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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_KINEMATICS_LOADED
 #define LAGER_PHYSICS_KINEMATICS_LOADED
 
 #include <cmath>
 #include <lager/core/interval.hh>
 #include <lager/core/particle.hh>
 
 namespace lager {
 namespace physics {
 
 // =======================================================================================
 // calculate the allowed Q2 range for a given lepton beam, target and y
 //
 // The lower bound is given by the kinematics of t-channel scattering,
 // while the upper bound is given by either t-channel kinematics, or the
 // requirement that the final W be larger than the target mass
 // =======================================================================================
 inline interval<double> Q2_range(const particle& beam, const particle& target,
                                  const double y) {
   const double E = (beam.p()).Dot(target.p()) / target.mass();
   const double E2 = E * E;
   const double m2 = beam.mass2();
   // lower and upper bound from t-channel process on electron leg
   const double comp1 = -2. * m2 + 2. * E2 * (1. - y);
   const double comp2 = 2. * sqrt((E2 - m2) * (E2 * (1. - y) * (1. - y) - m2));
   const double Q2_low = comp1 - comp2;
   const double Q2_high1 = comp1 + comp2;
   // alternative upper bound from requirement that final state has at least the
   // invariant mass of the target mass (W2min = target.mass^2, meaning that 2 M
   // nu = Q2)
   const double Q2_high2 = 2 * target.mass() * E * y;
   return {Q2_low, fmin(Q2_high1, Q2_high2)};
 }
 
 // =======================================================================================
 // calculate the allowed t range
 //
 // input:
 //   * W2 (=s)
 //   * Q2 (-photon mass squared)
 //   * Mt (target mass)
 //   * Mv (VM mass)
 //   * Mr (recoil mass)
 // =======================================================================================
 inline interval<double> t_range(const double W2, const double Q2,
                                 const double Mt, const double Mv,
                                 const double Mr) {
   const double Mt2 = Mt * Mt;
   const double Mr2 = Mr * Mr;
   const double Mv2 = Mv * Mv;
   const double W = sqrt(W2);
   // CM relations for energy and momenta
   const double Et_cm = (W2 + Q2 + Mt2) / (2. * W);
   const double Pt_cm = sqrt(Et_cm * Et_cm - Mt2);
   const double Er_cm = (W2 - Mv2 + Mr2) / (2. * W);
   const double Pr_cm = sqrt(Er_cm * Er_cm - Mr2);
   // t_low when recoil direction changes by 90 degrees compared to target,
   // t_high when the recoil in the target direction
   // note: what we call t_high is also refered to as t_min
   const double t_low = Mt2 + Mr2 - 2. * Et_cm * Er_cm - 2. * Pt_cm * Pr_cm;
   const double t_high = Mt2 + Mr2 - 2. * Et_cm * Er_cm + 2. * Pt_cm * Pr_cm;
   // that's all!
   return {t_low, t_high};
 }
 
 } // namespace physics
 } // namespace lager
 
 #endif

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