Rivet analyses

title: A2_2017_I1486671

Form factors for the decays $\omega\to\pi^0e^+e^-$ and $\eta\to\gamma e^+e^-$

Experiment: A2 (MAMI)

Inspire ID: 1486671

Status: VALIDATED NOHEPDATA

Authors: - Peter Richardson

References: - Phys.Rev. C95 (2017) no.3, 035208

Beams: * *

Beam energies: ANY

Run details: - omega and eta production with both the dalitz decay and radiative decay for normalization

Measurement of the form factors $\left|F_{\omega\pi^0}(q^2)\right|$ for the decay $\omega\to\pi^0e^+e^-$ and $\left|F_{\eta}(q^2)\right|$ for the decay $\eta\to\gamma e^+e^-$ by the A2 experiment at MAMI.

Source code:A2_2017_I1486671.cc

```c++ // -- C++ --

include "Rivet/Analysis.hh"

include "Rivet/Projections/UnstableParticles.hh"

namespace Rivet {

/// @brief form factors for omega->pi and eta->gamma class A2_2017_I1486671 : public Analysis { public:

/// Constructor
RIVET_DEFAULT_ANALYSIS_CTOR(A2_2017_I1486671);


/// @name Analysis methods
/// @{

/// Book histograms and initialise projections before the run
void init() {
  // Initialise and register projections
  declare(UnstableParticles(), "UFS");
  // Book histograms
  book(_h_eta, 1, 1, 1);
  book(_h_omega, 2, 1, 1);
  book(_weight_eta, "TMP/weight_eta");
  book(_weight_omega, "TMP/weight_omega");
}

void findDecayProducts(const Particle& mother,
                       unsigned int& nstable,
                       unsigned int& npi,
                       unsigned int& nep,
                       unsigned int& nem,
                       unsigned int& ngamma,
                       FourMomentum& ptot) {
  for (const Particle& p : mother.children()) {
    int id = p.pid();
    if (id == PID::EMINUS) {
      ++nem;
      ++nstable;
      ptot += p.momentum();
    }
    else if (id == PID::EPLUS) {
      ++nep;
      ++nstable;
      ptot += p.momentum();
    }
    else if (id == PID::PI0) {
      ++npi;
      ++nstable;
    }
    else if (id == PID::GAMMA && p.children().empty()) {
      ++ngamma;
      ++nstable;
    }
    else if (!p.children().empty()) {
      findDecayProducts(p, nstable, npi, nep, nem, ngamma, ptot);
    }
    else
      ++nstable;
  }
}

/// Perform the per-event analysis
void analyze(const Event& event) {
  static double me = 0.5109989461 * MeV;
  static double momega = 782.65 * MeV;
  static double meta = 547.862 * MeV;
  static double mpi = 134.9770 * MeV;

  // Loop over eta and omega mesons
  for (const Particle& p :
       apply<UnstableParticles>(event, "UFS").particles(Cuts::pid == 223 or Cuts::pid == 221)) {
    unsigned nstable(0), npi(0), nep(0), nem(0), ngamma(0);
    FourMomentum ptot;
    findDecayProducts(p, nstable, npi, nep, nem, ngamma, ptot);
    if (p.pid() == 221) {
      if (nstable == 3 && nem == 1 && nem == 1 && ngamma == 1) {
        double q = ptot.mass();
        double beta = sqrt(1. - 4 * sqr(me / q));
        double p = 1. - sqr(q / meta);
        double fact = beta * MeV / q * (1. + 2. * sqr(me / q)) * pow(p, 3);
        _h_eta->fill(q / MeV, 1. / fact);
      }
      else if (nstable == 2 && ngamma == 2) {
        _weight_eta->fill();
      }
    }
    else {
      if (nstable == 3 && nem == 1 && nem == 1 && npi == 1) {
        double q = ptot.mass();
        double beta = sqrt(1. - 4 * sqr(me / q));
        double p = sqrt(sqr(1. + sqr(q) / (sqr(momega) - sqr(mpi)))
                        - 4. * sqr(momega * q / (sqr(momega) - sqr(mpi))));
        double fact = beta * MeV / q * (1. + 2. * sqr(me / q)) * pow(p, 3);
        _h_omega->fill(q / MeV, 1. / fact);
      }
      else if (nstable == 2 && ngamma == 1 && npi == 1) {
        _weight_omega->fill();
      }
    }
  }
}


/// Normalise histograms etc., after the run
void finalize() {
  static double alpha = 7.2973525664e-3;
  scale(_h_eta, 0.75 * M_PI / alpha / *_weight_eta);
  scale(_h_omega, 1.5 * M_PI / alpha / *_weight_omega);
}

/// @}


/// @name Histograms
/// @{
Histo1DPtr _h_eta, _h_omega;
CounterPtr _weight_eta, _weight_omega;
/// @}

};

RIVET_DECLARE_PLUGIN(A2_2017_I1486671);

} ```