Decay3Body.cc

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#include <cmath>
#include "SimG4Core/CustomPhysics/interface/Decay3Body.h"

#include <CLHEP/Units/SystemOfUnits.h>
#include <CLHEP/Units/GlobalPhysicalConstants.h>
#include "DataFormats/Math/interface/Vector3D.h"
#include "DataFormats/Math/interface/LorentzVector.h"
#include "Math/GenVector/Rotation3D.h"
#include "Math/GenVector/EulerAngles.h"
#include "Math/GenVector/Boost.h"
#include <vector>
#include <cmath>

#include "Randomize.hh"

using CLHEP::GeV;

Decay3Body::Decay3Body() {}

Decay3Body::~Decay3Body() {}

void Decay3Body::doDecay(const G4LorentzVector& mother,
                         G4LorentzVector& daughter1,
                         G4LorentzVector& daughter2,
                         G4LorentzVector& daughter3) {
  double m0 = mother.m();
  double m1 = daughter1.m();
  double m2 = daughter2.m();
  double m3 = daughter3.m();
  double sumM2 = m0 * m0 + m1 * m1 + m2 * m2 + m3 * m3;
  double tolerance = 1.0e-9;

  math::XYZTLorentzVectorD mmm(mother.px(), mother.py(), mother.pz(), mother.e());

  if (m0 < m1 + m2 + m3) {
    std::cout << "Error: Daughters too heavy!" << std::endl;
    std::cout << "M: " << m0 / GeV << " < m1+m2+m3: " << m1 / GeV + m2 / GeV + m3 / GeV << std::endl;
    return;
  } else {
    double m2_12max = sqr(m0 - m3);
    double m2_12min = sqr(m1 + m2);
    double m2_23max = sqr(m0 - m1);
    double m2_23min = sqr(m2 + m3);

    double x1, x2;
    double m2_12 = 0.0;
    double m2_23 = 0.0;
    double E2_12, E3_12;
    double m2_23max_12, m2_23min_12;

    do {
      // Pick values for m2_12 and m2_23 uniformly:
      x1 = G4UniformRand();
      m2_12 = m2_12min + x1 * (m2_12max - m2_12min);
      x2 = G4UniformRand();
      m2_23 = m2_23min + x2 * (m2_23max - m2_23min);

      // From the allowed range of m2_23 (given m2_12), determine if the point is valid:
      // (formulae taken from PDG booklet 2004 kinematics, page 305, Eqs. 38.22a+b)
      E2_12 = (m2_12 - m1 * m1 + m2 * m2) / (2.0 * sqrt(m2_12));
      E3_12 = (m0 * m0 - m2_12 - m3 * m3) / (2.0 * sqrt(m2_12));
      m2_23max_12 = sqr(E2_12 + E3_12) - sqr(sqrt(sqr(E2_12) - m2 * m2) - sqrt(sqr(E3_12) - m3 * m3));
      m2_23min_12 = sqr(E2_12 + E3_12) - sqr(sqrt(sqr(E2_12) - m2 * m2) + sqrt(sqr(E3_12) - m3 * m3));
    } while ((m2_23 > m2_23max_12) || (m2_23 < m2_23min_12));

    // Determine the value of the third invariant mass squared:
    double m2_13 = sumM2 - m2_12 - m2_23;

    // Calculate the energy and size of the momentum of the three daughters:
    double e1 = (m0 * m0 + m1 * m1 - m2_23) / (2.0 * m0);
    double e2 = (m0 * m0 + m2 * m2 - m2_13) / (2.0 * m0);
    double e3 = (m0 * m0 + m3 * m3 - m2_12) / (2.0 * m0);
    double p1 = sqrt(e1 * e1 - m1 * m1);
    double p2 = sqrt(e2 * e2 - m2 * m2);
    double p3 = sqrt(e3 * e3 - m3 * m3);

    // Calculate cosine of the relative angles between the three daughters:
    double cos12 = (m1 * m1 + m2 * m2 + 2.0 * e1 * e2 - m2_12) / (2.0 * p1 * p2);
    double cos13 = (m1 * m1 + m3 * m3 + 2.0 * e1 * e3 - m2_13) / (2.0 * p1 * p3);
    double cos23 = (m2 * m2 + m3 * m3 + 2.0 * e2 * e3 - m2_23) / (2.0 * p2 * p3);
    if (fabs(cos12) > 1.0)
      std::cout << "Error: Undefined angle12!" << std::endl;
    if (fabs(cos13) > 1.0)
      std::cout << "Error: Undefined angle13!" << std::endl;
    if (fabs(cos23) > 1.0)
      std::cout << "Error: Undefined angle23!" << std::endl;

    // Find the four vectors of the particles in a chosen (i.e. simple) frame:
    double xi = 2.0 * pi * G4UniformRand();
    math::XYZVectorD q1(0.0, 0.0, p1);
    math::XYZVectorD q2(sin(acos(cos12)) * cos(xi) * p2, sin(acos(cos12)) * sin(xi) * p2, cos12 * p2);
    math::XYZVectorD q3(-sin(acos(cos13)) * cos(xi) * p3, -sin(acos(cos13)) * sin(xi) * p3, cos13 * p3);

    // Rotate all three daughters momentum with the angles theta and phi:
    double theta = acos(2.0 * G4UniformRand() - 1.0);
    double phi = 2.0 * pi * G4UniformRand();
    double psi = 2.0 * pi * G4UniformRand();

    ROOT::Math::EulerAngles ang(phi, theta, psi);
    ROOT::Math::Rotation3D rot(ang);

    math::XYZVectorD q1rot = rot * q1;
    math::XYZVectorD q2rot = rot * q2;
    math::XYZVectorD q3rot = rot * q3;

    math::XYZTLorentzVectorD daughter1_orig(q1rot.X(), q1rot.Y(), q1rot.Z(), e1);
    math::XYZTLorentzVectorD daughter2_orig(q2rot.X(), q2rot.Y(), q2rot.Z(), e2);
    math::XYZTLorentzVectorD daughter3_orig(q3rot.X(), q3rot.Y(), q3rot.Z(), e3);

    ROOT::Math::Boost cmboost(mmm.BoostToCM());

    // Check of total angle and momentum:
    if (acos(cos12) + acos(cos13) + acos(cos23) - 2.0 * pi > tolerance)
      std::cout << "Error: Total angle not 2pi! " << acos(cos12) + acos(cos13) + acos(cos23) - 2.0 * pi << std::endl;
    if (fabs(daughter1_orig.px() + daughter2_orig.px() + daughter3_orig.px()) / GeV > tolerance)
      std::cout << "Error: Total 3B Px not conserved! "
                << (daughter1_orig.px() + daughter2_orig.px() + daughter3_orig.px()) / GeV << std::endl;
    if (fabs(daughter1_orig.py() + daughter2_orig.py() + daughter3_orig.py()) / GeV > tolerance)
      std::cout << "Error: Total 3B Py not conserved! "
                << (daughter1_orig.py() + daughter2_orig.py() + daughter3_orig.py()) / GeV << std::endl;
    if (fabs(daughter1_orig.pz() + daughter2_orig.pz() + daughter3_orig.pz()) / GeV > tolerance)
      std::cout << "Error: Total 3B Pz not conserved! " << (daughter1.pz() + daughter2.pz() + daughter3.pz()) / GeV
                << std::endl;

    // Boost the daughters back to the frame of the mother:

    math::XYZTLorentzVectorD temp1(cmboost(daughter1_orig));
    math::XYZTLorentzVectorD temp2(cmboost(daughter2_orig));
    math::XYZTLorentzVectorD temp3(cmboost(daughter3_orig));

    daughter1.setPx(temp1.Px());
    daughter1.setPy(temp1.Py());
    daughter1.setPz(temp1.Pz());
    daughter1.setE(temp1.e());

    daughter2.setPx(temp2.Px());
    daughter2.setPy(temp2.Py());
    daughter2.setPz(temp2.Pz());
    daughter2.setE(temp2.e());

    daughter3.setPx(temp3.Px());
    daughter3.setPy(temp3.Py());
    daughter3.setPz(temp3.Pz());
    daughter3.setE(temp3.e());

    return;
  }
}

double Decay3Body::sqr(double a) { return a * a; }