TGenPhaseSpace.cxx

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// @(#)root/physics:$Id$
// Author: Rene Brun , Valerio Filippini  06/09/2000

//_____________________________________________________________________________________
//
//  Utility class to generate n-body event,
//  with constant cross-section (default)
//  or with Fermi energy dependence (opt="Fermi").
//  The event is generated in the center-of-mass frame,
//  but the decay products are finally boosted
//  using the betas of the original particle.
//
//  The code is based on the GENBOD function (W515 from CERNLIB)
//  using the Raubold and Lynch method
//      F. James, Monte Carlo Phase Space, CERN 68-15 (1968)
//
// see example of use in $ROOTSYS/tutorials/physics/PhaseSpace.C
//
// Note that Momentum, Energy units are Gev/C, GeV

#include "TGenPhaseSpace.h"
#include "TRandom.h"
#include "TMath.h"
#include <stdlib.h>

const Int_t kMAXP = 18;

ClassImp(TGenPhaseSpace)

////////////////////////////////////////////////////////////////////////////////
///the PDK function

Double_t TGenPhaseSpace::PDK(Double_t a, Double_t b, Double_t c)
{
   Double_t x = (a-b-c)*(a+b+c)*(a-b+c)*(a+b-c);
   x = TMath::Sqrt(x)/(2*a);
   return x;
}

////////////////////////////////////////////////////////////////////////////////
///special max function

Int_t DoubleMax(const void *a, const void *b)
{
   Double_t aa = * ((Double_t *) a);
   Double_t bb = * ((Double_t *) b);
   if (aa > bb) return  1;
   if (aa < bb) return -1;
   return 0;

}

////////////////////////////////////////////////////////////////////////////////
///copy constructor

TGenPhaseSpace::TGenPhaseSpace(const TGenPhaseSpace &gen) : TObject(gen)
{
   fNt      = gen.fNt;
   fWtMax   = gen.fWtMax;
   fTeCmTm  = gen.fTeCmTm;
   fBeta[0] = gen.fBeta[0];
   fBeta[1] = gen.fBeta[1];
   fBeta[2] = gen.fBeta[2];
   for (Int_t i=0;i<fNt;i++) {
      fMass[i]   = gen.fMass[i];
      fDecPro[i] = gen.fDecPro[i];
   }
}


////////////////////////////////////////////////////////////////////////////////
/// Assignment operator

TGenPhaseSpace& TGenPhaseSpace::operator=(const TGenPhaseSpace &gen)
{
   TObject::operator=(gen);
   fNt      = gen.fNt;
   fWtMax   = gen.fWtMax;
   fTeCmTm  = gen.fTeCmTm;
   fBeta[0] = gen.fBeta[0];
   fBeta[1] = gen.fBeta[1];
   fBeta[2] = gen.fBeta[2];
   for (Int_t i=0;i<fNt;i++) {
      fMass[i]   = gen.fMass[i];
      fDecPro[i] = gen.fDecPro[i];
   }
   return *this;
}

////////////////////////////////////////////////////////////////////////////////
///  Generate a random final state.
///  The function returns the weigth of the current event.
///  The TLorentzVector of each decay product can be obtained using GetDecay(n).
///
/// Note that Momentum, Energy units are Gev/C, GeV

Double_t TGenPhaseSpace::Generate()
{
   Double_t rno[kMAXP];
   rno[0] = 0;
   Int_t n;
   if (fNt>2) {
      for (n=1; n<fNt-1; n++)  rno[n]=gRandom->Rndm();   // fNt-2 random numbers
      qsort(rno+1 ,fNt-2 ,sizeof(Double_t) ,DoubleMax);  // sort them
   }
   rno[fNt-1] = 1;

   Double_t invMas[kMAXP], sum=0;
   for (n=0; n<fNt; n++) {
      sum      += fMass[n];
      invMas[n] = rno[n]*fTeCmTm + sum;
   }

   //
   //-----> compute the weight of the current event
   //
   Double_t wt=fWtMax;
   Double_t pd[kMAXP];
   for (n=0; n<fNt-1; n++) {
      pd[n] = PDK(invMas[n+1],invMas[n],fMass[n+1]);
      wt *= pd[n];
   }

   //
   //-----> complete specification of event (Raubold-Lynch method)
   //
   fDecPro[0].SetPxPyPzE(0, pd[0], 0 , TMath::Sqrt(pd[0]*pd[0]+fMass[0]*fMass[0]) );

   Int_t i=1;
   Int_t j;
   while (1) {
      fDecPro[i].SetPxPyPzE(0, -pd[i-1], 0 , TMath::Sqrt(pd[i-1]*pd[i-1]+fMass[i]*fMass[i]) );

      Double_t cZ   = 2*gRandom->Rndm() - 1;
      Double_t sZ   = TMath::Sqrt(1-cZ*cZ);
      Double_t angY = 2*TMath::Pi() * gRandom->Rndm();
      Double_t cY   = TMath::Cos(angY);
      Double_t sY   = TMath::Sin(angY);
      for (j=0; j<=i; j++) {
         TLorentzVector *v = fDecPro+j;
         Double_t x = v->Px();
         Double_t y = v->Py();
         v->SetPx( cZ*x - sZ*y );
         v->SetPy( sZ*x + cZ*y );   // rotation around Z
         x = v->Px();
         Double_t z = v->Pz();
         v->SetPx( cY*x - sY*z );
         v->SetPz( sY*x + cY*z );   // rotation around Y
      }

      if (i == (fNt-1)) break;

      Double_t beta = pd[i] / sqrt(pd[i]*pd[i] + invMas[i]*invMas[i]);
      for (j=0; j<=i; j++) fDecPro[j].Boost(0,beta,0);
      i++;
   }

   //
   //---> final boost of all particles
   //
   for (n=0;n<fNt;n++) fDecPro[n].Boost(fBeta[0],fBeta[1],fBeta[2]);

   //
   //---> return the weigth of event
   //
   return wt;
}

////////////////////////////////////////////////////////////////////////////////
///return Lorentz vector corresponding to decay n

TLorentzVector *TGenPhaseSpace::GetDecay(Int_t n)
{
   if (n>fNt) return 0;
   return fDecPro+n;
}


////////////////////////////////////////////////////////////////////////////////
/// input:
/// TLorentzVector &P:    decay particle (Momentum, Energy units are Gev/C, GeV)
/// Int_t nt:             number of decay products
/// Double_t *mass:       array of decay product masses
/// Option_t *opt:        default -> constant cross section
///                       "Fermi" -> Fermi energy dependece
/// return value:
/// kTRUE:      the decay is permitted by kinematics
/// kFALSE:     the decay is forbidden by kinematics
///

Bool_t TGenPhaseSpace::SetDecay(TLorentzVector &P, Int_t nt,
   const Double_t *mass, Option_t *opt)
{
   Int_t n;
   fNt = nt;
   if (fNt<2 || fNt>18) return kFALSE;  // no more then 18 particle

   //
   //
   //
   fTeCmTm = P.Mag();           // total energy in C.M. minus the sum of the masses
   for (n=0;n<fNt;n++) {
      fMass[n]  = mass[n];
      fTeCmTm  -= mass[n];
   }

   if (fTeCmTm<=0) return kFALSE;    // not enough energy for this decay

   //
   //------> the max weigth depends on opt:
   //   opt == "Fermi"  --> fermi energy dependence for cross section
   //   else            --> constant cross section as function of TECM (default)
   //
   if (strcasecmp(opt,"fermi")==0) {
      // ffq[] = pi * (2*pi)**(FNt-2) / (FNt-2)!
      Double_t ffq[] = {0
                     ,3.141592, 19.73921, 62.01255, 129.8788, 204.0131
                     ,256.3704, 268.4705, 240.9780, 189.2637
                     ,132.1308,  83.0202,  47.4210,  24.8295
                     ,12.0006,   5.3858,   2.2560,   0.8859 };
      fWtMax = TMath::Power(fTeCmTm,fNt-2) * ffq[fNt-1] / P.Mag();

   } else {
      Double_t emmax = fTeCmTm + fMass[0];
      Double_t emmin = 0;
      Double_t wtmax = 1;
      for (n=1; n<fNt; n++) {
         emmin += fMass[n-1];
         emmax += fMass[n];
         wtmax *= PDK(emmax, emmin, fMass[n]);
      }
      fWtMax = 1/wtmax;
   }

   //
   //---->  save the betas of the decaying particle
   //
   if (P.Beta()) {
      Double_t w = P.Beta()/P.Rho();
      fBeta[0] = P(0)*w;
      fBeta[1] = P(1)*w;
      fBeta[2] = P(2)*w;
   }
   else fBeta[0]=fBeta[1]=fBeta[2]=0;

   return kTRUE;
}