CMSCGEN.cc

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//
// CMSCGEN.cc   version 3.0    Thomas Hebbeker 2007-05-15
//
// implemented in CMSSW by P. Biallass 2007-05-28
// see header for documentation and CMS internal note 2007 "Improved Parametrization of the Cosmic Muon Flux for the generator CMSCGEN" by Biallass + Hebbeker
//

#include <CLHEP/Random/RandomEngine.h>
#include <CLHEP/Random/JamesRandom.h>

#include "GeneratorInterface/CosmicMuonGenerator/interface/CMSCGEN.h"

CMSCGEN::CMSCGEN() : initialization(0), RanGen2(nullptr), delRanGen(false) {}

CMSCGEN::~CMSCGEN() {
  if (delRanGen)
    delete RanGen2;
}

void CMSCGEN::setRandomEngine(CLHEP::HepRandomEngine *v) {
  if (delRanGen)
    delete RanGen2;
  RanGen2 = v;
  delRanGen = false;
}

int CMSCGEN::initialize(double pmin_in,
                        double pmax_in,
                        double thetamin_in,
                        double thetamax_in,
                        CLHEP::HepRandomEngine *rnd,
                        bool TIFOnly_constant,
                        bool TIFOnly_linear) {
  if (delRanGen)
    delete RanGen2;
  RanGen2 = rnd;
  delRanGen = false;

  //set bools for TIFOnly options (E<2GeV with unphysical energy dependence)
  TIFOnly_const = TIFOnly_constant;
  TIFOnly_lin = TIFOnly_linear;

  // units: GeV

  // WARNING: coordinate system:
  //   - to outside world define z axis downwards, i.e.
  //          muon coming from above, vertically: cos = 1
  //      (used for backward compatibility)
  //   - internally use frame with z axis upwards, i.e.
  //          muon coming from above, vertically: cos = -1
  //     (corresponds to CMS note definition)

  //set cmin and cmax, here convert between coordinate systems:
  cmin_in = -TMath::Cos(thetamin_in);  //input angle already converted from Deg to Rad!
  cmax_in = -TMath::Cos(thetamax_in);  //input angle already converted from Deg to Rad!

  //allowed energy range
  pmin_min = 3.;
  //pmin_max = 100.;
  pmin_max = 3000.;
  pmax = 3000.;
  //allowed angular range
  //cmax_max = -0.1,
  cmax_max = -0.01, cmax_min = -0.9999;

  if (TIFOnly_const == true || TIFOnly_lin == true)
    pmin_min = 0.;  //forTIF

  // set pmin
  if (pmin_in < pmin_min || pmin_in > pmin_max) {
    std::cout << " >>> CMSCGEN.initialize <<< warning: illegal pmin_in =" << pmin_in;
    return (-1);
  } else if (pmax_in > pmax) {
    std::cout << " >>> CMSCGEN.initialize <<< warning: illegal pmax_in =" << pmax_in;
    return (-1);
  } else {
    pmin = pmin_in;
    pmax = pmax_in;
    xemax = 1. / (pmin * pmin);
    xemin = 1. / (pmax * pmax);
  }

  // set cmax and cmin
  if (cmax_in < cmax_min || cmax_in > cmax_max) {
    std::cout << " >>> CMSCGEN.initialize <<< warning: illegal cmax_in =" << cmax_in;
    return (-1);
  } else {
    cmax = cmax_in;
    cmin = cmin_in;
  }

  initialization = 1;

  if (TIFOnly_const == true || TIFOnly_lin == true)
    pmin_min = 3.;  //forTIF

  //  Lmin = log10(pmin_min);
  Lmin = log10(pmin);
  Lmax = log10(pmax);
  Lfac = 100. / (Lmax - Lmin);

  //
  // +++ coefficients for energy spectrum
  //

  pe[0] = -1.;
  pe[1] = 6.22176;
  pe[2] = -13.9404;
  pe[3] = 18.1643;
  pe[4] = -9.22784;
  pe[5] = 1.99234;
  pe[6] = -0.156434;
  pe[7] = 0.;
  pe[8] = 0.;

  //
  // +++ coefficients for cos theta distribution
  //

  b0c[0] = 0.6639;
  b0c[1] = -0.9587;
  b0c[2] = 0.2772;

  b1c[0] = 5.820;
  b1c[1] = -6.864;
  b1c[2] = 1.367;

  b2c[0] = 10.39;
  b2c[1] = -8.593;
  b2c[2] = 1.547;

  //
  // +++ calculate correction table for different cos theta dependence!
  //     reference range: c1  to  c2
  //
  //  explanation: the parametrization of the energy spectrum as used above
  //    is the integral over the c = cos(zenith angle) range -1...-0.1
  //    since the c distribution depends on energy, the integrated energy
  //    spectrum depends on this range. Here a correction factor is determined,
  //    based on the linear c dependence of the c distribution.
  //    The correction is calculated for 100 bins in L = log10(energy).
  //
  // +++ in same loop calculate integrated flux
  //      (integrated over angles and momentum)

  c1 = -1.;
  c2 = -0.1;

  double cemax0 = 1.0;
  double L, L2;
  double s;
  double p, p1, p2;
  double integral_here, integral_ref;
  double c_cut;

  integrated_flux = 0.;

  for (int k = 1; k <= 100; k++) {
    L = Lmin + (k - 0.5) / Lfac;
    L2 = L * L;
    p = pow(10, L);
    p1 = pow(10, L - 0.5 / Lfac);
    p2 = pow(10, L + 0.5 / Lfac);

    b0 = b0c[0] + b0c[1] * L + b0c[2] * L2;
    b1 = b1c[0] + b1c[1] * L + b1c[2] * L2;
    b2 = b2c[0] + b2c[1] * L + b2c[2] * L2;

    // cut out explicitly regions of zero flux
    // (for low momentum and near horizontal showers)
    // since parametrization for z distribution doesn't work here
    // (can become negative)

    c_cut = -0.42 + L * 0.35;

    if (c_cut > c2)
      c_cut = c2;

    integral_ref =
        b0 * (c_cut - c1) + b1 / 2. * (c_cut * c_cut - c1 * c1) + b2 / 3. * (c_cut * c_cut * c_cut - c1 * c1 * c1);

    if (c_cut > cmax)
      c_cut = cmax;

    integral_here = b0 * (c_cut - cmin) + b1 / 2. * (c_cut * c_cut - cmin * cmin) +
                    b2 / 3. * (c_cut * c_cut * c_cut - cmin * cmin * cmin);

    corr[k] = integral_here / integral_ref;

    s = (((((((pe[8] * L + pe[7]) * L + pe[6]) * L + pe[5]) * L + pe[4]) * L + pe[3]) * L + pe[2]) * L + pe[1]) * L +
        pe[0];

    integrated_flux += 1. / pow(p, 3) * s * corr[k] * (p2 - p1);

    /*
    std::cout << k << " " 
    << corr[k] << " " 
    << p << " " 
    << s << " " 
    << p1 << " " 
    << p2 << " " 
    << integrated_flux << " " 
    << std::endl;
      */

    // std::cout << k << " " << corr[k] << " " << std::endl;
  }

  integrated_flux *= 1.27E3;
  std::cout << " >>> CMSCGEN.initialize <<< "
            << " Integrated flux = " << integrated_flux << " /m**2/s " << std::endl;

  //  find approximate peak value, for Monte Carlo sampling
  //      peak is near L = 2

  double ce;

  ce = (((((((pe[8] * 2. + pe[7]) * 2. + pe[6]) * 2. + pe[5]) * 2. + pe[4]) * 2. + pe[3]) * 2. + pe[2]) * 2. + pe[1]) *
           2. +
       pe[0];

  // normalize to 0.5 (not 1) to have some margin if peak is not at L=2
  //
  ce = 0.5 / ce;

  for (int k = 0; k < 9; k++) {
    pe[k] = pe[k] * ce;
  }

  cemax = cemax0 * corr[50];

  return initialization;
}

int CMSCGEN::initialize(double pmin_in,
                        double pmax_in,
                        double thetamin_in,
                        double thetamax_in,
                        int RanSeed,
                        bool TIFOnly_constant,
                        bool TIFOnly_linear) {
  CLHEP::HepRandomEngine *rnd = new CLHEP::HepJamesRandom;
  //set seed for Random Generator (seed can be controled by config-file), P.Biallass 2006
  rnd->setSeed(RanSeed, 0);
  delRanGen = true;
  return initialize(pmin_in, pmax_in, thetamin_in, thetamax_in, rnd, TIFOnly_constant, TIFOnly_linear);
}

int CMSCGEN::generate() {
  if (initialization == 0) {
    std::cout << " >>> CMSCGEN <<< warning: not initialized" << std::endl;
    return -1;
  }

  // note: use historical notation (fortran version l3cgen.f)

  //
  // +++ determine x = 1/e**2
  //
  //  explanation: the energy distribution
  //        dn/d(1/e**2) = dn/de * e**3 = dn/dlog10(e) * e**2
  //     is parametrized by a polynomial. accordingly xe = 1/e**2 is sampled
  //     and e calculated
  //
  //     need precise random variable with high precison since for
  //     emin = 3 GeV energies around 3000 GeV are very rare!
  //

  double r1, r2, r3;
  double xe, e, ce, L, L2;
  int k;
  double prob;

  double c_max;
  double z, z_max;

  while (true) {
    prob = RanGen2->flat();
    r1 = double(prob);
    prob = RanGen2->flat();
    r2 = double(prob);

    xe = xemin + r1 * (xemax - xemin);

    if ((1. / sqrt(xe) < 3) &&
        TIFOnly_const == true) {  //generate constant energy dependence for E<2GeV, only used for TIF
      //compute constant to match to CMSCGEN spectrum
      e = 3.;
      L = log10(e);
      L2 = L * L;

      ce = (((((((pe[8] * L + pe[7]) * L + pe[6]) * L + pe[5]) * L + pe[4]) * L + pe[3]) * L + pe[2]) * L + pe[1]) * L +
           pe[0];

      k = int((L - Lmin) * Lfac + 1.);
      k = TMath::Max(1, TMath::Min(k, 100));
      ce = ce * corr[k];

      e = 1. / sqrt(xe);
      if (r2 < (e * e * e * ce / (cemax * 3. * 3. * 3.)))
        break;

    } else if ((1. / sqrt(xe) < 3) &&
               TIFOnly_lin == true) {  //generate linear energy dependence for E<2GeV, only used for TIF
      //compute constant to match to CMSCGEN spectrum
      e = 3.;
      L = log10(e);
      L2 = L * L;

      ce = (((((((pe[8] * L + pe[7]) * L + pe[6]) * L + pe[5]) * L + pe[4]) * L + pe[3]) * L + pe[2]) * L + pe[1]) * L +
           pe[0];

      k = int((L - Lmin) * Lfac + 1.);
      k = TMath::Max(1, TMath::Min(k, 100));
      ce = ce * corr[k];

      e = 1. / sqrt(xe);
      if (r2 < (e * e * e * e * ce / (cemax * 3. * 3. * 3. * 3.)))
        break;

    } else {  //this is real CMSCGEN energy-dependence

      e = 1. / sqrt(xe);
      L = log10(e);
      L2 = L * L;

      ce = (((((((pe[8] * L + pe[7]) * L + pe[6]) * L + pe[5]) * L + pe[4]) * L + pe[3]) * L + pe[2]) * L + pe[1]) * L +
           pe[0];

      k = int((L - Lmin) * Lfac + 1.);
      k = TMath::Max(1, TMath::Min(k, 100));
      ce = ce * corr[k];

      if (cemax * r2 < ce)
        break;

    }  //end of CMSCGEN energy-dependence
  }    //end of while

  pq = e;

  //
  // +++ charge ratio 1.280
  //
  prob = RanGen2->flat();
  r3 = double(prob);

  double charg = 1.;
  if (r3 < 0.439)
    charg = -1.;

  pq = pq * charg;

  //
  //  +++ determine cos(angle)
  //
  //  simple trial and rejection method
  //

  // first calculate energy dependent coefficients b_i

  if (TIFOnly_const == true && e < 3.) {  //forTIF (when E<2GeV use angles of 2GeV cosmic)
    L = log10(3.);
    L2 = L * L;
  }
  if (TIFOnly_lin == true && e < 3.) {  //forTIF (when E<2GeV use angles of 2GeV cosmic)
    L = log10(3.);
    L2 = L * L;
  }

  b0 = b0c[0] + b0c[1] * L + b0c[2] * L2;
  b1 = b1c[0] + b1c[1] * L + b1c[2] * L2;
  b2 = b2c[0] + b2c[1] * L + b2c[2] * L2;

  //
  // need to know the maximum of z(c)
  //
  // first calculate c for which c distribution z(c) = maximum
  //
  // (note: maximum of curve is NOT always at c = -1, but never at c = -0.1)
  //

  // try extremal value (from z'(c) = 0), but only if z''(c) < 0
  //
  // z'(c) = b1 + b2 * c   =>  at c_max = - b1 / (2 b_2) is z'(c) = 0
  //
  // z''(c) = b2

  c_max = -1.;

  if (b2 < 0.) {
    c_max = -0.5 * b1 / b2;
    if (c_max < -1.)
      c_max = -1.;
    if (c_max > -0.1)
      c_max = -0.1;
  }

  z_max = b0 + b1 * c_max + b2 * c_max * c_max;

  // again cut out explicitly regions of zero flux
  double c_cut = -0.42 + L * 0.35;
  if (c_cut > cmax)
    c_cut = cmax;

  // now we throw dice:

  while (true) {
    prob = RanGen2->flat();
    r1 = double(prob);
    prob = RanGen2->flat();
    r2 = double(prob);
    c = cmin + (c_cut - cmin) * r1;
    z = b0 + b1 * c + b2 * c * c;
    if (z > z_max * r2)
      break;
  }

  return 0;
}

double CMSCGEN::momentum_times_charge() {
  if (initialization == 1) {
    return pq;
  } else {
    std::cout << " >>> CMSCGEN <<< warning: not initialized" << std::endl;
    return -9999.;
  }
}

double CMSCGEN::cos_theta() {
  if (initialization == 1) {
    // here convert between coordinate systems:
    return -c;
  } else {
    std::cout << " >>> CMSCGEN <<< warning: not initialized" << std::endl;
    return -0.9999;
  }
}

double CMSCGEN::flux() {
  if (initialization == 1) {
    return integrated_flux;
  } else {
    std::cout << " >>> CMSCGEN <<< warning: not initialized" << std::endl;
    return -0.9999;
  }
}

int CMSCGEN::initializeNuMu(double pmin_in,
                            double pmax_in,
                            double thetamin_in,
                            double thetamax_in,
                            double Enumin_in,
                            double Enumax_in,
                            double Phimin_in,
                            double Phimax_in,
                            double ProdAlt_in,
                            CLHEP::HepRandomEngine *rnd) {
  if (delRanGen)
    delete RanGen2;
  RanGen2 = rnd;
  delRanGen = false;

  ProdAlt = ProdAlt_in;

  Rnunubar = 1.2;

  sigma = (0.72 * Rnunubar + 0.09) / (1 + Rnunubar) * 1.e-38;  //cm^2GeV^-1

  AR = (0.69 + 0.06 * Rnunubar) / (0.09 + 0.72 * Rnunubar);

  //set smin and smax, here convert between coordinate systems:
  pmin = pmin_in;
  pmax = pmax_in;
  cmin = TMath::Cos(thetamin_in);                //input angle already converted from Deg to Rad!
  cmax = TMath::Cos(thetamax_in);                //input angle already converted from Deg to Rad!
  enumin = (Enumin_in < 10.) ? 10. : Enumin_in;  //no nu's below 10GeV
  enumax = Enumax_in;

  //do initial run of flux rate to determine Maximum
  integrated_flux = 0.;
  dNdEmudEnuMax = 0.;
  negabs = 0.;
  negfrac = 0.;
  int trials = 100000;
  for (int i = 0; i < trials; ++i) {
    double ctheta = cmin + (cmax - cmin) * RanGen2->flat();
    double Emu = pmin + (pmax - pmin) * RanGen2->flat();
    double Enu = enumin + (enumax - enumin) * RanGen2->flat();
    double rate = dNdEmudEnu(Enu, Emu, ctheta);
    //std::cout << "trial=" << i << " ctheta=" << ctheta << " Emu=" << Emu << " Enu=" << Enu
    //      << " rate=" << rate << std::endl;
    //std::cout << "cmin=" << cmin << " cmax=" << cmax
    //      << " pmin=" << pmin << " pmax=" << pmax
    //      << " enumin=" << enumin << " enumax=" << enumax << std::endl;
    if (rate > 0.) {
      integrated_flux += rate;
      if (rate > dNdEmudEnuMax)
        dNdEmudEnuMax = rate;
    } else
      negabs++;
  }
  negfrac = negabs / trials;
  integrated_flux /= trials;

  std::cout << "CMSCGEN::initializeNuMu: After " << trials << " trials:" << std::endl;
  std::cout << "dNdEmudEnuMax=" << dNdEmudEnuMax << std::endl;
  std::cout << "negfrac=" << negfrac << std::endl;

  //multiply by phase space boundaries
  integrated_flux *= (cmin - cmax);
  integrated_flux *= (Phimax_in - Phimin_in);
  integrated_flux *= (pmax - pmin);
  integrated_flux *= (enumax - enumin);
  //remove negative phase space areas which do not contribute anything
  integrated_flux *= (1. - negfrac);
  std::cout << " >>> CMSCGEN.initializeNuMu <<< "
            << " Integrated flux = " << integrated_flux << " units??? " << std::endl;

  initialization = 1;

  return initialization;
}

int CMSCGEN::initializeNuMu(double pmin_in,
                            double pmax_in,
                            double thetamin_in,
                            double thetamax_in,
                            double Enumin_in,
                            double Enumax_in,
                            double Phimin_in,
                            double Phimax_in,
                            double ProdAlt_in,
                            int RanSeed) {
  CLHEP::HepRandomEngine *rnd = new CLHEP::HepJamesRandom;
  //set seed for Random Generator (seed can be controled by config-file), P.Biallass 2006
  rnd->setSeed(RanSeed, 0);
  delRanGen = true;
  return initializeNuMu(
      pmin_in, pmax_in, thetamin_in, thetamax_in, Enumin_in, Enumax_in, Phimin_in, Phimax_in, ProdAlt_in, rnd);
}

double CMSCGEN::dNdEmudEnu(double Enu, double Emu, double ctheta) {
  double cthetaNu = 1. + ctheta;  //swap cos(theta) from down to up range
  double thetas = asin(sin(acos(cthetaNu)) * (Rearth - SurfaceOfEarth) / (Rearth + ProdAlt));
  double costhetas = cos(thetas);
  double dNdEnudW =
      0.0286 * pow(Enu, -2.7) *
      (1. / (1. + (6. * Enu * costhetas) / 115.) + 0.213 / (1. + (1.44 * Enu * costhetas) / 850.));  //cm^2*s*sr*GeV
  double dNdEmudEnu = N_A * sigma / alpha * dNdEnudW * 1. / (1. + Emu / epsilon) *
                      (Enu - Emu + AR / 3 * (Enu * Enu * Enu - Emu * Emu * Emu) / (Enu * Enu));
  return dNdEmudEnu;
}

int CMSCGEN::generateNuMu() {
  if (initialization == 0) {
    std::cout << " >>> CMSCGEN <<< warning: not initialized" << std::endl;
    return -1;
  }

  double ctheta, Emu;
  while (true) {
    ctheta = cmin + (cmax - cmin) * RanGen2->flat();
    Emu = pmin + (pmax - pmin) * RanGen2->flat();
    double Enu = enumin + (enumax - enumin) * RanGen2->flat();
    double rate = dNdEmudEnu(Enu, Emu, ctheta);
    if (rate > dNdEmudEnuMax * RanGen2->flat())
      break;
  }

  c = -ctheta;  //historical sign convention

  pq = Emu;
  //
  // +++ nu/nubar ratio (~1.2)
  //
  double charg = 1.;  //nubar -> mu+
  if (RanGen2->flat() > Rnunubar / (1. + Rnunubar))
    charg = -1.;  //neutrino -> mu-

  pq = pq * charg;

  //int flux += this event rate

  return 1;
}