G4MuonDecayChannelWithSpin.cc

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//
// G4MuonDecayChannelWithSpin class implementation
//
// References:
// - Florian Scheck "Muon Physics", in Physics Reports
//   (Review Section of Physics Letters) 44, No. 4 (1978)
//   187-248. North-Holland Publishing Company, Amsterdam at page 210 cc.
// - W.E. Fisher and F. Scheck, Nucl. Phys. B83 (1974) 25.
 
// Authors: P.Gumplinger and T.MacPhail, 17 August 2004
// --------------------------------------------------------------------
 
#include "G4MuonDecayChannelWithSpin.hh"
 
#include "G4DecayProducts.hh"
#include "G4LorentzVector.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "Randomize.hh"
 
G4MuonDecayChannelWithSpin::G4MuonDecayChannelWithSpin(const G4String& theParentName,
                                                       G4double theBR)
  : G4MuonDecayChannel(theParentName, theBR)
{}
 
G4MuonDecayChannelWithSpin&
G4MuonDecayChannelWithSpin::operator=(const G4MuonDecayChannelWithSpin& right)
{
  if (this != &right) {
    kinematics_name = right.kinematics_name;
    verboseLevel = right.verboseLevel;
    rbranch = right.rbranch;
 
    // copy parent name
    delete parent_name;
    parent_name = new G4String(*right.parent_name);
 
    // clear daughters_name array
    ClearDaughtersName();
 
    // recreate array
    numberOfDaughters = right.numberOfDaughters;
    if (numberOfDaughters > 0) {
      daughters_name = new G4String*[numberOfDaughters];
      // copy daughters name
      for (G4int index = 0; index < numberOfDaughters; ++index) {
        daughters_name[index] = new G4String(*right.daughters_name[index]);
      }
    }
  }
  return *this;
}
 
G4DecayProducts* G4MuonDecayChannelWithSpin::DecayIt(G4double)
{
  // This version assumes V-A coupling with 1st order radiative correctons,
  //              the standard model Michel parameter values, but
  //              gives incorrect energy spectrum for neutrinos
 
#ifdef G4VERBOSE
  if (GetVerboseLevel() > 1) G4cout << "G4MuonDecayChannelWithSpin::DecayIt ";
#endif
 
  CheckAndFillParent();
  CheckAndFillDaughters();
 
  // parent mass
  G4double parentmass = G4MT_parent->GetPDGMass();
 
  G4double EMMU = parentmass;
 
  // daughters'mass
  G4double daughtermass[3];
  // G4double sumofdaughtermass = 0.0;
  for (G4int index = 0; index < 3; ++index) {
    daughtermass[index] = G4MT_daughters[index]->GetPDGMass();
    // sumofdaughtermass += daughtermass[index];
  }
 
  G4double EMASS = daughtermass[0];
 
  // create parent G4DynamicParticle at rest
  G4ThreeVector dummy;
  auto parentparticle = new G4DynamicParticle(G4MT_parent, dummy, 0.0);
  // create G4Decayproducts
  auto products = new G4DecayProducts(*parentparticle);
  delete parentparticle;
 
  // calculate electron energy
 
  G4double michel_rho = 0.75;  // Standard Model Michel rho
  G4double michel_delta = 0.75;  // Standard Model Michel delta
  G4double michel_xsi = 1.00;  // Standard Model Michel xsi
  G4double michel_eta = 0.00;  // Standard Model eta
 
  G4double rndm, x, ctheta;
 
  G4double FG;
  G4double FG_max = 2.00;
 
  G4double W_mue = (EMMU * EMMU + EMASS * EMASS) / (2. * EMMU);
  G4double x0 = EMASS / W_mue;
 
  G4double x0_squared = x0 * x0;
 
  // ***************************************************
  //     x0 <= x <= 1.   and   -1 <= y <= 1
  //
  //     F(x,y) = f(x)*g(x,y);   g(x,y) = 1.+g(x)*y
  // ***************************************************
 
  // ***** sampling F(x,y) directly (brute force) *****
 
  const std::size_t MAX_LOOP = 10000;
  for (std::size_t loop_count = 0; loop_count < MAX_LOOP; ++loop_count) {
    // Sample the positron energy by sampling from F
 
    rndm = G4UniformRand();
 
    x = x0 + rndm * (1. - x0);
 
    G4double x_squared = x * x;
 
    G4double F_IS, F_AS, G_IS, G_AS;
 
    F_IS = 1. / 6. * (-2. * x_squared + 3. * x - x0_squared);
    F_AS = 1. / 6. * std::sqrt(x_squared - x0_squared) * (2. * x - 2. + std::sqrt(1. - x0_squared));
 
    G_IS = 2. / 9. * (michel_rho - 0.75) * (4. * x_squared - 3. * x - x0_squared);
    G_IS = G_IS + michel_eta * (1. - x) * x0;
 
    G_AS = 3. * (michel_xsi - 1.) * (1. - x);
    G_AS =
      G_AS + 2. * (michel_xsi * michel_delta - 0.75) * (4. * x - 4. + std::sqrt(1. - x0_squared));
    G_AS = 1. / 9. * std::sqrt(x_squared - x0_squared) * G_AS;
 
    F_IS = F_IS + G_IS;
    F_AS = F_AS + G_AS;
 
    // *** Radiative Corrections ***
 
    const G4double omega = std::log(EMMU / EMASS);
    G4double R_IS = F_c(x, x0, omega);
 
    G4double F = 6. * F_IS + R_IS / std::sqrt(x_squared - x0_squared);
 
    // *** Radiative Corrections ***
 
    G4double R_AS = F_theta(x, x0, omega);
 
    rndm = G4UniformRand();
 
    ctheta = 2. * rndm - 1.;
 
    G4double G = 6. * F_AS - R_AS / std::sqrt(x_squared - x0_squared);
 
    FG = std::sqrt(x_squared - x0_squared) * F * (1. + (G / F) * ctheta);
 
    if (FG > FG_max) {
      G4Exception("G4MuonDecayChannelWithSpin::DecayIt()", "PART113", JustWarning,
                  "Problem in Muon Decay: FG > FG_max");
      FG_max = FG;
    }
 
    rndm = G4UniformRand();
 
    if (FG >= rndm * FG_max) break;
  }
 
  G4double energy = x * W_mue;
 
  rndm = G4UniformRand();
 
  G4double phi = twopi * rndm;
 
  if (energy < EMASS) energy = EMASS;
 
  // Calculate daughter momentum
  G4double daughtermomentum[3];
 
  daughtermomentum[0] = std::sqrt(energy * energy - EMASS * EMASS);
 
  G4double stheta = std::sqrt(1. - ctheta * ctheta);
  G4double cphi = std::cos(phi);
  G4double sphi = std::sin(phi);
 
  // Coordinates of the decay positron with respect to the muon spin
  G4double px = stheta * cphi;
  G4double py = stheta * sphi;
  G4double pz = ctheta;
 
  G4ThreeVector direction0(px, py, pz);
 
  direction0.rotateUz(parent_polarization);
 
  auto daughterparticle0 =
    new G4DynamicParticle(G4MT_daughters[0], daughtermomentum[0] * direction0);
 
  products->PushProducts(daughterparticle0);
 
  // daughter 1 ,2 (neutrinos)
  // create neutrinos in the C.M frame of two neutrinos
  G4double energy2 = parentmass - energy;
  G4double vmass = std::sqrt((energy2 - daughtermomentum[0]) * (energy2 + daughtermomentum[0]));
  G4double beta = -1.0 * daughtermomentum[0] / energy2;
  G4double costhetan = 2. * G4UniformRand() - 1.0;
  G4double sinthetan = std::sqrt((1.0 - costhetan) * (1.0 + costhetan));
  G4double phin = twopi * G4UniformRand() * rad;
  G4double sinphin = std::sin(phin);
  G4double cosphin = std::cos(phin);
 
  G4ThreeVector direction1(sinthetan * cosphin, sinthetan * sinphin, costhetan);
  auto daughterparticle1 = new G4DynamicParticle(G4MT_daughters[1], direction1 * (vmass / 2.));
  auto daughterparticle2 =
    new G4DynamicParticle(G4MT_daughters[2], direction1 * (-1.0 * vmass / 2.));
 
  // boost to the muon rest frame
  G4LorentzVector p4;
  p4 = daughterparticle1->Get4Momentum();
  p4.boost(direction0.x() * beta, direction0.y() * beta, direction0.z() * beta);
  daughterparticle1->Set4Momentum(p4);
  p4 = daughterparticle2->Get4Momentum();
  p4.boost(direction0.x() * beta, direction0.y() * beta, direction0.z() * beta);
  daughterparticle2->Set4Momentum(p4);
  products->PushProducts(daughterparticle1);
  products->PushProducts(daughterparticle2);
  daughtermomentum[1] = daughterparticle1->GetTotalMomentum();
  daughtermomentum[2] = daughterparticle2->GetTotalMomentum();
 
  // output message
#ifdef G4VERBOSE
  if (GetVerboseLevel() > 1) {
    G4cout << "G4MuonDecayChannelWithSpin::DecayIt ";
    G4cout << "  create decay products in rest frame " << G4endl;
    G4double TT = daughterparticle0->GetTotalEnergy() + daughterparticle1->GetTotalEnergy()
                  + daughterparticle2->GetTotalEnergy();
    G4cout << "e  " << daughterparticle0->GetTotalEnergy() / MeV << G4endl;
    G4cout << "nu1" << daughterparticle1->GetTotalEnergy() / MeV << G4endl;
    G4cout << "nu2" << daughterparticle2->GetTotalEnergy() / MeV << G4endl;
    G4cout << "total" << (TT - parentmass) / keV << G4endl;
    if (GetVerboseLevel() > 2) {
      products->DumpInfo();
    }
  }
#endif
 
  return products;
}
 
G4double G4MuonDecayChannelWithSpin::R_c(G4double x, G4double omega)
{
  auto n_max = (G4int)(100. * x);
 
  if (n_max < 10) n_max = 10;
 
  G4double L2 = 0.0;
 
  for (G4int n = 1; n <= n_max; ++n) {
    L2 += std::pow(x, n) / (n * n);
  }
 
  G4double r_c;
 
  r_c = 2. * L2 - (pi * pi / 3.) - 2.;
  r_c = r_c + omega * (1.5 + 2. * std::log((1. - x) / x));
  r_c = r_c - std::log(x) * (2. * std::log(x) - 1.);
  r_c = r_c + (3. * std::log(x) - 1. - 1. / x) * std::log(1. - x);
 
  return r_c;
}