G4ProcessHelper.cxx

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/*
  Copyright (C) 2002-2022 CERN for the benefit of the ATLAS collaboration
*/
 
#include "G4ProcessHelper.hh"
#include "CustomParticle.h"
#include "TruthUtils/HepMCHelpers.h"
#include "G4ParticleTable.hh"
#include "G4DecayTable.hh"
#include "CLHEP/Random/RandFlat.h"
#include "CLHEP/Units/PhysicalConstants.h"
#include <iostream>
#include <fstream>
#include <stdexcept>
 
#include "CxxUtils/checker_macros.h"
 
G4ProcessHelper::G4ProcessHelper()
  : theRmesoncloud(0)
  , theRbaryoncloud(0)
{
  G4cout << "G4ProcessHelper constructor: start" << G4endl;
  particleTable = G4ParticleTable::GetParticleTable();
  theProton = particleTable->FindParticle("proton");
  theNeutron = particleTable->FindParticle("neutron");
 
 
  // I opted for string based read-in, as it would make physics debugging easier later on
 
  std::ifstream process_stream ("ProcessList.txt");
  G4String line;
  while(getline(process_stream,line)){
    std::vector<G4String> tokens;
 
    //Getting a line
    ReadAndParse(line,tokens,"#");
 
    //Important info
    G4String incident = tokens[0];
    // G4cout << "Incident particle: " << incident << G4endl;
    G4ParticleDefinition* incidentDef = particleTable->FindParticle(incident);
    G4int incidentPDG = incidentDef->GetPDGEncoding();
    known_particles[incidentDef]=true;
 
    G4String target = tokens[1];
    // G4cout << "Target particle: " << target << G4endl;
 
    // Making a ReactionProduct
    ReactionProduct prod;
    for (unsigned int i = 2; i != tokens.size();i++){
      G4String part = tokens[i];
      if (particleTable->contains(part))
        {
          prod.push_back(particleTable->FindParticle(part)->GetPDGEncoding());
        } else {
        G4cout<<"Particle: "<<part<<" is unknown."<<G4endl;
        G4Exception("G4ProcessHelper", "UnkownParticle", FatalException,
                    "Initialization: The reaction product list contained an unknown particle");
      }
    }
    if (target == "proton"){
      pReactionMap[incidentPDG].push_back(prod);
    } else if (target == "neutron") {
      nReactionMap[incidentPDG].push_back(prod);
    } else {
      G4Exception("G4ProcessHelper", "IllegalTarget", FatalException,
                  "Initialization: The reaction product list contained an illegal target particle");
    }
  }
 
  process_stream.close();
  G4cout << "Found " << pReactionMap.size() << " proton interactions and " << nReactionMap.size() << " neutron interactions in ProcessList.txt." << G4endl;
 
  std::map<G4String,G4double> parameters;
  ReadInPhysicsParameters(parameters);
 
  resonant = false;
  reggemodel = false;
  if (parameters["Resonant"]!=0.) resonant=true;
  ek_0 = parameters["ResonanceEnergy"]*CLHEP::GeV;
  gamma = parameters["Gamma"]*CLHEP::GeV;
  amplitude = parameters["Amplitude"]*CLHEP::millibarn;
  xsecmultiplier = parameters["XsecMultiplier"];
  suppressionfactor = parameters["ReggeSuppression"];
  hadronlifetime = parameters["HadronLifeTime"];
  mixing = parameters["Mixing"];
  if(parameters["ReggeModel"]!=0.) reggemodel=true;
  doDecays=parameters["DoDecays"];
 
  G4cout<<"Read in physics parameters:"<<G4endl;
  G4cout<<"Resonant = "<< resonant <<G4endl;
  G4cout<<"ResonanceEnergy = "<<ek_0/CLHEP::GeV<<" GeV"<<G4endl;
  G4cout<<"XsecMultiplier = "<<xsecmultiplier<<G4endl;
  G4cout<<"Gamma = "<<gamma/CLHEP::GeV<<" GeV"<<G4endl;
  G4cout<<"Amplitude = "<<amplitude/CLHEP::millibarn<<" millibarn"<<G4endl;
  G4cout<<"ReggeSuppression = "<<100*suppressionfactor<<" %"<<G4endl;
  G4cout<<"HadronLifeTime = "<<hadronlifetime;
  if (doDecays) G4cout<<" ns"<<G4endl;
  else G4cout<<" s"<<G4endl;
  G4cout<<"ReggeModel = "<< reggemodel <<G4endl;
  G4cout<<"Mixing = "<< mixing*100 <<" %"<<G4endl;
  G4cout<<"DoDecays = "<< doDecays << G4endl;
 
  if ((!doDecays && hadronlifetime>0.) ||
      (doDecays && hadronlifetime<=0.) ){
    G4cout << "WARNING: Inconsistent treatment of R-Hadron properties! Lifetime of " << hadronlifetime
           << " and doDecays= " << doDecays << G4endl;
  }
 
  G4ParticleTable::G4PTblDicIterator* theParticleIterator;
  theParticleIterator = particleTable->GetIterator();
 
  theParticleIterator->reset();
  while( (*theParticleIterator)() ){
    CustomParticle* particle = dynamic_cast<CustomParticle*>(theParticleIterator->value());
    std::string name = theParticleIterator->value()->GetParticleName();
    G4DecayTable* table = theParticleIterator->value()->GetDecayTable();
    if(particle!=0&&table!=0&&name.find("cloud")>name.size()) {
      particle->SetPDGLifeTime(hadronlifetime*CLHEP::s);
      particle->SetPDGStable(false);
      G4cout<<"Lifetime of: "<<name<<" set to: "<<particle->GetPDGLifeTime()/CLHEP::s<<" s."<<G4endl;
      G4cout<<"Stable: "<<particle->GetPDGStable()<<G4endl;
    }
    if (particle && doDecays==1){
      // Make them decay immediately!!
      particle->SetPDGStable(false);
      particle->SetPDGLifeTime(hadronlifetime*CLHEP::ns);
      G4cout<<"Forcing a decay for "<<name<<G4endl;
      G4cout<<"Lifetime of: "<<name<<" set to: "<<particle->GetPDGLifeTime()/CLHEP::ns<<" ns."<<G4endl;
      G4cout<<"Stable: "<<particle->GetPDGStable()<<G4endl;
    }
 
    G4cout << "Done with particle " << name << G4endl;
  }
  theParticleIterator->reset();
  G4cout << "G4ProcessHelper constructor: end" << G4endl;
  return;
}
 
 
void G4ProcessHelper::ReadInPhysicsParameters(std::map<G4String,G4double>&  parameters) const
  {
    parameters["Resonant"]=0.;
    parameters["ResonanceEnergy"]=0.;
    parameters["XsecMultiplier"]=1.;
    parameters["Gamma"]=0.;
    parameters["Amplitude"]=0.;
    parameters["ReggeSuppression"]=0.;
    parameters["HadronLifeTime"]=0.;
    parameters["ReggeModel"]=0.;
    parameters["Mixing"]=0.;
    parameters["DoDecays"]=0;
 
    std::ifstream physics_stream ("PhysicsConfiguration.txt");
    G4String line;
    char** endptr=0;
    while (getline(physics_stream,line)) {
      std::vector<G4String> tokens;
      //Getting a line
      ReadAndParse(line,tokens,"=");
      G4String key = tokens[0];
      G4double val = strtod(tokens[1],endptr);
      parameters[key]=val;
    }
    physics_stream.close();
  }
 
 
const G4ProcessHelper* G4ProcessHelper::Instance()
{
  static const G4ProcessHelper instance;
  return &instance;
}
 
 
G4bool G4ProcessHelper::ApplicabilityTester(const G4ParticleDefinition& aPart) const {
  try {
    return known_particles.at(&aPart);
  }
  catch (const std::out_of_range& e) {
    return false;
  }
}
 
G4double G4ProcessHelper::GetInclusiveCrossSection(const G4DynamicParticle *aParticle,
                                                   const G4Element *anElement) const {
  //We really do need a dedicated class to handle the cross sections. They might not always be constant
 
  //Disassemble the PDG-code
  G4int thePDGCode = aParticle->GetDefinition()->GetPDGEncoding();
  double boost = (aParticle->GetKineticEnergy()+aParticle->GetMass())/aParticle->GetMass();
  G4double theXsec = 0;
  G4String name = aParticle->GetDefinition()->GetParticleName();
 
  if(!reggemodel){
      //Flat cross section
      if(MC::SUSY::isRGlueball(thePDGCode)) {
        theXsec = 24 * CLHEP::millibarn;
      } else {
        std::vector<G4int> nq=MC::SUSY::containedQuarks(thePDGCode);
        for (std::vector<G4int>::iterator it = nq.begin();
             it != nq.end();
             ++it)
          {
            // 12 mb taken from asymptotic pion-nucleon scattering cross sections
            if (*it == 1 || *it == 2) theXsec += 12 * CLHEP::millibarn;
            // 6 mb taken from asymptotic kaon-nucleon scattering cross sections
            // No data for D or B, so setting to behave like a kaon
            if (*it == 3 || *it == 4 || *it == 5) theXsec += 6 * CLHEP::millibarn;
          }
      }
  } else {
    // From Eur. Phys. J. C (2010) 66: 493-501
    // DOI 10.1140/epjc/s10052-010-1262-1
    double R = Regge(boost);
    double P = Pom(boost);
    if(thePDGCode>0)
      {
        if(MC::SUSY::isSMeson(thePDGCode)) theXsec=(P+R)*CLHEP::millibarn;
        if(MC::SUSY::isSBaryon(thePDGCode)) theXsec=2*P*CLHEP::millibarn;
        if(MC::SUSY::isRMeson(thePDGCode)||MC::SUSY::isRGlueball(thePDGCode)) theXsec=(R+2*P)*CLHEP::millibarn;
        if(MC::SUSY::isRBaryon(thePDGCode)) theXsec=3*P*CLHEP::millibarn;
      }
    else
      {
        if(MC::SUSY::isSMeson(thePDGCode)) theXsec=P*CLHEP::millibarn;
        if(MC::SUSY::isSBaryon(thePDGCode)) theXsec=(2*(P+R)+30/sqrt(boost))*CLHEP::millibarn;
        if(MC::SUSY::isRMeson(thePDGCode)||MC::SUSY::isRGlueball(thePDGCode)) theXsec=(R+2*P)*CLHEP::millibarn;
        if(MC::SUSY::isRBaryon(thePDGCode)) theXsec=3*P*CLHEP::millibarn;
      }
  }
 
 
 
  //Adding resonance
 
  if(resonant)
    {
    // Described in Section 5.1 of http://r-hadrons.web.cern.ch/r-hadrons/download/mackeprang_thesis.pdf
    // mentioned but dismissed in Section 3.3 of https://arxiv.org/pdf/hep-ex/0404001.pdf
      double e_0 = ek_0 + aParticle->GetDefinition()->GetPDGMass(); //Now total energy
 
      e_0 = sqrt(aParticle->GetDefinition()->GetPDGMass()*aParticle->GetDefinition()->GetPDGMass()
                 + theProton->GetPDGMass()*theProton->GetPDGMass()
                 + 2.*e_0*theProton->GetPDGMass());
      double sqrts=sqrt(aParticle->GetDefinition()->GetPDGMass()*aParticle->GetDefinition()->GetPDGMass()
                        + theProton->GetPDGMass()*theProton->GetPDGMass() + 2*aParticle->GetTotalEnergy()*theProton->GetPDGMass());
 
      double res_result = amplitude*(gamma*gamma/4.)/((sqrts-e_0)*(sqrts-e_0)+(gamma*gamma/4.));//Non-relativistic Breit Wigner
 
      theXsec += res_result;
    }
 
 
  return theXsec * pow(anElement->GetN(),0.7)*1.25 * xsecmultiplier;// * 0.523598775598299;
 
}
 
ReactionProduct G4ProcessHelper::GetFinalState(const G4Track& aTrack, G4ParticleDefinition*& aTarget) const {
  return GetFinalStateInternal(aTrack,aTarget,false);
}
 
// Version where we know if we baryonize already
ReactionProduct G4ProcessHelper::GetFinalStateInternal(const G4Track& aTrack,G4ParticleDefinition*& aTarget, const bool baryonize_failed) const {
 
  const G4DynamicParticle* aDynamicParticle = aTrack.GetDynamicParticle();
 
  //-----------------------------------------------
  // Choose n / p as target
  // and get ReactionProductList pointer
  //-----------------------------------------------
 
  G4Material* aMaterial = aTrack.GetMaterial();
  const G4ElementVector* theElementVector = aMaterial->GetElementVector() ;
  const G4double* NbOfAtomsPerVolume = aMaterial->GetVecNbOfAtomsPerVolume();
 
  G4double NumberOfProtons=0;
  G4double NumberOfNucleons=0;
 
  for ( size_t elm=0 ; elm < aMaterial->GetNumberOfElements() ; elm++ )
    {
      //Summing number of protons per unit volume
      NumberOfProtons += NbOfAtomsPerVolume[elm]*(*theElementVector)[elm]->GetZ();
      //Summing nucleons (not neutrons)
      NumberOfNucleons += NbOfAtomsPerVolume[elm]*(*theElementVector)[elm]->GetN();
    }
 
  const ReactionMap* reactionMap;
  if(CLHEP::RandFlat::shoot()<NumberOfProtons/NumberOfNucleons){
      reactionMap = &pReactionMap;
      aTarget = theProton;
  } else {
    reactionMap = &nReactionMap;
    aTarget = theNeutron;
  }
 
  G4int theIncidentPDG = aDynamicParticle->GetDefinition()->GetPDGEncoding();
 
  if(reggemodel
     &&MC::SUSY::isSMeson(theIncidentPDG)
     &&CLHEP::RandFlat::shoot()*mixing>0.5
     &&aDynamicParticle->GetDefinition()->GetPDGCharge()==0.
     )
    {
      //      G4cout<<"Oscillating..."<<G4endl;
      theIncidentPDG *= -1;
    }
 
 
  bool baryonise=false;
 
  if(!baryonize_failed
     && reggemodel
     && CLHEP::RandFlat::shoot()>0.9
     && (
        (MC::SUSY::isSMeson(theIncidentPDG)&&theIncidentPDG>0)
        ||
        MC::SUSY::isRMeson(theIncidentPDG)
        )
     ){
    baryonise=true;
  }
 
  // Reference directly to the ReactionProductList we are looking at. Makes life easier :-)
  const ReactionProductList&  aReactionProductList = reactionMap->at(theIncidentPDG);
 
  //-----------------------------------------------
  // Count processes
  // kinematic check
  // compute number of 2 -> 2 and 2 -> 3 processes
  //-----------------------------------------------
 
  G4int N22 = 0; //Number of 2 -> 2 processes
  G4int N23 = 0; //Number of 2 -> 3 processes. Couldn't think of more informative names
 
  //This is the list to be populated
  ReactionProductList theReactionProductList;
  std::vector<bool> theChargeChangeList;
 
  for (const ReactionProduct& prod : aReactionProductList) {
    G4int secondaries = prod.size();
    // If the reaction is not possible we will not consider it
    /*    if(ReactionIsPossible(*prod_it,aDynamicParticle)
          &&(
          !baryonise||(baryonise&&ReactionGivesBaryon(*prod_it))
          ))*/
    if(ReactionIsPossible(prod,*aTarget,aDynamicParticle)
       &&(
          (baryonise&&ReactionGivesBaryon(prod))
          ||
          (!baryonise&&!ReactionGivesBaryon(prod))
          ||
          (MC::SUSY::isSBaryon(theIncidentPDG))
          ||
          (MC::SUSY::isRBaryon(theIncidentPDG))
          ||!reggemodel
          )
       )
      {
        // The reaction is possible. Let's store and count it
        theReactionProductList.push_back(prod);
        if (secondaries == 2){
          N22++;
        } else if (secondaries ==3) {
          N23++;
        } else {
          G4cerr << "ReactionProduct has unsupported number of secondaries: "<<secondaries<<G4endl;
        }
      }
  }
 
  if (theReactionProductList.size()==0 && baryonize_failed){
    G4Exception("G4ProcessHelper", "NoProcessPossible", FatalException,
                "GetFinalState: No process could be selected from the given list.");
  } else if (theReactionProductList.size()==0 && !baryonize_failed) {
    // Baryonization had not yet failed -- try again
    G4cout << "G4ProcessHelper::GetFinalStateInternal WARNING  Could not select an appropriate process in first pass" << G4endl;
    return GetFinalStateInternal(aTrack,aTarget,true);
  }
 
  // For the Regge model no phase space considerations. We pick a process at random
  if(reggemodel)
    {
      int n_rps = theReactionProductList.size();
      int select = (int)(CLHEP::RandFlat::shoot()*n_rps);
      //      G4cout<<"Possible: "<<n_rps<<", chosen: "<<select<<G4endl;
      return theReactionProductList[select];
    }
 
  // Fill a probability map. Remember total probability
  // 2->2 is 0.15*1/n_22 2->3 uses phase space
  G4double p22 = 0.15;
  G4double p23 = 1-p22; // :-)
 
  std::vector<G4double> Probabilities;
  std::vector<G4bool> TwotoThreeFlag;
 
  G4double CumulatedProbability = 0;
 
  // To each ReactionProduct we assign a cumulated probability and a flag
  // discerning between 2 -> 2 and 2 -> 3
  for (unsigned int i = 0; i != theReactionProductList.size(); i++){
    if (theReactionProductList[i].size() == 2) {
      if(0==N22) { throw std::runtime_error("G4ProcessHelper::GetFinalState: N22 is zero!"); }
      CumulatedProbability += p22/N22;
      TwotoThreeFlag.push_back(false);
    } else {
      if(0==N23) { throw std::runtime_error("G4ProcessHelper::GetFinalState: N23 is zero!"); }
      CumulatedProbability += p23/N23;
      TwotoThreeFlag.push_back(true);
    }
    Probabilities.push_back(CumulatedProbability);
  }
 
  //Renormalising probabilities
  for (std::vector<G4double>::iterator it = Probabilities.begin();
       it != Probabilities.end();
       ++it)
    {
      *it /= CumulatedProbability;
    }
 
  // Choosing ReactionProduct
 
  G4bool selected = false;
  G4int tries = 0;
  //  ReactionProductList::iterator prod_it;
 
  //Keep looping over the list until we have a choice, or until we have tried 100 times
  unsigned int i=0;
  while(!selected && tries < 100){
    i=0;
    G4double dice = CLHEP::RandFlat::shoot();
    while( i<theReactionProductList.size() && dice>Probabilities[i] ){
      i++;
    }
 
    if(!TwotoThreeFlag[i]) {
      // 2 -> 2 processes are chosen immediately
      selected = true;
    } else {
      // 2 -> 3 processes require a phase space lookup
      if (PhaseSpace(theReactionProductList[i],*aTarget,aDynamicParticle)>CLHEP::RandFlat::shoot()) selected = true;
    }
    //    double suppressionfactor=0.5;
    auto table ATLAS_THREAD_SAFE = particleTable;  // safe because table has been loaded by now
    if(selected && table->FindParticle(theReactionProductList[i][0])->GetPDGCharge()!=aDynamicParticle->GetDefinition()->GetPDGCharge())
      {
        /*
          G4cout<<"Incoming particle "<<aDynamicParticle->GetDefinition()->GetParticleName()
          <<" has charge "<<aDynamicParticle->GetDefinition()->GetPDGCharge()<<G4endl;
          G4cout<<"Suggested particle "<<particleTable->FindParticle(theReactionProductList[i][0])->GetParticleName()
          <<" has charge "<<particleTable->FindParticle(theReactionProductList[i][0])->GetPDGCharge()<<G4endl;
        */
        if(CLHEP::RandFlat::shoot()<suppressionfactor) selected = false;
      }
    tries++;
    //    G4cout<<"Tries: "<<tries<<G4endl;
  }
  if(tries>=100) G4cerr<<"Could not select process!!!!"<<G4endl;
 
  //Return the chosen ReactionProduct
  return theReactionProductList[i];
}
 
G4double G4ProcessHelper::ReactionProductMass(const ReactionProduct& aReaction,const G4ParticleDefinition& aTarget,const G4DynamicParticle* aDynamicParticle) const{
  // Incident energy:
  G4double E_incident = aDynamicParticle->GetTotalEnergy();
  //G4cout<<"Total energy: "<<E_incident<<" Kinetic: "<<aDynamicParticle->GetKineticEnergy()<<G4endl;
  // sqrt(s)= sqrt(m_1^2 + m_2^2 + 2 E_1 m_2)
  G4double m_1 = aDynamicParticle->GetDefinition()->GetPDGMass();
  G4double m_2 = aTarget.GetPDGMass();
  //G4cout<<"M_R: "<<m_1/CLHEP::GeV<<" GeV, M_np: "<<m_2/CLHEP::GeV<<" GeV"<<G4endl;
  G4double sqrts = sqrt(m_1*m_1 + m_2*(m_2 + 2 * E_incident));
  //G4cout<<"sqrt(s) = "<<sqrts/CLHEP::GeV<<" GeV"<<G4endl;
  // Sum of rest masses after reaction:
  G4double M_after = 0;
  for (ReactionProduct::const_iterator r_it = aReaction.begin(); r_it !=aReaction.end(); ++r_it){
    //G4cout<<"Mass contrib: "<<(particleTable->FindParticle(*r_it)->GetPDGMass())/CLHEP::MeV<<" MeV"<<G4endl;
    auto table ATLAS_THREAD_SAFE = particleTable;  // safe because table has been loaded by now
    M_after += table->FindParticle(*r_it)->GetPDGMass();
  }
  //G4cout<<"Intending to return this ReactionProductMass: " << sqrts << " - " <<  M_after << " MeV"<<G4endl;
  return sqrts - M_after;
}
 
G4bool G4ProcessHelper::ReactionIsPossible(const ReactionProduct& aReaction,const G4ParticleDefinition& aTarget,const G4DynamicParticle* aDynamicParticle) const{
  if (ReactionProductMass(aReaction,aTarget,aDynamicParticle)>0) return true;
  return false;
}
 
G4bool G4ProcessHelper::ReactionGivesBaryon(const ReactionProduct& aReaction) const{
  for (ReactionProduct::const_iterator it = aReaction.begin();it!=aReaction.end();++it)
    if(MC::SUSY::isSBaryon(*it)||MC::SUSY::isRBaryon(*it)) return true;
  return false;
}
 
G4double G4ProcessHelper::PhaseSpace(const ReactionProduct& aReaction,const G4ParticleDefinition& aTarget,const G4DynamicParticle* aDynamicParticle) const {
  G4double qValue = ReactionProductMass(aReaction,aTarget,aDynamicParticle);
  // Eq 4 of https://arxiv.org/pdf/hep-ex/0404001.pdf
  G4double phi = sqrt(1+qValue/(2*0.139*CLHEP::GeV))*pow(qValue/(1.1*CLHEP::GeV),3./2.);
  return (phi/(1+phi));
}
 
void G4ProcessHelper::ReadAndParse(const G4String& str,
                                   std::vector<G4String>& tokens,
                                   const G4String& delimiters) const
{
  // Skip delimiters at beginning.
  G4String::size_type lastPos = str.find_first_not_of(delimiters, 0);
  if (lastPos==G4String::npos) return;
 
  // Find first "non-delimiter".
  G4String::size_type pos     = str.find_first_of(delimiters, lastPos);
 
  while (G4String::npos != pos || G4String::npos != lastPos)
    {
      //Skipping leading / trailing whitespaces
      G4String temp = str.substr(lastPos, pos - lastPos);
      while(temp.c_str()[0] == ' ') temp.erase(0,1);
      while(temp[temp.size()-1] == ' ') temp.erase(temp.size()-1,1);
 
      // Found a token, add it to the vector.
      tokens.push_back(temp);
 
      // Skip delimiters.  Note the "not_of"
      lastPos = str.find_first_not_of(delimiters, pos);
      if (lastPos==G4String::npos) continue;
 
      // Find next "non-delimiter"
      pos = str.find_first_of(delimiters, lastPos);
    }
}
 
double G4ProcessHelper::Regge(const double boost) const
{
  // https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-010-1262-1.pdf Eq 1
  // Originally from https://arxiv.org/pdf/0710.3930.pdf
  double a=2.165635078566177;
  double b=0.1467453738547229;
  double c=-0.9607903711871166;
  return 1.5*exp(a+b/boost+c*log(boost));
}
 
 
double G4ProcessHelper::Pom(const double boost) const
{
  // https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-010-1262-1.pdf Eq 2
  // Originally from https://arxiv.org/pdf/0710.3930.pdf
  double a=4.138224000651535;
  double b=1.50377557581421;
  double c=-0.05449742257808247;
  double d=0.0008221235048211401;
  return a + b*sqrt(boost) + c*boost + d*pow(boost,1.5);
}