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 // lAger: General Purpose l/A-event Generator
 // Copyright (C) 2016-2021 Sylvester Joosten <sjoosten@anl.gov>
 //
 // This file is part of lAger.
 //
 // lAger is free software: you can redistribute it and/or modify
 // it under the terms of the GNU General Public License as published by
 // the Free Shoftware Foundation, either version 3 of the License, or
 // (at your option) any later version.
 //
 // lAger is distributed in the hope that it will be useful,
 // but WITHOUT ANY WARRANTY; without even the implied warranty of
 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 // GNU General Public License for more details.
 //
 // You should have received a copy of the GNU General Public License
 // along with lAger.  If not, see <https://www.gnu.org/licenses/>.
 //
 
 #ifndef LAGER_PHYSICS_VM_LOADED
 #define LAGER_PHYSICS_VM_LOADED
 
 #include <TMath.h>
 #include <cmath>
 
 #include <lager/physics/kinematics.hh>
 
 // =============================================================================
 // VM Physics routines
 // =============================================================================
 
 namespace lager {
 namespace physics {
 
 // =============================================================================
 // R VM parameterization
 //
 // from
 //      Martynov, et. al., “Photoproduction of Vector Mesons in the Soft Dipole
 //      Pomeron Model.” PRD 67 (7), 2003. doi:10.1103/PhysRevD.67.074023.
 // eq. 31.
 //
 // J/psi parameters c(or a) and n
 //  * c: 2.164
 //  * n: 2.131
 // from eq. 18:
 //
 //      R. Fiore et al., "Exclusive Jpsi electroproduction in a dual model."
 //      PRD80:116001, 2009"
 //
 // Arguments:
 //  * Q2: -photon mass squared
 //  * Mv: VM mass
 //  * c: multiplicative parameter
 //  * n: power constant
 // =============================================================================
 inline double R_vm_martynov(const double Q2, const double Mv, const double c,
                             const double n) {
   const double Mv2 = Mv * Mv;
   return pow((c * Mv2 + Q2) / (c * Mv2), n) - 1.;
 }
 
 // =============================================================================
 // Dipole (multipole) form factor to relate real photo-production cross section
 // to sigma_T
 //
 // This form deviates from the classical VMD form (which has a fixed power of
 // 2), to better fit the world data for rho0 production.
 //
 // Cf.:
 //      A. Airapetian et al, "Exclusive Leptoproduction of rho0 Mesons on
 //      Hydrogen at Intermediate W Values", EPJ C 17 (2000) 389-398
 //
 //      Adams et al., "Diffractive production of ρ0 mesons in muon–proton
 //      interactions 470 GeV", ZPC74 (1997) 237-261.
 //
 // An optimized power of n=2.575 was taken from a fit result from
 //
 //      M Tytgat, "Diffractive production of ρ0 and ω vector mesons at HERMES",
 //      DESY-Thesis 2001-018 (2001)
 //
 // Arguments:
 //  * Q2: -photon mass squared
 //  * Mv: VM mass
 //  * n: power constant (2 for VMD; 2.575 from HERMES fit)
 // =============================================================================
 inline double dipole_ff_vm(const double Q2, const double Mv, const double n) {
   const double Mv2 = Mv * Mv;
   return pow(Mv2 / (Mv2 + Q2), n);
 }
 inline double multipole_ff_vm(const double Q2, const double Mv,
                               const double n) {
   return dipole_ff_vm(Q2, Mv, n);
 }
 
 // =============================================================================
 // t-channel photo-production cross section for heavy vector mesons
 // Values are in units of nb/GeV^2.
 //
 // Formulism from
 //      brodsky et. al., Phys.Lett.B498:23-28,2001
 //      (http://arxiv.org/abs/hep-ph/0010343)
 //
 // Both dsigma/dt and dsigma/d(exp_bt) are available. The latter is useful for a
 // more efficient MC implementation
 //
 // Parameter values from Eric's fit to the J/psi world data:
 //  * c2g: 6.499e3 [GeV^-2]
 //  * c3g: 2.894e3 [GeV^-2]
 //  * b: 1.13 [GeV^-2]
 //
 // Arguments:
 //  * s: photon-target system invariant mass squared
 //  * t: mandelstam t
 //  * Mt: target mass
 //  * Mv: VM mass
 //  * b: b-parameter of target form-factor
 //  * c2g: 2-gluon constant
 //  * c3g: 3-gluon constant
 //
 // =============================================================================
 inline double dsigma_dt_vm_brodsky(const double s, const double t,
                                    const double Mt, const double Mv,
                                    const double b, const double c2g,
                                    const double c3g = 0) {
   const double Mt2 = Mt * Mt;
   const double Mv2 = Mv * Mv;
   const double x = (2. * Mt * Mv + Mv2) / (s - Mt2);
   // form factor
   const double ff = exp(b * t);
   // phase space factor
   const double v = 1. / (16. * TMath::Pi());
   // 2 gluon term
   const double A2g = c2g * v * (1 - x) * (1 - x) / Mv2;
   // 3 gluon term
   const double A3g = c3g * v / (Mv2 * Mv2);
   return (A2g + A3g) * ff;
 }
 inline double dsigma_dexp_bt_vm_brodsky(const double s, const double Mt,
                                         const double Mv, const double b,
                                         const double c2g,
                                         const double c3g = 0) {
   const double Mt2 = Mt * Mt;
   const double Mv2 = Mv * Mv;
   const double x = (2. * Mt * Mv + Mv2) / (s - Mt2);
   // form factor (absorbed by the jacobian for d(bt) -> d(exp_bt)
   const double ff = 1.;
   // phase space factor
   const double v = 1. / (16. * TMath::Pi());
   // 2 gluon term
   const double A2g = c2g * v * (1 - x) * (1 - x) / Mv2;
   // 3 gluon term
   const double A3g = c3g * v / (Mv2 * Mv2);
   // extra jacobian for dt -> d(bt)
   const double jacobian = 1 / b;
   return (A2g + A3g) * ff * jacobian;
 }
 
 // =============================================================================
 // Electroproduction of phi mesons according the formalism
 // of the CLAS12 exclusive phi meson electroproduction proposal
 // https://www.jlab.org/exp_prog/proposals/12/PR12-12-007.pdf
 //
 // This is the transverse part of the cross section, also valid for
 // photoproduction. Note that this is the integrated cross section, which needs
 // to be multiplied with a normalized form factor F(t)/F_int for a differential
 // cross section
 // =============================================================================
 inline double sigmaT_phi_clas(const double Q2, const double W, const double Mt,
                               const double Mv, const double alpha_1,
                               const double alpha_2, const double alpha_3,
                               const double nu_T) { //, const double B0,
   // double alpha_prime) {
   const double Wth = Mt + Mv;
   const double cT =
       alpha_1 * pow((1 - Wth * Wth / (W * W)), alpha_2) * pow(W, alpha_3);
   const double sigmaT = cT * multipole_ff_vm(Q2, Mv, nu_T);
   return sigmaT;
 }
 inline double R_phi_clas(const double Q2, const double Mv, const double c_R) {
   const double Mv2 = Mv * Mv;
   return c_R * Q2 / Mv2;
 }
 
 inline double exp_ff_normalized(const double Q2, const double W, const double t,
                                 const double Mt, const double Mv,
                                 const double B0, const double alphaP) {
   const double B = B0 + 4 * alphaP * std::log(W);
   const double F = exp(B * t);
   const double t_min = t_range(W * W, Q2, Mt, Mv, Mt).max;
   const double F_int = exp(B * t_min) / B;
   return F / F_int;
 }
 inline double dipole_ff_normalized(const double Q2, const double W,
                                    const double t, const double Mt,
                                    const double Mv, const double Mg2) {
   const double Mg8 = pow(Mg2, 4);
   const double F = Mg8 / pow(Mg2 - t, 4);
   const double t_min = t_range(W * W, Q2, Mt, Mv, Mt).max;
   const double F_int = Mg8 / (3 * pow(Mg2 - t_min, 3));
   return F / F_int;
 }
 // =============================================================================
 // General VM decay distributions in the VM helicity frame for the
 // cases of  (1) VM --> Scaler+scaler
 //       and (2) VM -> fermion+fermion
 // Note that case (1) corresponds equation 31 (for W0) in
 //     K. Schilling et al, Nucl.Phys.B 15 (1970) 397-412
 // while case (2) has the corresponding formula for decay in spin-1/2
 // particles
 //
 // Both expressions are a function of the decay angles in the VM helicity
 // frame
 //  cth: cosine of the polar angle
 //  phi: azimuthal angle with the VM production plane
 //  sdme_04_00:  r^04_00 (=rho^0_00 for photoproduction)
 //  sdme_04_10:  Re(r^04_10) (=Re(rho^0_10) for photoproduction)
 //  sdme_04_1m1: r^04_1-1 (=rho^0_1-1 for photoproduction)
 // =============================================================================
 inline double vm_decay_scalars(const double cth, const double phi,
                                const double sdme_04_00, const double sdme_04_10,
                                const double sdme_04_1m1) {
   const double theta = acos(cth);
   const double sth = sin(theta);
   const double factor = 3 / (4. * TMath::Pi());
   const double t1 = 0.5 * (1 - sdme_04_00);
   const double t2 = 0.5 * (3 * sdme_04_00 - 1) * cth * cth;
   const double t3 =
       -1 * TMath::Sqrt2() * sdme_04_10 * sin(2 * theta) * cos(phi);
   const double t4 = -1 * sdme_04_1m1 * sth * sth * cos(2 * phi);
   return t1 + t2 + t3 + t4;
 }
 inline double vm_decay_fermions(const double cth, const double phi,
                                 const double sdme_04_00,
                                 const double sdme_04_10,
                                 const double sdme_04_1m1) {
   const double theta = acos(cth);
   const double sth = sin(theta);
   const double factor = 3 / (4. * TMath::Pi());
   const double t1 = 0.5 * (1 + sdme_04_00);
   const double t2 = -0.5 * (3 * sdme_04_00 - 1) * cth * cth;
   const double t3 = 1 * TMath::Sqrt2() * sdme_04_10 * sin(2 * theta) * cos(phi);
   const double t4 = 1 * sdme_04_1m1 * sth * sth * cos(2 * phi);
   LOG_JUNK2("vm_decay_fermions",
             "cos(theta): " + std::to_string(cth) +
                 ", theta: " + std::to_string(theta) +
                 ", t1: " + std::to_string(t1) + ", t2: " + std::to_string(t2) +
                 ", t3: " + std::to_string(t3) + ", t4: " + std::to_string(t4));
   return t1 + t2 + t3 + t4;
 }
 
 } // namespace physics
 } // namespace lager
 
 #endif

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