scatteractionphoton.cc

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/*
 *
 *    Copyright (c) 2016-2022
 *      SMASH Team
 *
 *    GNU General Public License (GPLv3 or later)
 *
 */
 
#include "smash/scatteractionphoton.h"
 
#include <algorithm>
 
#include "smash/angles.h"
#include "smash/constants.h"
#include "smash/crosssectionsphoton.h"
#include "smash/forwarddeclarations.h"
#include "smash/outputinterface.h"
#include "smash/particletype.h"
#include "smash/pow.h"
#include "smash/random.h"
 
namespace smash {
static constexpr int LScatterAction = LogArea::ScatterAction::id;
 
ScatterActionPhoton::ScatterActionPhoton(
    const ParticleList &in, const double time, const int n_frac_photons,
    const double hadronic_cross_section_input)
    : ScatterAction(in[0], in[1], time),
      reac_(photon_reaction_type(in)),
      number_of_fractional_photons_(n_frac_photons),
      hadron_out_t_(outgoing_hadron_type(in)),
      hadron_out_mass_(sample_out_hadron_mass(hadron_out_t_)),
      hadronic_cross_section_(hadronic_cross_section_input) {}
 
ScatterActionPhoton::ReactionType ScatterActionPhoton::photon_reaction_type(
    const ParticleList &in) {
  if (in.size() != 2) {
    return ReactionType::no_reaction;
  }
 
  PdgCode a = in[0].pdgcode();
  PdgCode b = in[1].pdgcode();
 
  // swap so that pion is first and there are less cases to be listed
  if (!a.is_pion()) {
    std::swap(a, b);
  }
 
  switch (pack(a.code(), b.code())) {
    case (pack(pdg::pi_p, pdg::pi_z)):
    case (pack(pdg::pi_z, pdg::pi_p)):
      return ReactionType::pi_z_pi_p_rho_p;
 
    case (pack(pdg::pi_m, pdg::pi_z)):
    case (pack(pdg::pi_z, pdg::pi_m)):
      return ReactionType::pi_z_pi_m_rho_m;
 
    case (pack(pdg::pi_p, pdg::rho_z)):
      return ReactionType::pi_p_rho_z_pi_p;
 
    case (pack(pdg::pi_m, pdg::rho_z)):
      return ReactionType::pi_m_rho_z_pi_m;
 
    case (pack(pdg::pi_m, pdg::rho_p)):
      return ReactionType::pi_m_rho_p_pi_z;
 
    case (pack(pdg::pi_p, pdg::rho_m)):
      return ReactionType::pi_p_rho_m_pi_z;
 
    case (pack(pdg::pi_z, pdg::rho_p)):
      return ReactionType::pi_z_rho_p_pi_p;
 
    case (pack(pdg::pi_z, pdg::rho_m)):
      return ReactionType::pi_z_rho_m_pi_m;
 
    case (pack(pdg::pi_p, pdg::pi_m)):
    case (pack(pdg::pi_m, pdg::pi_p)):
      return ReactionType::pi_p_pi_m_rho_z;
 
    case (pack(pdg::pi_z, pdg::rho_z)):
      return ReactionType::pi_z_rho_z_pi_z;
 
    default:
      return ReactionType::no_reaction;
  }
}
 
void ScatterActionPhoton::perform_photons(const OutputsList &outputs) {
  for (int i = 0; i < number_of_fractional_photons_; i++) {
    generate_final_state();
    for (const auto &output : outputs) {
      if (output->is_photon_output()) {
        // we do not care about the local density
        output->at_interaction(*this, 0.0);
      }
    }
  }
}
 
ParticleTypePtr ScatterActionPhoton::outgoing_hadron_type(
    const ReactionType reaction) {
  static const ParticleTypePtr rho_z_particle_ptr =
      &ParticleType::find(pdg::rho_z);
  static const ParticleTypePtr rho_p_particle_ptr =
      &ParticleType::find(pdg::rho_p);
  static const ParticleTypePtr rho_m_particle_ptr =
      &ParticleType::find(pdg::rho_m);
  static const ParticleTypePtr pi_z_particle_ptr =
      &ParticleType::find(pdg::pi_z);
  static const ParticleTypePtr pi_p_particle_ptr =
      &ParticleType::find(pdg::pi_p);
  static const ParticleTypePtr pi_m_particle_ptr =
      &ParticleType::find(pdg::pi_m);
 
  switch (reaction) {
    case ReactionType::pi_z_pi_p_rho_p:
      return rho_p_particle_ptr;
      break;
    case ReactionType::pi_z_pi_m_rho_m:
      return rho_m_particle_ptr;
      break;
    case ReactionType::pi_p_pi_m_rho_z:
      return rho_z_particle_ptr;
      break;
 
    case ReactionType::pi_p_rho_z_pi_p:
    case ReactionType::pi_z_rho_p_pi_p:
      return pi_p_particle_ptr;
 
    case ReactionType::pi_m_rho_z_pi_m:
    case ReactionType::pi_z_rho_m_pi_m:
      return pi_m_particle_ptr;
 
    case ReactionType::pi_m_rho_p_pi_z:
    case ReactionType::pi_p_rho_m_pi_z:
    case ReactionType::pi_z_rho_z_pi_z:
      return pi_z_particle_ptr;
      break;
    default:
      // default constructor constructs p with invalid index
      ParticleTypePtr p{};
      return p;
  }
}
 
ParticleTypePtr ScatterActionPhoton::outgoing_hadron_type(
    const ParticleList &in) {
  auto reac = photon_reaction_type(in);
  return outgoing_hadron_type(reac);
}
 
bool ScatterActionPhoton::is_kinematically_possible(const double s_sqrt,
                                                    const ParticleList &in) {
  auto reac = photon_reaction_type(in);
  auto hadron = outgoing_hadron_type(in);
 
  if (reac == ReactionType::no_reaction)
    return false;
 
  if (default_mediator_ == MediatorType::PION &&
      reac == ReactionType::pi_z_rho_z_pi_z) {
    return false;
  }
 
  // C15 has only s-channel. Make sure that CM-energy is high
  // enough to produce mediating omega meson
  if ((reac == ReactionType::pi_m_rho_p_pi_z ||
       reac == ReactionType::pi_p_rho_m_pi_z) &&
      default_mediator_ == MediatorType::OMEGA) {
    if (s_sqrt < omega_mass) {
      return false;
    }
  }
 
  // for all other processes: if cm-energy is not high enough to produce final
  // state particle reject the collision.
  if (hadron->is_stable() && s_sqrt < hadron->mass()) {
    return false;
    // Make sure energy is high enough to not only create final state particle,
    // but to also assign momentum.
  } else if (!hadron->is_stable() &&
             s_sqrt < (hadron->min_mass_spectral() + really_small)) {
    return false;
  } else {
    return true;
  }
}
 
void ScatterActionPhoton::generate_final_state() {
  // we have only one reaction per incoming particle pair
  if (collision_processes_photons_.size() != 1) {
    logg[LScatterAction].fatal()
        << "Problem in ScatterActionPhoton::generate_final_state().\n";
    throw std::runtime_error("");
  }
  auto *proc = collision_processes_photons_[0].get();
 
  outgoing_particles_ = proc->particle_list();
  process_type_ = proc->get_type();
 
  FourVector middle_point = get_interaction_point();
 
  // t is defined to be the momentum exchanged between the rho meson and the
  // photon in pi + rho -> pi + photon channel. Therefore,
  // get_t_range needs to be called with m2 being the rho mass instead of the
  // pion mass. So, particles 1 and 2 are swapped if necessary.
 
  if (!incoming_particles_[0].pdgcode().is_pion()) {
    std::swap(incoming_particles_[0], incoming_particles_[1]);
  }
 
  // 2->2 inelastic scattering
  // Sample the particle momenta in CM system
  const double m1 = incoming_particles_[0].effective_mass();
  const double m2 = incoming_particles_[1].effective_mass();
 
  const double &m_out = hadron_out_mass_;
 
  const double s = mandelstam_s();
  const double sqrts = sqrt_s();
  std::array<double, 2> mandelstam_t = get_t_range(sqrts, m1, m2, m_out, 0.0);
  const double t1 = mandelstam_t[1];
  const double t2 = mandelstam_t[0];
  const double pcm_in = cm_momentum();
  const double pcm_out = pCM(sqrts, m_out, 0.0);
 
  const double t = random::uniform(t1, t2);
 
  double costheta = (t - pow_int(m2, 2) +
                     0.5 * (s + pow_int(m2, 2) - pow_int(m1, 2)) *
                         (s - pow_int(m_out, 2)) / s) /
                    (pcm_in * (s - pow_int(m_out, 2)) / sqrts);
 
  // on very rare occasions near the kinematic threshold numerical issues give
  // unphysical angles.
  if (costheta > 1 || costheta < -1) {
    logg[LScatterAction].warn()
        << "Cos(theta)of photon scattering out of physical bounds in "
           "the following scattering: "
        << incoming_particles_ << "Clamping to [-1,1].";
    if (costheta > 1.0)
      costheta = 1.0;
    if (costheta < -1.0)
      costheta = -1.0;
  }
  Angles phitheta(random::uniform(0.0, twopi), costheta);
  outgoing_particles_[0].set_4momentum(hadron_out_mass_,
                                       phitheta.threevec() * pcm_out);
  outgoing_particles_[1].set_4momentum(0.0, -phitheta.threevec() * pcm_out);
 
  // Set positions & boost to computational frame.
  for (ParticleData &new_particle : outgoing_particles_) {
    new_particle.set_4position(middle_point);
    new_particle.boost_momentum(
        -total_momentum_of_outgoing_particles().velocity());
  }
 
  const double E_Photon = outgoing_particles_[1].momentum()[0];
 
  // Weighing of the fractional photons
  if (number_of_fractional_photons_ > 1) {
    // if rho in final state take already sampled mass (same as m_out). If rho
    // is incoming take the mass of the incoming particle
    const double m_rho = rho_mass();
 
    // compute the differential cross section with form factor included
    const double diff_xs = diff_cross_section_w_ff(t, m_rho, E_Photon);
 
    weight_ = diff_xs * (t2 - t1) /
              (number_of_fractional_photons_ * hadronic_cross_section());
  } else {
    // compute the total cross section with form factor included
    const double total_xs = total_cross_section_w_ff(E_Photon);
 
    weight_ = total_xs / hadronic_cross_section();
  }
  // Scale weight by cross section scaling factor of incoming particles
  weight_ *= incoming_particles_[0].xsec_scaling_factor() *
             incoming_particles_[1].xsec_scaling_factor();
 
  // Photons are not really part of the normal processes, so we have to set a
  // constant arbitrary number.
  const auto id_process = ID_PROCESS_PHOTON;
  Action::check_conservation(id_process);
}
 
void ScatterActionPhoton::add_dummy_hadronic_process(
    double reaction_cross_section) {
  CollisionBranchPtr dummy_process = std::make_unique<CollisionBranch>(
      incoming_particles_[0].type(), incoming_particles_[1].type(),
      reaction_cross_section, ProcessType::TwoToTwo);
  add_collision(std::move(dummy_process));
}
 
double ScatterActionPhoton::sample_out_hadron_mass(
    const ParticleTypePtr out_t) {
  double mass = out_t->mass();
  const double cms_energy = sqrt_s();
  if (cms_energy <= out_t->min_mass_kinematic()) {
    throw InvalidResonanceFormation(
        "Problem in ScatterActionPhoton::sample_hadron_mass");
  }
 
  if (!out_t->is_stable()) {
    mass = out_t->sample_resonance_mass(0, cms_energy);
  }
 
  return mass;
}
 
double ScatterActionPhoton::rho_mass() const {
  assert(reac_ != ReactionType::no_reaction);
  switch (reac_) {
    // rho in final state. use already sampled mass
    case ReactionType::pi_p_pi_m_rho_z:
    case ReactionType::pi_z_pi_m_rho_m:
    case ReactionType::pi_z_pi_p_rho_p:
      return hadron_out_mass_;
    // rho in initial state, use its mass
    case ReactionType::pi_m_rho_p_pi_z:
    case ReactionType::pi_p_rho_m_pi_z:
    case ReactionType::pi_p_rho_z_pi_p:
    case ReactionType::pi_m_rho_z_pi_m:
    case ReactionType::pi_z_rho_m_pi_m:
    case ReactionType::pi_z_rho_p_pi_p:
    case ReactionType::pi_z_rho_z_pi_z:
      return (incoming_particles_[0].is_rho())
                 ? incoming_particles_[0].effective_mass()
                 : incoming_particles_[1].effective_mass();
    case ReactionType::no_reaction:
    default:
      throw std::runtime_error(
          "Invalid ReactionType in ScatterActionPhoton::rho_mass()");
  }
}
 
CollisionBranchList ScatterActionPhoton::create_collision_branch() {
  CollisionBranchList process_list;
 
  static ParticleTypePtr photon_particle = &ParticleType::find(pdg::photon);
  double xsection = total_cross_section();
 
  process_list.push_back(std::make_unique<CollisionBranch>(
      *hadron_out_t_, *photon_particle, xsection, ProcessType::TwoToTwo));
  collision_branch_created_ = true;
  return process_list;
}
 
double ScatterActionPhoton::total_cross_section(MediatorType mediator) const {
  CollisionBranchList process_list;
  CrosssectionsPhoton<ComputationMethod::Analytic> xs_object;
 
  const double s = mandelstam_s();
  // the mass of the mediating particle depends on the channel. For an incoming
  // rho it is the mass of the incoming particle, for an outgoing rho it is the
  // sampled mass
  const double m_rho = rho_mass();
  double xsection = 0.0;
 
  switch (reac_) {
    case ReactionType::pi_p_pi_m_rho_z:
      xsection = xs_object.xs_pi_pi_rho0(s, m_rho);
      break;
 
    case ReactionType::pi_z_pi_m_rho_m:
    case ReactionType::pi_z_pi_p_rho_p:
      xsection = xs_object.xs_pi_pi0_rho(s, m_rho);
      break;
 
    case ReactionType::pi_m_rho_z_pi_m:
    case ReactionType::pi_p_rho_z_pi_p:
      xsection = xs_object.xs_pi_rho0_pi(s, m_rho);
      break;
 
    case ReactionType::pi_m_rho_p_pi_z:
    case ReactionType::pi_p_rho_m_pi_z:
      if (mediator == MediatorType::SUM) {
        xsection = xs_object.xs_pi_rho_pi0(s, m_rho);
        break;
      } else if (mediator == MediatorType::PION) {
        xsection = xs_object.xs_pi_rho_pi0_rho_mediated(s, m_rho);
        break;
      } else if (mediator == MediatorType::OMEGA) {
        xsection = xs_object.xs_pi_rho_pi0_omega_mediated(s, m_rho);
        break;
      } else {
        throw std::runtime_error("");
      }
    case ReactionType::pi_z_rho_m_pi_m:
    case ReactionType::pi_z_rho_p_pi_p:
      if (mediator == MediatorType::SUM) {
        xsection = xs_object.xs_pi0_rho_pi(s, m_rho);
        break;
      } else if (mediator == MediatorType::PION) {
        xsection = xs_object.xs_pi0_rho_pi_rho_mediated(s, m_rho);
        break;
      } else if (mediator == MediatorType::OMEGA) {
        xsection = xs_object.xs_pi0_rho_pi_omega_mediated(s, m_rho);
        break;
      } else {
        throw std::runtime_error("");
      }
 
    case ReactionType::pi_z_rho_z_pi_z:
      xsection = xs_object.xs_pi0_rho0_pi0(s, m_rho);
      break;
 
    case ReactionType::no_reaction:
      // never reached
      break;
  }
 
  if (xsection == 0.0) {
    // Vanishing cross sections are problematic for the creation of a
    // CollisionBranch. For infrastructure reasons it is however necessary to
    // create such a collision branch whenever the underlying hadronic
    // scattering is a candidate for a photon interaction. In these cases we
    // need to manually set a dummy value for the cross section and produce the
    // photon. This photon will however automatically be assigned a 0 weight
    // because of the vanishing cross section and therefore not be of relevance
    // for any analysis.
    // In other cases, where the collision branch was already created, we
    // do not want to overwrite the cross section, of course.
    xsection = collision_branch_created_ ? 0.0 : 0.01;
  } else if (xsection < 0) {
    // Due to numerical reasons it can happen that the calculated cross sections
    // are negative (approximately -1e-15) if sqrt(s) is close to the threshold
    // energy. In those cases the cross section is manually set to 0.1 mb, which
    // is a reasonable value for the processes we are looking at (C14,C15,C16).
    xsection = 0.1;
    logg[LScatterAction].warn(
        "Calculated negative cross section.\nParticles ", incoming_particles_,
        " mass rho particle: ", m_rho, ", sqrt_s: ", std::sqrt(s));
  }
  return xsection;
}
 
double ScatterActionPhoton::total_cross_section_w_ff(const double E_photon) {
  /* C12, C13, C15, C16 need special treatment. These processes have identical
     incoming and outgoing particles, but diffrent mediating particles and
     hence different form factors. If both channels are added up
     (MediatorType::SUM), each contribution is corrected by the corresponding
     form factor.
  */
  switch (reac_) {
    case ReactionType::pi_m_rho_p_pi_z:
    case ReactionType::pi_p_rho_m_pi_z:
    case ReactionType::pi_z_rho_m_pi_m:
    case ReactionType::pi_z_rho_p_pi_p: {
      if (default_mediator_ == MediatorType::SUM) {
        std::pair<double, double> FF = form_factor_pair(E_photon);
        std::pair<double, double> xs = total_cross_section_pair();
        const double xs_ff =
            pow_int(FF.first, 4) * xs.first + pow_int(FF.second, 4) * xs.second;
        return cut_off(xs_ff);
      } else if (default_mediator_ == MediatorType::PION) {
        const double FF = form_factor_pion(E_photon);
        const double xs = total_cross_section();
        return cut_off(pow_int(FF, 4) * xs);
      } else if (default_mediator_ == MediatorType::OMEGA) {
        const double FF = form_factor_omega(E_photon);
        const double xs = total_cross_section();
        return cut_off(pow_int(FF, 4) * xs);
      }
      break;
    }
    case ReactionType::pi_z_pi_p_rho_p:
    case ReactionType::pi_z_pi_m_rho_m:
    case ReactionType::pi_p_rho_z_pi_p:
    case ReactionType::pi_m_rho_z_pi_m:
    case ReactionType::pi_p_pi_m_rho_z: {
      const double FF = form_factor_pion(E_photon);
      const double xs = total_cross_section();
      const double xs_ff = pow_int(FF, 4) * xs;
      return cut_off(xs_ff);
    }
 
    case ReactionType::pi_z_rho_z_pi_z: {
      const double FF = form_factor_omega(E_photon);
      const double xs = total_cross_section();
      const double xs_ff = pow_int(FF, 4) * xs;
      return cut_off(xs_ff);
    }
 
    case ReactionType::no_reaction:
    default:
      throw std::runtime_error("");
      return 0;
  }
}
 
double ScatterActionPhoton::diff_cross_section(const double t,
                                               const double m_rho,
                                               MediatorType mediator) const {
  const double s = mandelstam_s();
  double diff_xsection = 0.0;
 
  CrosssectionsPhoton<ComputationMethod::Analytic> xs_object;
 
  switch (reac_) {
    case ReactionType::pi_p_pi_m_rho_z:
      diff_xsection = xs_object.xs_diff_pi_pi_rho0(s, t, m_rho);
      break;
 
    case ReactionType::pi_z_pi_m_rho_m:
    case ReactionType::pi_z_pi_p_rho_p:
      diff_xsection = xs_object.xs_diff_pi_pi0_rho(s, t, m_rho);
      break;
 
    case ReactionType::pi_m_rho_z_pi_m:
    case ReactionType::pi_p_rho_z_pi_p:
      diff_xsection = xs_object.xs_diff_pi_rho0_pi(s, t, m_rho);
      break;
 
    case ReactionType::pi_m_rho_p_pi_z:
    case ReactionType::pi_p_rho_m_pi_z:
      if (mediator == MediatorType::SUM) {
        diff_xsection =
            xs_object.xs_diff_pi_rho_pi0_rho_mediated(s, t, m_rho) +
            xs_object.xs_diff_pi_rho_pi0_omega_mediated(s, t, m_rho);
      } else if (mediator == MediatorType::OMEGA) {
        diff_xsection =
            xs_object.xs_diff_pi_rho_pi0_omega_mediated(s, t, m_rho);
      } else if (mediator == MediatorType::PION) {
        diff_xsection = xs_object.xs_diff_pi_rho_pi0_rho_mediated(s, t, m_rho);
      }
      break;
 
    case ReactionType::pi_z_rho_m_pi_m:
    case ReactionType::pi_z_rho_p_pi_p:
      if (mediator == MediatorType::SUM) {
        diff_xsection =
            xs_object.xs_diff_pi0_rho_pi_rho_mediated(s, t, m_rho) +
            xs_object.xs_diff_pi0_rho_pi_omega_mediated(s, t, m_rho);
      } else if (mediator == MediatorType::OMEGA) {
        diff_xsection =
            xs_object.xs_diff_pi0_rho_pi_omega_mediated(s, t, m_rho);
      } else if (mediator == MediatorType::PION) {
        diff_xsection = xs_object.xs_diff_pi0_rho_pi_rho_mediated(s, t, m_rho);
      }
      break;
 
    case ReactionType::pi_z_rho_z_pi_z:
      diff_xsection = xs_object.xs_diff_pi0_rho0_pi0(s, t, m_rho);
      break;
    case ReactionType::no_reaction:
      // never reached
      break;
  }
 
  // Rarely, it can happen that the computed differential cross sections slip
  // slightly below zero for numerical reasons. This is unphysical. We
  // approximate them with dSigma/dt = 0.01 mb/GeV^2, which is a reasonable
  // value in the kinetic regime where this occurs.
  if (diff_xsection < 0) {
    diff_xsection = 0.01;
  }
  return diff_xsection;
}
 
double ScatterActionPhoton::diff_cross_section_w_ff(const double t,
                                                    const double m_rho,
                                                    const double E_photon) {
  /* C12, C13, C15, C16 need special treatment. These processes have identical
     incoming and outgoing particles, but diffrent mediating particles and
     hence different form factors. If both channels are added up
     (MediatorType::SUM), each contribution is corrected by the corresponding
     form factor.
  */
  switch (reac_) {
    case ReactionType::pi_m_rho_p_pi_z:
    case ReactionType::pi_p_rho_m_pi_z:
    case ReactionType::pi_z_rho_m_pi_m:
    case ReactionType::pi_z_rho_p_pi_p: {
      if (default_mediator_ == MediatorType::SUM) {
        std::pair<double, double> FF = form_factor_pair(E_photon);
        std::pair<double, double> diff_xs = diff_cross_section_pair(t, m_rho);
        const double xs_ff = pow_int(FF.first, 4) * diff_xs.first +
                             pow_int(FF.second, 4) * diff_xs.second;
        return cut_off(xs_ff);
      } else if (default_mediator_ == MediatorType::PION) {
        const double FF = form_factor_pion(E_photon);
        const double diff_xs = diff_cross_section(t, m_rho);
        return cut_off(pow_int(FF, 4) * diff_xs);
      } else if (default_mediator_ == MediatorType::OMEGA) {
        const double FF = form_factor_omega(E_photon);
        const double diff_xs = diff_cross_section(t, m_rho);
        return cut_off(pow_int(FF, 4) * diff_xs);
      }
      break;
    }
    case ReactionType::pi_z_pi_p_rho_p:
    case ReactionType::pi_z_pi_m_rho_m:
    case ReactionType::pi_p_rho_z_pi_p:
    case ReactionType::pi_m_rho_z_pi_m:
    case ReactionType::pi_p_pi_m_rho_z: {
      const double FF = form_factor_pion(E_photon);
      const double xs = diff_cross_section(t, m_rho);
      const double xs_ff = pow_int(FF, 4) * xs;
      return cut_off(xs_ff);
    }
 
    case ReactionType::pi_z_rho_z_pi_z: {
      const double FF = form_factor_omega(E_photon);
      const double xs = diff_cross_section(t, m_rho);
      const double xs_ff = pow_int(FF, 4) * xs;
      return cut_off(xs_ff);
    }
 
    case ReactionType::no_reaction:
    default:
      throw std::runtime_error("");
      return 0;
  }
}
 
double ScatterActionPhoton::form_factor_pion(const double E_photon) const {
  const double Lambda = 1.0;
  const double Lambda2 = Lambda * Lambda;
 
  const double t_ff = 34.5096 * std::pow(E_photon, 0.737) -
                      67.557 * std::pow(E_photon, 0.7584) +
                      32.858 * std::pow(E_photon, 0.7806);
  const double ff = 2 * Lambda2 / (2 * Lambda2 - t_ff);
 
  return ff * ff;
}
 
double ScatterActionPhoton::form_factor_omega(const double E_photon) const {
  const double Lambda = 1.0;
  const double Lambda2 = Lambda * Lambda;
 
  const double t_ff = -61.595 * std::pow(E_photon, 0.9979) +
                      28.592 * std::pow(E_photon, 1.1579) +
                      37.738 * std::pow(E_photon, 0.9317) -
                      5.282 * std::pow(E_photon, 1.3686);
  const double ff = 2 * Lambda2 / (2 * Lambda2 - t_ff);
 
  return ff * ff;
}
 
std::pair<double, double> ScatterActionPhoton::form_factor_pair(
    const double E_photon) {
  return std::pair<double, double>(form_factor_pion(E_photon),
                                   form_factor_omega(E_photon));
}
 
std::pair<double, double> ScatterActionPhoton::total_cross_section_pair() {
  const double xs_pion = total_cross_section(MediatorType::PION);
  const double xs_omega = total_cross_section(MediatorType::OMEGA);
 
  return std::pair<double, double>(xs_pion, xs_omega);
}
 
std::pair<double, double> ScatterActionPhoton::diff_cross_section_pair(
    const double t, const double m_rho) {
  const double diff_xs_pion = diff_cross_section(t, m_rho, MediatorType::PION);
  const double diff_xs_omega =
      diff_cross_section(t, m_rho, MediatorType::OMEGA);
 
  return std::pair<double, double>(diff_xs_pion, diff_xs_omega);
}
 
}  // namespace smash