f$a_1\f$
  * - \f$g^P_{\rho_k}\f$ is the \f$p\f$-wave coupling of the \f$\rho_k\f$ multiplet
  *     to the \f$a_1\f$.
  * - \f$g^D_{\rho_k}\f$ is the \f$d\f$-wave coupling of the \f$\rho_k\f$ multiplet
  *     to the \f$a_1\f$.
  * - \f$s_3=m^2_{12}\f$ is the invariant mass squared of particles 1 and 2.
  * - \f$s_2=m^2_{13}\f$ is the invariant mass squared of particles 1 and 3.
  * - \f$s_1=m^2_{23}\f$ is the invariant mass squared of particles 2 and 3.
  *
  * The Breit-Wigner factors are given by
     \f$B^L_Y(s_i) = \frac{m^2_Y}{m^2_Y-s_i+im_Y\Gamma^{Y,L}(s_i)}\f$
  * where
  * \f$\Gamma^{Y,L}(s_i) = \Gamma^Y\left(\frac{p(s_i)}{p(M_Y}\right)^{2L+1}\frac{m_Y}{\sqrt{s_i}}\f$
  * \f$m_Y\f$ and \f$\Gamma^Y\f$ are the mass and width of the particle \f$Y\f$ 
  * respectively. \f$p(s_i)\f$ is the momentum of the outgoing pion in the 
  * rest frame of the resonance \f$Y\f$.
  *
  * @see a1ThreePionCLEODecayer
  * @see ThreePionCLEOa1MatrixElement
  * 
  */
 class ThreePionCLEOCurrent: public WeakCurrent {
 
   /**
    * The matrix element for the running \f$a_1\f$ width is a friend to 
    * keep some members private.
    */
   friend class ThreePionCLEOa1MatrixElement;
 
 public:
 
   /**
    * Default constructor
    */
   ThreePionCLEOCurrent();
 
   /**
    * Hadronic current. This method is purely virtual and must be implemented in
    * all classes inheriting from this one.
    * @param resonance If specified only include terms with this particle
    * @param flavour Information on the required flavours of the quarks
    * @param imode The mode
    * @param ichan The phase-space channel the current is needed for.
    * @param scale The invariant mass of the particles in the current.
    * @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 current. 
    */
   virtual vector<LorentzPolarizationVectorE> 
   current(tcPDPtr resonance,
       FlavourInfo flavour,
       const int imode, const int ichan,Energy & scale,
       const tPDVector & outgoing,
       const vector<Lorentz5Momentum> & momenta,
       DecayIntegrator::MEOption meopt) const;
 
   /**
    * Accept the decay. Checks the mesons against the list.
    * @param id The id's of the particles in the current.
    * @return Can this current have the external particles specified.
    */
   virtual bool accept(vector<int> id);
 
   /**
    * Return the decay mode number for a given set of particles in the current. 
    * Checks the mesons against the list.
    * @param id The id's of the particles in the current.
    * @return The number of the mode
    */
   virtual unsigned int decayMode(vector<int> id);
 
   /**
    * The particles produced by the current. This returns the mesons for the mode.
    * @param icharge The total charge of the particles in the current.
    * @param imode The mode for which the particles are being requested
    * @param iq The PDG code for the quark
    * @param ia The PDG code for the antiquark
    * @return The external particles for the current.
    */
   virtual tPDVector particles(int icharge, unsigned int imode, int iq, int ia);
 
 public:
 
   /** @name Methods for the construction of the phase space integrator. */
   //@{
   /**
    * Complete the construction of the decay mode for integration.classes inheriting
    * from this one.
    * This method is purely virtual and must be implemented in the classes inheriting
    * from WeakCurrent.
    * @param icharge   The total charge of the outgoing particles in the current.
    * @param resonance If specified only include terms with this particle
    * @param flavour Information on the required flavours of the quarks
    * @param imode     The mode in the current being asked for.
    * @param mode      The phase space mode for the integration
    * @param iloc      The location of the of the first particle from the current in
    *                  the list of outgoing particles.
    * @param ires      The location of the first intermediate for the current.
    * @param phase     The prototype phase space channel for the integration.
    * @param upp       The maximum possible mass the particles in the current are
    *                  allowed to have.
    * @return Whether the current was sucessfully constructed.
    */
   virtual bool createMode(int icharge, tcPDPtr resonance,
               FlavourInfo flavour,
               unsigned int imode,PhaseSpaceModePtr mode,
               unsigned int iloc,int ires,
               PhaseSpaceChannel phase, Energy upp );
   //@}
 
   /**
    * 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
    * @param create Whether or not to add a statement creating the object
    */
   virtual void dataBaseOutput(ofstream & os,bool header,bool create) const;
 
   /**
    * the matrix element for the a1 decay to calculate the running width
    * @param iopt The mode
    * @param q2 The mass of the decaying off-shell \f$a_1\f$, \f$q^2\f$.
    * @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 squared summed over spins.
    */
   double threeBodyMatrixElement(const int iopt, const Energy2 q2,
                 const Energy2 s3, const Energy2 s2, 
                 const Energy2 s1, const Energy  m1,
                 const Energy  m2, const Energy  m3) 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:
   
   /**
    * Calculate CLEO form factors for the current. Implements the form factors
    * described above.
    * @param imode The mode
    * @param ichan The phase space channel
    * @param q2 The scale \f$q^2\f$ for the current.
    * @param s1 The invariant mass squared of particles 2 and 3, \f$s_1=m^2_{23}\f$.
    * @param s2 The invariant mass squared of particles 1 and 3, \f$s_2=m^2_{13}\f$.
    * @param s3 The invariant mass squared of particles 1 and 2, \f$s_3=m^2_{12}\f$.
    * @param F1 The form factor \f$F_1\f$.
    * @param F2 The form factor \f$F_2\f$.
    * @param F3 The form factor \f$F_3\f$.
    */
   void CLEOFormFactor(int imode,int ichan,Energy2 q2,Energy2 s1, Energy2 s2,
               Energy2 s3,Complex & F1, Complex & F2, Complex & F3) const;
 
 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();
 
   /**
    * Check sanity of the object during the setup phase.
    */
   virtual void doupdate();
   //@}
 
 private:
 
   /**
    * Private and non-existent assignment operator.
    */
   ThreePionCLEOCurrent & operator=(const ThreePionCLEOCurrent &) = delete;
 
 private:
 
   /**
    * The \f$a_1\f$ running width
    * @param q2 The scale \f$q^2\f$ for the Breit-Wigner
    * @return The \f$a_1\f$ running width.
    */
   Energy a1width(Energy2 q2) const;
 
   /**
    * Initialize the \f$a_1\f$ running width
    * @param iopt Initialization option (-1 full calculation, 0 set up the interpolation)
    */
   void inita1Width(int iopt);
   
   /**
    * \f$a_1\f$ Breit-Wigner
    * @param q2 The scale \f$q^2\f$ for the Breit-Wigner
    * @return The Breit-Wigner
    */
   Complex a1BreitWigner(Energy2 q2) const {
     Complex ii(0.,1.);
     Energy2 m2=_a1mass*_a1mass; Energy q=sqrt(q2);
     Complex output=m2/(m2-q2-ii*q*a1width(q2));
     return output;
   }
 
 private:
   
   /**
    * Masses of the \f$\rho\f$ resonances.
    */
   vector<Energy> _rhomass;
 
   /**
    * Widths of the \f$\rho\f$ resonances.
    */
   vector<Energy> _rhowidth;
 
   /**
    * Mass of the \f$f_2\f$ resonance
    */
   Energy _f2mass;
 
   /**
    * Width of the \f$f_2\f$ resonance
    */
   Energy _f2width;
 
   /**
    * Mass of the \f$f_0(1370)\f$ resonance
    */
   Energy _f0mass;
 
   /**
    * Width of the \f$f_0(1370)\f$ resonance
    */
   Energy _f0width;
 
   /**
    * Mass of the \f$\sigma\f$ resonance
    */
   Energy _sigmamass;
 
   /**
    * Width of the \f$\sigma\f$ resonance
    */
   Energy _sigmawidth;
 
   /**
    * Mass of the neutral pion.
    */
   Energy _mpi0;
 
   /**
    * Mass of the charged pion.
    */
   Energy _mpic;
 
   /**
    * The \f$a_1\f$ mass
    */
   Energy _a1mass;
 
   /**
    * The \f$a_1\f$ width
    */
   Energy _a1width;
 
   /**
    * Mass of the \f$K^*\f$ resonace
    */
   Energy _mKstar;
 
   /**
    * Mass of the \f$K\f$ resonace
    */
   Energy _mK;
 
   /**
    * Coupling for the \f$KK^*\f$ term in the running width.
    */
   double _gammk;
 
   /**
    * pion decay constant
    */
   Energy _fpi;
 
   /**
    *  The prefactor
    */
   InvEnergy _fact;
 
   /**
    * Magnitude of the \f$p\f$-wave couplings of the rho resonance, \f$g^P_{\rho_k}\f$, 
    * (\f$\beta_{1,2}\f$ in the CLEO paper.)
    */
   vector<double> _rhomagP;
 
   /**
    * Phase of the \f$p\f$-wave couplings of the rho resonance, \f$g^P_{\rho_k}\f$,
    * (\f$\beta_{1,2}\f$ in the CLEO paper.)
    */
   vector<double> _rhophaseP;
 
   /**
    *\f$p\f$-wave couplings of the rho resonance, \f$g^P_{\rho_k}\f$, 
    * (\f$\beta_{1,2}\f$ in the CLEO paper.)
    */
   vector<Complex> _rhocoupP;
 
   /**
    * Magnitude of the \f$d\f$-wave couplings of the rho resonance, \f$g^D_{\rho_k}\f$,
    * (\f$\beta_{3,4}\f$ in the CLEO paper.)
    */
   vector<InvEnergy2> _rhomagD;
 
   /**
    * Phase of the \f$d\f$-wave couplings of the rho resonance, \f$g^D_{\rho_k}\f$, 
    * (\f$\beta_{3,4}\f$ in the CLEO paper.)
    */
   vector<double>_rhophaseD;
 
   /**
    * \f$d\f$-wave couplings of the rho resonance, \f$g^D_{\rho_k}\f$,
    * (\f$\beta_{3,4}\f$ in the CLEO paper.)
    */
   vector<complex<InvEnergy2> > _rhocoupD;
 
   /**
    * Magntiude of the coupling of the \f$f_2\f$ resonance, \f$g_{f_2}\f$,
    * (\f$\beta_5\f$ in the CLEO paper.)
    */
   InvEnergy2 _f2mag;
 
   /**
    * Phase of the coupling of the \f$f_2\f$ resonance, \f$g_{f_2}\f$,
    * (\f$\beta_5\f$ in the CLEO paper.)
    */
   double _f2phase;
 
   /**
    * Coupling of the \f$f_2\f$ resonance, \f$g_{f_2}\f$,
    * (\f$\beta_5\f$ in the CLEO paper.)
    */
   complex<InvEnergy2> _f2coup;
 
   /**
    * Magntiude of the coupling of the \f$f_0(1370)\f$ resonance, \f$g_{f_0}\f$,
    * (\f$\beta_6\f$ in the CLEO paper.)
    */
   double _f0mag;
 
   /**
    * Phase of the coupling of the \f$f_0(1370)\f$ resonance, \f$g_{f_0}\f$,
    * (\f$\beta_6\f$ in the CLEO paper.)
    */
   double _f0phase;
 
   /**
    * Coupling of the \f$f_0(1370)\f$ resonance, \f$g_{f_0}\f$,
    * (\f$\beta_6\f$ in the CLEO paper.)
    */
   Complex _f0coup;
 
   /**
    * Magntiude of the coupling of the \f$\sigma\f$ resonance, \f$g_\sigma\f$,
    * (\f$\beta_7\f$ in the CLEO paper.)
    */
   double _sigmamag;
 
   /**
    * Phase of the coupling of the \f$\sigma\f$ resonance, \f$g_\sigma\f$,
    * (\f$\beta_7\f$ in the CLEO paper.)
    */
   double _sigmaphase;
 
   /**
    * Coupling of the \f$\sigma\f$ resonance, \f$g_\sigma\f$,
    * (\f$\beta_7\f$ in the CLEO paper.)
    */
   Complex _sigmacoup;
   
   /**
    * The \f$a_1\f$ width for the running \f$a_1\f$ width calculation.
    */
   vector<Energy>  _a1runwidth;
 
   /**
    * The \f$q^2\f$ for the running \f$a_1\f$  width calculation.
    */
   vector<Energy2> _a1runq2;
 
 
   /**
    * The interpolator for the running \f$a_1\f$ width calculation.
    */
   Interpolator<Energy,Energy2>::Ptr _a1runinter;
 
   /**
    * Initialize the running \f$a_1\f$ width.
    */
   bool _initializea1;
 
   /**
    * Option for the \f$a_1\f$ width
    */
   bool _a1opt;
 
   /**
    *  The maximum mass of the hadronic system
    */
   Energy _maxmass;
 
   /**
    *  The maximum mass when the running width was calculated
    */
   Energy _maxcalc;
 
 };
 
 }
 
 #endif /* THEPEG_ThreePionCLEOCurrent_H */

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