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 // -*- C++ -*-
 //
 // a1ThreePionCLEODecayer.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_a1ThreePionCLEODecayer_H
 #define HERWIG_a1ThreePionCLEODecayer_H
 //
 // This is the declaration of the a1ThreePionCLEODecayer class.
 //
 #include "Herwig/Decay/DecayIntegrator.h"
 #include "Herwig/Decay/PhaseSpaceMode.h"
 #include "Herwig/Utilities/Kinematics.h"
 #include "ThePEG/Helicity/LorentzPolarizationVector.h"
 
 namespace Herwig {
 using namespace ThePEG;
 
 /** \ingroup Decay
  *
  *  The  <code>a1ThreePionCLEODecayer</code> class is designed to implement the decay
  *  of the \f$a_1\f$ to three pions using the model of Phys.Rev.D61:012002,2000,
  *  (hep-ex/9902022) (CLEO) which was fitted to the one charged and two neutral pion
  *  channel for the charged \f$a_1\f$ decay in \f$\tau \to a_1 -> \pi\pi\pi\f$.
  *  The other modes are infered from this using isospin. This is a sophisticated model
  *  including the coupling of the \f$a_1\f$ to the \f$\rho\f$, \f$\rho(1450)\f$, 
  *  \f$f(1370)\f$ and \f$\sigma\f$ sigma mesons.
  *
  *  In this case the current is given by
  *  \f[\mathcal{M} = \epsilon_\mu
  *     \left[F_1(p_2-p_3)^\mu+F_2(p_3-p_1)^\mu+F_3(p_1-p_2)^\mu\right].\f]
  *
  *
  * The form factors for the \f$a_1^0 \to \pi^0 \pi^0 \pi^0\f$ mode are
  * \f[F_1=
  * \phantom{-}\frac23\left(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(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{18}\frac{(4m_{\pi^0}^2-s_2)(q^2+s_2-m_{\pi^0}^2)}{s_2}B^D_{f_2}(s_2)
  *   +\frac1{18}\frac{(4m_{\pi^0}^2-s_3)(q^2-m_{\pi^0}^2+s_3)}{s_3}B^D_{f_2}(s_3)\right)
  *\f]
  *
  * \f[F_2=\phantom{-}\frac23(g_\sigma B^S_\sigma(s_3)+g_{f_0}B^S_{f_0}(s_3))
  *          -\frac23(g_\sigma B^S_\sigma(s_1)+g_{f_0}B^S_{f_0}(s_1))
  *          +g_{f_2}\left( \frac12(s_3-s1)B^D_{f_2}(s_2)
  *   -\frac1{18}\frac{(4m_{\pi^0}^2-s_1)(q^2+s_1-m_{\pi^0}^2)}{s_1}B^D_{f_2}(s_1)
  *   +\frac1{18}\frac{(4m_{\pi^0}^2-s_3)(q^2-m_{\pi^0}^2+s_3)}{s_3}B^D_{f_2}(s_3)\right)
  *\f]
  * \f[F_3=-\frac23(g_\sigma B^S_\sigma(s_1)+g_{f_0}B^S_{f_0}(s_1))
  *          +\frac23(g_\sigma B^S_\sigma(s_2)+g_{f_0}B^S_{f_0}(s_2))
  *          +g_{f_2}\left( \frac12(s_1-s_2)B^D_{f_2}(s_3)
  *  -\frac1{18}\frac{(4m_{\pi^0}^2-s_1)(q^2+s_1-m_{\pi^0}^2)}{s_1}B^D_{f_2}(s_1)
  *  +\frac1{18}\frac{(4m_{\pi^0}^2-s_2)(q^2+s_2-m_{\pi^0}^2)}{s_2}B^D_{f_2}(s_2)\right)
  *\f]
  *
  * The form factors for the \f$a_1^+ \to \pi^0 \pi^0 \pi^+\f$ mode are
  *
  * \f[F_1=\sum_k\left\{-\frac{g^P_{\rho_k}}3B_{\rho_k}^P(s_1)
  *          -g^D_{\rho_k}B_{\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$a_1^0\to\pi^+\pi^-\pi^0\f$.
  *
  * \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_3-m_{\pi^0}^2-s_1+m_{\pi^+}^2)\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^0}^2+s_3)(4m_{\pi^+}^2-s_3)B^D_{f_2}(s_3)\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_3-m_{\pi^0}^2-s_2+m_{\pi^+}^2)\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^0}^2+s_3)(4m_{\pi^+}^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)(s_3-m_{\pi^0}^2-s_2+m_{\pi^+}^2)
  *                       +\frac13B_{\rho_k}^P(s_2)(s_3-m_{\pi^0}^2-s_1+m_{\pi^+}^2)
  *          \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 resonanc \f$Y\f$.
  *
  * @see ThreePionCLEOCurrent
  * @see DecayIntegrator
  *
  */
 class a1ThreePionCLEODecayer: public DecayIntegrator {
   
 public:
   
   /**
    * Default constructor.
    */
   a1ThreePionCLEODecayer();
 
   /**
    * 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.
    */
   a1ThreePionCLEODecayer & operator=(const a1ThreePionCLEODecayer &) = delete;
   
 private:
 
   /**
    * Breit wigner for the \f$\rho\f$, \f$B^P_{\rho_k}(q^2)\f$.
    * @param ires The \f$\rho\f$ multiplet to used.
    * @param q2 The scale, \f$q^2\f$.
    * @param icharge Which pion masses to use for the momentum calculation
    * @return The Breit-Wigner
    */
   Complex rhoBreitWigner(int ires, Energy2 q2,int icharge) const {
     Energy q=sqrt(q2);
     Complex ii(0.,1.);
     double ratio = icharge==0 ? 
       Kinematics::pstarTwoBodyDecay(q,_mpic,_mpic)/_prhocc[ires] :
       Kinematics::pstarTwoBodyDecay(q,_mpic,_mpi0)/_prhoc0[ires];
     Energy gamrun=_rhowidth[ires]*pow(ratio,3)*_rhomass[ires]/q;
     return sqr(_rhomass[ires])
       /(sqr(_rhomass[ires])-q2-ii*_rhomass[ires]*gamrun);
   }
 
   /**
    * Breit wigner for the \f$\sigma\f$, \f$B^S_\sigma(q^2)\f$.
    * @param q2 The scale, \f$q^2\f$.
    * @param icharge Which pion masses to use for the momentum calculation
    * @return The Breit-Wigner
    */
   Complex sigmaBreitWigner(Energy2 q2,int icharge) const {
     Energy q=sqrt(q2);
     Complex ii(0.,1.);
     double ratio = icharge==0 ? 
       Kinematics::pstarTwoBodyDecay(q,_mpic,_mpic)/_psigmacc :
       Kinematics::pstarTwoBodyDecay(q,_mpi0,_mpi0)/_psigma00;
     Energy gamrun=_sigmawidth*ratio*_sigmamass/q;
     return sqr(_sigmamass)/(sqr(_sigmamass)-q2-ii*_sigmamass*gamrun);
   }
   
   /**
    * Breit wigner for the \f$f_0(1370)\f$, \f$B^S_{f_0}(q^2)\f$.
    * @param q2 The scale, \f$q^2\f$.
    * @param icharge Which pion masses to use for the momentum calculation
    * @return The Breit-Wigner
    */
   Complex f0BreitWigner(Energy2 q2,int icharge) const {
     Energy q=sqrt(q2);
     Complex ii(0.,1.);
     double ratio = icharge==0 ? 
       Kinematics::pstarTwoBodyDecay(q,_mpic,_mpic)/_pf0cc :
       Kinematics::pstarTwoBodyDecay(q,_mpi0,_mpi0)/_pf000;
     Energy gamrun=_f0width*ratio*_f0mass/q;
     return sqr(_f0mass)/(sqr(_f0mass)-q2-ii*_f0mass*gamrun);
   }
   
   /**
    * Breit wigner for the \f$f_2\f$, \f$B^D_{f_2}(q^2)\f$.
    * @param q2 The scale, \f$q^2\f$.
    * @param icharge Which pion masses to use for the momentum calculation
    * @return The Breit-Wigner
    */
   Complex f2BreitWigner(Energy2 q2,int icharge) const {
     Energy q=sqrt(q2);
     Complex ii(0.,1.);
     double ratio = icharge==0 ?
       Kinematics::pstarTwoBodyDecay(q,_mpic,_mpic)/_pf2cc :
       Kinematics::pstarTwoBodyDecay(q,_mpi0,_mpi0)/_pf200;
     Energy gamrun=_f2width*pow(ratio,5)*_f2mass/q;
     return sqr(_f2mass)/(sqr(_f2mass)-q2-ii*_f2mass*gamrun);
   }
   
   /**
    * Calculate the form factors
    * @param iopt The mode being calculated in the order given above
    * @param ichan The phase space channel in the order given in the doinit member.
    * @param q2 The sacale \f$q^2\f$.
    * @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 formFactors(int iopt,int ichan,Energy2 q2,Energy2 s1,Energy2 s2,
            Energy2 s3,
            complex<InvEnergy> & F1,
            complex<InvEnergy> & F2,
            complex<InvEnergy> & F3) const;
 
 private:
 
   /**
    * Masses of the rho resonaces
    */
   vector<Energy> _rhomass;
 
   /**
    * Widths of the rho resonaces
    */
   vector<Energy> _rhowidth;
 
   /**
    * Momentum of the particles produced in charged rho decay
    */
   vector<Energy> _prhocc;
 
   /**
    * Momentum of the particles produced in neutral rho decay
    */
   vector<Energy> _prhoc0;
 
   /**
    * Mass of the \f$f_2\f$.
    */
   Energy _f2mass;
 
   /**
    * Width of the \f$f_2\f$.
    */
   Energy _f2width;
 
   /**
    * Momentum for the decay of the \f$f_2\f$ to two charged pions.
    */
   Energy _pf2cc;
 
   /**
    * Momentum for the decay of the \f$f_2\f$ to two neutral pions.
    */
   Energy _pf200;
 
   /**
    * Mass of the \f$f_0(1370)\f$.
    */
   Energy _f0mass;
 
   /**
    * Width of the \f$f_0(1370)\f$.
    */
   Energy _f0width;
 
   /**
    * Momentum for the decay of the \f$f_0(1370)\f$ to two charged pions.
    */
   Energy _pf0cc;
 
   /**
    * Momentum for the decay of the \f$f_0(1370)\f$ to two neutral pions.
    */
   Energy _pf000;
 
   /**
    * Mass of the \f$\sigma\f$ meson.
    */
   Energy _sigmamass;
 
   /**
    * Width of the \f$\sigma\f$ meson.
    */
   Energy _sigmawidth;
 
   /**
    * Momentum for the decay of the \f$\sigma\f$ to two charged pions.
    */
   Energy _psigmacc;
 
   /**
    * Momentum for the decay of the \f$\sigma\f$ to two neutral pions.
    */
   Energy _psigma00;
 
   /**
    * Mass of the neutral pion
    */
   Energy _mpi0;
 
   /**
    * Mass of the charged pion
    */
   Energy _mpic;
 
   /**
    * overall coupling for the decay
    */
   InvEnergy _coupling;
 
   /**
    * 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;
 
   /**
    * Use local values of the mass parameters
    */
   bool _localparameters;
   
   /**
    * Weights for the channels for the zero charged pion channel.
    */
   mutable vector<double> _zerowgts;
   
   /**
    * Weights for the channels for the one charged pion channel.
    */
   mutable vector<double> _onewgts;
   
   /**
    * Weights for the channels for the two charged pion channel.
    */
   mutable vector<double> _twowgts;
   
   /**
    * Weights for the channels for the three charged pion channel.
    */
   mutable vector<double> _threewgts;
 
   /**
    * Maximum weight for the zero charged pion channel.
    */
   mutable double _zeromax;
 
   /**
    * Maximum weight for the one charged pion channel.
    */
   mutable double _onemax;
 
   /**
    * Maximum weight for the two charged pion channel.
    */
   mutable double _twomax;
 
   /**
    * Maximum weight for the three charged pion channel.
    */
   mutable double _threemax;
 
   /**
    *  Spin density matrix
    */
   mutable RhoDMatrix _rho;
 
   /**
    *  Polarization vectors
    */
   mutable vector<Helicity::LorentzPolarizationVector> _vectors;
 };
   
 }
 
 
 #endif /* HERWIG_a1ThreePionCLEODecayer_H */

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