TGenPhaseSpace.cxx

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

/** \class TGenPhaseSpace
    \ingroup Physics

 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 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 weight 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 weight 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 dependence
/// 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 weight 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;
}