AtlasPID.h

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/*
  Copyright (C) 2002-2025 CERN for the benefit of the ATLAS collaboration
*/
#ifndef TRUTHUTILS_ATLASPID_H
#define TRUTHUTILS_ATLASPID_H
#include <vector>
#include <cmath>
#include <algorithm>
#include <array>
#include <cstdlib>
class DecodedPID: public std::pair<int,std::vector<int>> {
public:
  inline DecodedPID(const int& p){
    this->first=p;
    this->second.reserve(10);
    int ap = std::abs(p);
    for(; ap; ap/=10) this->second.push_back( ap%10 );
    std::reverse(this->second.begin(), this->second.end());
  }
  inline DecodedPID shift(const size_t n) const { return DecodedPID(this->first%int(std::pow(10,ndigits()-n)));}
  inline const int& operator()(const size_t n) const { return this->second.at(n);}
  inline const int& last() const { return this->second.back();}
  inline const int& pid() const { return this->first;}
  inline int max_digit(const  int m,const  int n) const { return *std::max_element(second.rbegin() + m, second.rbegin() + n);}
  inline int min_digit(const  int m,const  int n) const { return *std::min_element(second.rbegin() + m, second.rbegin() + n);}
  inline size_t ndigits() const { return this->second.size();}
};
 
static const int TABLESIZE = 100;
static const std::array<int,TABLESIZE> triple_charge = {
  +0, -1, +2, -1, +2, -1, +2, -1, +2, +0,
  +0, -3, +0, -3, +0, -3, +0, -3, +0, +0,
  +0, +0, +0, +0, +3, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +3, +0, +0, +3, +6, +0,
  +0, +0, -1, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0
};
 
//Note: The PDG rules assign the range 51-60 for generic DM, with explicit spins defined for 51-55.
// To keep the rest of this range consistent within ATLAS, 56, 57 and 58 are assigned spins 0, +1/2, +1 (respectively) as seen in arXiv:2504.10597v2
static const std::array<int,TABLESIZE> double_spin = {
  +0, +1, +1, +1, +1, +1, +1, +1, +1, +0,
  +0, +1, +1, +1, +1, +1, +1, +1, +1, +0,
  +2, +2, +2, +2, +2, +0, +0, +0, +0, +0,
  +0, +0, +2, +2, +2, +0, +0, +0, +0, +4,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +1, +2, +0, +2, +0, +1, +2, +0, 
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0,
  +0, +0, +0, +0, +0, +0, +0, +0, +0, +0
};
 
 
static const int DQUARK = 1;
static const int UQUARK = 2;
static const int SQUARK = 3;
static const int CQUARK = 4;
static const int BQUARK = 5;
static const int TQUARK = 6;
static const int BPRIME = 7; // 4th Generation quark
static const int TPRIME = 8; // 4th Generation quark
static const int QUARK_LIMIT = BPRIME; // Quark pdg_ids less than this are considered in (R-)Hadrons and Diquarks
 
static const int ELECTRON = 11;
static const int POSITRON = -ELECTRON;
static const int NU_E = 12;
static const int MUON = 13;
static const int NU_MU = 14;
static const int TAU = 15;
static const int NU_TAU = 16;
static const int LPRIME = 17; // 4th Generation charged lepton
static const int NUPRIME = 18; // 4th Generation neutrino
 
static const int GLUON = 21;
// APID: 9 rather than 21 is used to denote a gluon/gluino in composite states. (From PDG 11g)
static const int COMPOSITEGLUON = 9;
static const int PHOTON = 22;
static const int Z0BOSON = 23;
static const int WPLUSBOSON = 24;
static const int HIGGSBOSON = 25;
static const int ZPRIME = 32; // Z′/Z^0_2
static const int ZDBLPRIME = 33; // Z′′/Z^0_3
static const int WPLUSPRIME = 34; // W ′/W^+_2
static const int HIGGS2 = 35; // H^0/H^0_2  FIXME Any better ideas?
static const int HIGGS3 = 36; // A^0/H^0_3 FIXME Any better ideas?
static const int HIGGSPLUS = 37; // H^+
static const int HIGGSPLUSPLUS = 38; // H^++
static const int GRAVITON = 39;
static const int HIGGS4 = 40; // a^0/H^0_4 FIXME Any better ideas?
static const int LEPTOQUARK = 42;
 
static const int DARKPHOTON = 60000;
static const int MAVTOP = 60001;
 
static const int PIPLUS = 211;
static const int PIMINUS = -PIPLUS;
static const int PI0 = 111;
static const int K0L = 130;
 
static const int K0S = 310;
static const int K0 = 311;
static const int KPLUS = 321;
static const int DPLUS = 411;
static const int DSTAR = 413;
static const int D0 = 421;
static const int DSPLUS = 431;
static const int JPSI = 443;
static const int B0 = 511;
static const int BCPLUS = 541;
static const int PROTON = 2212;
static const int NEUTRON = 2112;
static const int LAMBDA0 = 3122;
static const int LAMBDACPLUS = 4122;
static const int LAMBDAB0 = 5122;
static const int PSI2S = 20443;
 
static const int  RH_NU_E = 9900012;
static const int  RH_NU_MU = 9900014;
static const int  RH_NU_TAU = 9900016;
static const int  WBOSON_LRSM = 9900024;
 
static const int LEAD = 1000822080;
static const int OXYGEN = 1000080160;
static const int NEON = 1000100200;
static const int HELIUM =  1000020040;
 
static const int POMERON = 990;
static const int ODDERON = 9990;
static const int REGGEON = 110;
 
static const int GEANTINOPLUS = 998;
static const int GEANTINO0 = 999;
 
 
template<class T> inline bool isQuark(const T& p) {return isQuark(p->pdg_id());}
template<> inline bool isQuark(const int& p) { return p != 0 && (std::abs(p) <= TPRIME || std::abs(p) == MAVTOP);}
template<> inline bool isQuark(const DecodedPID& p){ return isQuark(p.pid()); }
 
// APID: the fourth generation quarks are not standard model quarks
template<class T> inline bool isSMQuark(const T& p) {return isSMQuark(p->pdg_id());}
template<> inline bool isSMQuark(const int& p) { return p != 0 && std::abs(p) <= TQUARK;}
template<> inline bool isSMQuark(const DecodedPID& p){ return isSMQuark(p.pid()); }
 
template<class T> inline bool isStrange(const T& p) {return isStrange(p->pdg_id());}
template<> inline bool isStrange(const int& p){ return std::abs(p) == SQUARK;}
 
template<class T> inline bool isCharm(const T& p){return isCharm(p->pdg_id());}
template<> inline bool isCharm(const int& p){ return std::abs(p) == CQUARK;}
 
template<class T> inline bool isBottom(const T& p){return isBottom(p->pdg_id());}
template<> inline bool isBottom(const int& p){ return std::abs(p) == BQUARK;}
 
template<class T> inline bool isTop(const T& p){return isTop(p->pdg_id());}
template<> inline bool isTop(const int& p){ return std::abs(p) == TQUARK;}
 
template<class T> inline bool isLepton(const T& p){return isLepton(p->pdg_id());}
template<> inline bool isLepton(const int& p){ auto sp = std::abs(p); return sp >= ELECTRON && sp <= NUPRIME; }
template<> inline bool isLepton(const DecodedPID& p){ return isLepton(p.pid()); }
 
template<class T> inline bool isSMLepton(const T& p){return isSMLepton(p->pdg_id());}
template<> inline bool isSMLepton(const int& p){ auto sp = std::abs(p); return sp >= ELECTRON && sp <= NU_TAU; }
template<> inline bool isSMLepton(const DecodedPID& p){ return isSMLepton(p.pid()); }
 
template<class T> inline bool isChLepton(const T& p){return isChLepton(p->pdg_id());}
template<> inline bool isChLepton(const int& p){ auto sp = std::abs(p); return sp >= ELECTRON && sp <= LPRIME && sp%2 == 1; }
 
template<class T> inline bool isElectron(const T& p){return isElectron(p->pdg_id());}
template<> inline bool isElectron(const int& p){ return std::abs(p) == ELECTRON;}
 
template<class T> inline bool isMuon(const T& p){return isMuon(p->pdg_id());}
template<> inline bool isMuon(const int& p){ return std::abs(p) == MUON;}
 
template<class T> inline bool isTau(const T& p){return isTau(p->pdg_id());}
template<> inline bool isTau(const int& p){ return std::abs(p) == TAU;}
 
template<class T> inline bool isNeutrino(const T& p){return isNeutrino(p->pdg_id());}
template<> inline bool isNeutrino(const int& p){ auto sp = std::abs(p); return sp == NU_E || sp == NU_MU || sp == NU_TAU || sp == NUPRIME;  }
 
template<class T> inline bool isSMNeutrino(const T& p){return isSMNeutrino(p->pdg_id());}
template<> inline bool isSMNeutrino(const int& p){ auto sp = std::abs(p); return sp == NU_E || sp == NU_MU || sp == NU_TAU;  }
 
template<class T> inline bool isFourthGeneration(const T& p){return isFourthGeneration(p->pdg_id());}
template<> inline bool isFourthGeneration(const int& p) {return std::abs(p) == BPRIME || std::abs(p) == TPRIME || std::abs(p) == LPRIME || std::abs(p) == NUPRIME;}
 
template<class T> inline bool isDiquark(const T& p){return isDiquark(p->pdg_id());}
template<> inline bool isDiquark(const DecodedPID& p){
  if ( p.ndigits() == 4 && p(0) >= p(1) && p(1) !=0 && p(2) == 0 && (p.last() == 1 || p.last() == 3)
       && p.max_digit(2,4) < QUARK_LIMIT
       ) return true;
  return false;
}
template<> inline bool isDiquark(const int& p){ auto value_digits = DecodedPID(p); return isDiquark(value_digits);}
 
template<class T> inline bool isMeson(const T& p){return isMeson(p->pdg_id());}
template<> inline bool isMeson(const DecodedPID& p){
  if (p.ndigits() < 3 ) return false;
  if (p.ndigits() == 7 && (p(0) == 1 || p(0) == 2)) return false; // APID don't match SUSY particles
  if (std::abs(p.pid()) == K0S) return true;
  if (std::abs(p.pid()) == K0L) return true;
  if (std::abs(p.pid()) == K0) return true;
  if (p.last() % 2 != 1 ) return false;
  if (p.max_digit(1,3) >= QUARK_LIMIT ) return false; // Ignore pdg_ids which would describe states including fourth generation quarks
  if (p.min_digit(1,3) == 0 ) return false;
  if (*(p.second.rbegin() + 2) < *(p.second.rbegin() + 1) ) return false; // Quark ordering (nq2 >= nq3)
  if (*(p.second.rbegin() + 2) == *(p.second.rbegin() + 1) && p.pid() < 0 ) return false; // Illegal antiparticle check (nq2 == nq3)
  if (p.ndigits() == 3 ) return true;
  if (*(p.second.rbegin() + 3) != 0 ) return false; // Only two quarks! (nq1 == 0)
  if (p.ndigits() == 5 && p(0) == 1 ) return true;
  if (p.ndigits() == 5 && p(0) == 2 && p.last() > 1 ) return true;
  if (p.ndigits() == 5 && p(0) == 3 && p.last() > 1 ) return true;
  if (p.ndigits() == 6 && p.last() % 2 == 1 ) return true;
  if (p.ndigits() == 7 && p(0) == 9 && p(1) == 0 ) return true;
 
  return false;
}
template<> inline bool isMeson(const int& p){ auto value_digits = DecodedPID(p); return isMeson(value_digits);}
 
template<class T> inline bool isQuarkonium(const T& p){return isQuarkonium(p->pdg_id());}
template<> inline bool isQuarkonium(const DecodedPID& p) {
  if (!isMeson(p)) return false; //< all quarkonia are mesons
  return (*(p.second.rbegin() + 2) > SQUARK && p.last() > 0 && *(p.second.rbegin() + 1) == *(p.second.rbegin() + 2));
}
template<> inline bool isQuarkonium(const int& p){ auto value_digits = DecodedPID(p); return isQuarkonium(value_digits);}
 
template<class T> inline bool isBaryon(const T& p){return isBaryon(p->pdg_id());}
template<> inline bool isBaryon(const DecodedPID& p){
  if (p.ndigits() < 4 ) return false;
  if (p.max_digit(1,4) >= QUARK_LIMIT ) return false; // Ignore pdg_ids which would describe states including fourth generation quarks
  if (p.min_digit(1,4) == 0) return false; // Ignore pdg_ids with zero for nq1, nq2, nq3
  if (p.ndigits() == 4 && (p.last() == 2 || p.last() == 4|| p.last() == 6|| p.last() == 8) ) return true;
 
  if (p.ndigits() == 5 && p(0) == 1 &&  (p.last() == 2 || p.last() == 4) ) return true;
  if (p.ndigits() == 5 && p(0) == 3 &&  (p.last() == 2 || p.last() == 4) ) return true;
 
  if (p.ndigits() == 6 ) {
    if (p(0) == 1 && p(1) == 0 && p.last() == 2 ) return true;
    if (p(0) == 1 && p(1) == 0 && p.last() == 4 ) return true;
    if (p(0) == 1 && p(1) == 0 && p.last() == 6 ) return true;
    if (p(0) == 1 && p(1) == 1 && p.last() == 2 ) return true;
    if (p(0) == 1 && p(1) == 2 && p.last() == 4 ) return true;
 
    if (p(0) == 2 && p(1) == 0 && p.last() == 2 ) return true;
    if (p(0) == 2 && p(1) == 0 && p.last() == 4 ) return true;
    if (p(0) == 2 && p(1) == 0 && p.last() == 6 ) return true;
    if (p(0) == 2 && p(1) == 0 && p.last() == 8 ) return true;
    if (p(0) == 2 && p(1) == 1 && p.last() == 2 ) return true;
  }
 
  if (p.ndigits() == 5 ) {
    if (p(0) == 2 && p.last() == 2 ) return true;
    if (p(0) == 2 && p.last() == 4 ) return true;
    if (p(0) == 2 && p.last() == 6 ) return true;
    if (p(0) == 5 && p.last() == 2 ) return true;
    if (p(0) == 1 && p.last() == 6 ) return true;
    if (p(0) == 4 && p.last() == 2 ) return true;
  }
  return false;
}
template<> inline bool isBaryon(const int& p){ auto value_digits = DecodedPID(p); return isBaryon(value_digits);}
 
template<class T> inline bool isTetraquark(const T& p){return isTetraquark(p->pdg_id());}
template<> inline bool isTetraquark(const DecodedPID& p){
  return (p.ndigits() == 9 && p(0) == 1 && p(5) == 0 &&
          p.max_digit(1,3) < QUARK_LIMIT && p.min_digit(1,3) > 0 && // ignore 4th generation quarks for nq3 and nq4
          p.max_digit(4,6) < QUARK_LIMIT && p.min_digit(4,6) > 0 && // ignore 4th generation quarks for nq1 and nq2
          ( p(3) >= p(4) && p(6) >= p(7) ) && ( ( p(3) > p(6) ) || ( p(3) == p(6) && (p(4) >= p(7))))
          );
}
template<> inline bool isTetraquark(const int& p){ auto value_digits = DecodedPID(p); return isTetraquark(value_digits);}
 
// APID: states with fourth generation quarks are not pentaquarks
template<class T> inline bool isPentaquark(const T& p){return isPentaquark(p->pdg_id());}
template<> inline bool isPentaquark(const DecodedPID& p){
  return (p.ndigits() == 9 && p(0) == 1 &&
          p.max_digit(1,6) < QUARK_LIMIT && p.min_digit(1,6) > 0 && // ignore 4th generation (anti-)quarks
          ( p(3) >= p(4) && p(4) >= p(5) && p(5) >= p(6)) );
}
template<> inline bool isPentaquark(const int& p){ auto value_digits = DecodedPID(p); return isPentaquark(value_digits);}
 
// APID Mesons, Baryons, Tetraquarks and Pentaquarks are Hadrons
template<class T> inline bool isHadron(const T& p){return isHadron(p->pdg_id());}
template<> inline bool isHadron(const DecodedPID& p){ return isMeson(p) || isBaryon(p) || isTetraquark(p) || isPentaquark(p); }
template<> inline bool isHadron(const int& p){ auto value_digits = DecodedPID(p); return isHadron(value_digits);}
 
 
template<class T> inline bool isTrajectory(const T& p){return isTrajectory(p->pdg_id());}
template<> inline bool isTrajectory(const int& p){ return std::abs(p) == POMERON || std::abs(p) == ODDERON || std::abs(p) == REGGEON; }
 
 
template<class T> inline bool isBoson(const T& p){return isBoson(p->pdg_id());}
template<> inline bool isBoson(const int& p){ auto sp = std::abs(p); return sp > 20 && sp < 41; }
template<> inline bool isBoson(const DecodedPID& p){ return isBoson(p.pid()); }
 
template<class T> inline bool isGluon(const T& p){return isGluon(p->pdg_id());}
template<> inline bool isGluon(const int& p){ return p == GLUON; }
 
template<class T> inline bool isPhoton(const T& p){return isPhoton(p->pdg_id());}
template<> inline bool isPhoton(const int& p){ return p == PHOTON; }
 
template<class T> inline bool isZ(const T& p){return isZ(p->pdg_id());}
template<> inline bool isZ(const int& p){ return p == Z0BOSON; }
 
template<class T> inline bool isW(const T& p){return isW(p->pdg_id());}
template<> inline bool isW(const int& p){ return std::abs(p) == WPLUSBOSON; }
 
template<class T> inline bool isHeavyBoson(const T& p){return isHeavyBoson(p->pdg_id());}
template<> inline bool isHeavyBoson(const int& p){ return p == ZPRIME || p == ZDBLPRIME || std::abs(p) == WPLUSPRIME; }
 
template<class T> inline bool isHiggs(const T& p){return isHiggs(p->pdg_id());}
template<> inline bool isHiggs(const int& p){ return p == HIGGSBOSON; }
 
template<class T> inline bool isMSSMHiggs(const T& p){return isMSSMHiggs(p->pdg_id());}
template<> inline bool isMSSMHiggs(const int& p){ return p == HIGGS2 || p == HIGGS3 || std::abs(p) == HIGGSPLUS; }
 
template<class T> inline bool isGraviton(const T& p) {return isGraviton(p->pdg_id());}
template<> inline bool isGraviton(const int& p){ return p == GRAVITON; }
 
template<class T> inline bool isResonance(const T& p) { return isZ(p) || isW(p) || isHiggs(p) || isTop(p); } // APID: not including t' (pdg_id=8), Z', Z'' and W'+ or BSM Higgs bosons
 
template<class T> inline bool isLeptoQuark(const T& p){return isLeptoQuark(p->pdg_id());}
template<> inline bool isLeptoQuark(const int& p){ return std::abs(p) == LEPTOQUARK; }
 
template<class T> inline bool isPythia8Specific(const T& p){return isPythia8Specific(p->pdg_id());}
template<> inline bool isPythia8Specific(const DecodedPID& p){ return (p.ndigits() == 7 && p(0) == 9 && p(1) == 9);}
template<> inline bool isPythia8Specific(const int& p){ auto value_digits = DecodedPID(p); return isPythia8Specific(value_digits);}
 
template<class T> inline bool isNeutrinoRH(const T& p){return isNeutrinoRH(p->pdg_id());}
template<> inline bool isNeutrinoRH(const int& p){ return (std::abs(p) ==  RH_NU_E || std::abs(p) ==  RH_NU_MU|| std::abs(p) ==  RH_NU_TAU);}
 
template<class T> inline bool isGenSpecific(const T& p){return isGenSpecific(p->pdg_id());}
template<> inline bool isGenSpecific(const int& p){
  int ap = std::abs(p);
  if (ap >= 81 && ap <= 100) return true;
  if (ap >= 901 && ap <= 930) return true;
  if (ap >= 998 && ap <= 999) return true;
  if (ap >= 1901 && ap <= 1930) return true;
  if (ap >= 2901 && ap <= 2930) return true;
  if (ap >= 3901 && ap <= 3930) return true;
  return false;
}
 
template<class T> inline bool isGeantino(const T& p){return isGeantino(p->pdg_id());}
template<> inline bool isGeantino(const int& p){ return (std::abs(p) ==  GEANTINO0 || std::abs(p) ==  GEANTINOPLUS);}
 
template<class T> inline bool isGlueball(const T& p) { return isGlueball(p->pdg_id()); }
template<> inline bool isGlueball(const DecodedPID& p) {
  if (p.ndigits() > 4) return false; // APID avoid classifying R-Glueballs as SM Glueballs
  return
    ( ( p.ndigits() == 3 && p(0) == COMPOSITEGLUON && p(1) == COMPOSITEGLUON && (p.last() == 1 || p.last() == 5) ) ||
      ( p.ndigits() == 4 && p(0) == COMPOSITEGLUON && p(1) == COMPOSITEGLUON && p(2) == COMPOSITEGLUON &&  (p.last() == 3 || p.last() == 7) )  );
}
template<> inline bool isGlueball(const int& p) {  auto value_digits = DecodedPID(p); return isGlueball(value_digits); }
 
 
 
// APID: Super-partners of standard model quarks only
template<class T> inline bool isSquark(const T& p) { return isSquark(p->pdg_id()); }
template<> inline bool isSquark(const DecodedPID& p){
  auto pp = p.shift(1); return (p.ndigits() == 7 && (p(0) == 1 || p(0) == 2) && isSMQuark(pp));
}
template<> inline bool isSquark(const int& p){ auto value_digits = DecodedPID(p); return isSquark(value_digits);}
 
 
// APID: Super-partners of left-handed standard model quarks only
template<class T> inline bool isSquarkLH(const T& p) { return isSquarkLH(p->pdg_id()); }
template<> inline bool isSquarkLH(const DecodedPID& p){
  auto pp = p.shift(1); return (p.ndigits() == 7 && p(0) == 1 && isSMQuark(pp));
}
template<> inline bool isSquarkLH(const int& p){ auto value_digits = DecodedPID(p); return isSquarkLH(value_digits);}
 
 
// APID: Super-partners of right-handed standard model quarks only
template<class T> inline bool isSquarkRH(const T& p) { return isSquarkRH(p->pdg_id()); }
template<> inline bool isSquarkRH(const DecodedPID& p){
  auto pp = p.shift(1); return (p.ndigits() == 7 && p(0) == 2 && isSMQuark(pp));
}
template<> inline bool isSquarkRH(const int& p){ auto value_digits = DecodedPID(p); return isSquarkRH(value_digits);}
 
 
// APID: Super-partners of standard model leptons only
template<class T> inline bool isSlepton(const T& p) { return isSlepton(p->pdg_id()); }
template<> inline bool isSlepton(const DecodedPID& p){ auto pp = p.shift(1); return (p.ndigits() == 7 && (p(0) == 1 || p(0) == 2) && isSMLepton(pp));}
template<> inline bool isSlepton(const int& p){ auto value_digits = DecodedPID(p); return isSlepton(value_digits);}
 
 
// APID: Super-partners of left-handed standard model leptons only
template<class T> inline bool isSleptonLH(const T& p) { return isSleptonLH(p->pdg_id()); }
template<> inline bool isSleptonLH(const DecodedPID& p){
  auto pp = p.shift(1); return (p.ndigits() == 7 && p(0) == 1 && isSMLepton(pp));
}
template<> inline bool isSleptonLH(const int& p){ auto value_digits = DecodedPID(p); return isSleptonLH(value_digits);}
 
 
// APID: Super-partners of right-handed standard model leptons only
template<class T> inline bool isSleptonRH(const T& p) { return isSleptonRH(p->pdg_id()); }
template<> inline bool isSleptonRH(const DecodedPID& p){
  auto pp = p.shift(1); return (p.ndigits() == 7 && p(0) == 2 && isSMLepton(pp));
}
template<> inline bool isSleptonRH(const int& p){ auto value_digits = DecodedPID(p); return isSleptonRH(value_digits);}
 
 
// APID: Super-partners of gauge bosons including gravitons
template<class T> inline bool isGaugino(const T& p) { return isGaugino(p->pdg_id()); }
template<> inline bool isGaugino(const DecodedPID& p){
  auto pp = p.shift(1); return (p.ndigits() == 7 && p(0) == 1 && isBoson(pp.pid()));
}
template<> inline bool isGaugino(const int& p){ auto value_digits = DecodedPID(p); return isGaugino(value_digits);}
 
 
// APID: Super-partners of fundamental particles
template<class T> inline bool isSuperpartner(const T& p) { return isSuperpartner(p->pdg_id()); }
template<> inline bool isSuperpartner(const DecodedPID& p){
  return isSlepton(p) || isSquark(p) || isGaugino(p);
}
template<> inline bool isSuperpartner(const int& p){ auto value_digits = DecodedPID(p); return isSuperpartner(value_digits);}
 
 
template<class T> inline bool isTechnicolor(const T& p){return isTechnicolor(p->pdg_id());}
template <>
inline bool isTechnicolor(const DecodedPID& p) {
  const auto& pp = (p.ndigits() == 7) ? p.shift(2) : DecodedPID(0);
  return (p.ndigits() == 7 && p(0) == 3 && (p(1) == 0 || p(1) == 1) &&
          (isQuark(pp) || isLepton(pp) || isBoson(pp) || isGlueball(pp) ||
           isDiquark(pp) || isHadron(pp)));
}
template<> inline bool isTechnicolor(const int& p){ auto value_digits = DecodedPID(p); return isTechnicolor(value_digits);}
 
template<class T> inline bool isExcited(const T& p){return isExcited(p->pdg_id());}
template <>
inline bool isExcited(const DecodedPID& p) {
  const auto& pp = (p.ndigits() == 7) ? p.shift(2) : DecodedPID(0);
  return (p.ndigits() == 7 && (p(0) == 4 && p(1) == 0) &&
          (isLepton(pp) || isQuark(pp)));
}
template<> inline bool isExcited(const int& p){ auto value_digits = DecodedPID(p); return isExcited(value_digits);}
 
 
template<class T> inline bool isRGlueball(const T& p) { return isRGlueball(p->pdg_id()); }
template<> inline bool isRGlueball(const DecodedPID& p) {
  if (p.ndigits() != 7 || p(0) != 1) return false;
  auto pp = p.shift(1);
  return
    ( ( pp.ndigits() == 3 && pp(0) == COMPOSITEGLUON && pp(1) == COMPOSITEGLUON && (pp.last() == 1 || pp.last() == 3) ) ||
      ( pp.ndigits() == 4 && pp(0) == COMPOSITEGLUON && pp(1) == COMPOSITEGLUON && pp(2) == COMPOSITEGLUON && (pp.last() == 1 || pp.last() == 5) )  );
}
template<> inline bool isRGlueball(const int& p) {  auto value_digits = DecodedPID(p);  return isRGlueball(value_digits); }
 
// APID Define R-Mesons as gluino-quark-antiquark and squark-antiquark bound states (ignore 4th generation squarks/quarks)
// NB Current models only allow gluino-quark-antiquark, stop-antiquark and sbottom-antiquark states
template<class T> inline bool isRMeson(const T& p) { return isRMeson(p->pdg_id()); }
template<> inline bool isRMeson(const DecodedPID& p) {
  if (!(p.ndigits() == 7 && (p(0) == 1 || p(0) == 2))) return false;
  auto pp = p.shift(1);
  return (
          // Handle ~gluino-quark-antiquark states
          (pp.ndigits() == 4 && p(0) == 1 && pp(0) == COMPOSITEGLUON && pp.min_digit(1,3) > 0 && pp.max_digit(1,3) < QUARK_LIMIT && pp(2) <= pp(1) && (pp.last() == 1 || pp.last() == 3)) ||
          // Handle squark-antiquark states (previously called Smeson/mesoninos)
          (pp.ndigits() == 3 && pp.min_digit(1,3) > 0 && pp.max_digit(1,3) < QUARK_LIMIT && pp(1) <= pp(0) && pp.last() == 2)
          );
}
template<> inline bool isRMeson(const int& p) { auto value_digits = DecodedPID(p); return isRMeson(value_digits); }
 
// APID Define R-Baryons as gluino-quark-quark-quark and squark-quark-quark bound states (ignore 4th generation squarks/quarks)
// NB Current models only allow gluino-quark-quark-quark, stop-quark-quark and sbottom-quark-quark states
template<class T> inline bool isRBaryon(const T& p) { return isRBaryon(p->pdg_id()); }
template<> inline bool isRBaryon(const DecodedPID& p) {
  if (!(p.ndigits() == 7 && (p(0) == 1 || p(0) == 2))) return false;
  auto pp = p.shift(1);
  return (
          // Handle ~gluino-quark-quark-quark states
          (pp.ndigits() == 5 && p(0) == 1 && pp(0) == COMPOSITEGLUON && pp.min_digit(1,4) > 0 && pp.max_digit(1,4) < QUARK_LIMIT && pp(2) <= pp(1) && pp(3) <= pp(2) && (pp.last() == 2 || pp.last() == 4)) ||
          // Handle squark-quark-quark states (previously called Sbaryons)
          (pp.ndigits() == 4 && pp.min_digit(1,4) > 0 && pp.max_digit(1,4) < QUARK_LIMIT && pp(1) <= pp(0) && pp(2) <= pp(1) && (pp.last() == 1 || pp.last() == 3))
          );
}
template<> inline bool isRBaryon(const int& p) { auto value_digits = DecodedPID(p); return isRBaryon(value_digits); }
 
 
template<class T> inline bool isRHadron(const T& p) { return isRHadron(p->pdg_id()); }
template<> inline bool isRHadron(const DecodedPID& p) {
  return (isRBaryon(p) || isRMeson(p) || isRGlueball(p));
}
template<> inline bool isRHadron(const int& p) { auto value_digits = DecodedPID(p); return isRHadron(value_digits); }
 
 
template<class T> inline bool hasSquark(const T& p, const int& q) { return hasSquark(p->pdg_id(), q); }
template<> inline bool hasSquark(const DecodedPID& p, const int& q){
  auto pp = p.shift(1); return (
                                (isSquark(p) || isRHadron(p))
                                && pp.ndigits() != 2 // skip lepton and boson super-partners by vetoing ndigits==2
                                && pp(0) == q // After shifting, the first digit will always represent the squark in R-Hadron (and squark) PIDs
                                );
}
template<> inline bool hasSquark(const int& p, const int& q){ auto value_digits = DecodedPID(p); return hasSquark(value_digits, q);}
 
 
// APID Define isSUSY to return true for Superpartners of standard model particles and R-Hadrons
// TODO Should this include the MSSM extended Higgs sector??
template<class T> inline bool isSUSY(const T& p){return isSUSY(p->pdg_id());}
template<> inline bool isSUSY(const DecodedPID& p){return (isSuperpartner(p) || isRHadron(p));}
template<> inline bool isSUSY(const int& p){ auto value_digits = DecodedPID(p); return isSUSY(value_digits);}
 
 
template<class T> inline bool isKK(const T& p){return isKK(p->pdg_id());}
template<> inline bool isKK(const DecodedPID& p){return (p.ndigits() == 7 && (p(0) == 5 || p(0) == 6 ) && (p(1) != 9) );}
template<> inline bool isKK(const int& p){ auto value_digits = DecodedPID(p); return isKK(value_digits);}
 
template<class T> inline bool isMonopole(const T& p){return isMonopole(p->pdg_id());}
template<> inline bool isMonopole(const DecodedPID& p){return (p.ndigits() == 7 && p(0) == 4 && p(1) == 1  && (p(2) == 1 || p(2) == 2 ) && p(6) == 0);}
template<> inline bool isMonopole(const int& p){ auto value_digits = DecodedPID(p); return isMonopole(value_digits);}
 
template<class T> inline bool isDM(const T& p){return isDM(p->pdg_id());}
template<> inline bool isDM(const int& p){
  auto sp = std::abs(p);
  auto value_digits = DecodedPID(p);
  return (sp >= 51 && sp <= 60) || (value_digits.ndigits() == 7 && value_digits(0) == 5 && value_digits(1) == 9) || sp == DARKPHOTON; }
 
template<class T> inline bool isHiddenValley(const T& p){return isHiddenValley(p->pdg_id());}
template <>
inline bool isHiddenValley(const DecodedPID& p) {
  const auto& pp = (p.ndigits() == 7) ? p.shift(2) : DecodedPID(0);
  return (p.ndigits() == 7 && p(0) == 4 && p(1) == 9 &&
          (isQuark(pp) || isLepton(pp) || isBoson(pp) || isGlueball(pp) ||
           isDiquark(pp) || isHadron(pp)));
}
template<> inline bool isHiddenValley(const int& p){ auto value_digits = DecodedPID(p); return isHiddenValley(value_digits);}
 
template<class T> inline bool isGenericMultichargedParticle(const T& p){return isGenericMultichargedParticle(p->pdg_id());}
template<> inline bool isGenericMultichargedParticle(const DecodedPID& p){return (p.ndigits() == 8 && (p(0) == 1 || p(0) == 2) && p(1) == 0 && p(2) == 0 && p(7) == 0);}
template<> inline bool isGenericMultichargedParticle(const int& p){ auto value_digits = DecodedPID(p); return isGenericMultichargedParticle(value_digits);}
 
template<class T> inline bool isNucleus(const T& p){return isNucleus(p->pdg_id());}
template<> inline bool isNucleus(const DecodedPID& p){
  if (std::abs(p.pid()) == PROTON) return true;
  if (p.ndigits() != 10) return false;
  // charge should always be less than or equal to baryon number
  // the following line is A >= Z
  const int A = p(8) + 10*p(7) + 100*p(6);
  const int Z = p(5) + 10*p(4) + 100*p(3);
  return ( A >= Z &&  p(0) == 1 &&  p(1) == 0 );
}
template<> inline bool isNucleus(const int& p){ auto value_digits = DecodedPID(p); return isNucleus(value_digits);}
 
 
template<class T> inline bool hasQuark(const T& p, const int& q);
template<> inline bool hasQuark(const DecodedPID& p, const int& q){
  if (isQuark(p.pid())) { return (std::abs(p.pid()) == q );}
  if (isMeson(p)) { return *(p.second.rbegin() + 1) == q ||*(p.second.rbegin()+2) ==q;}
  if (isDiquark(p)) { auto i = std::find(p.second.rbegin() + 2,p.second.rbegin()+4,q); return (i!=p.second.rbegin()+4);}
  if (isBaryon(p)) { auto i = std::find(p.second.rbegin() + 1,p.second.rbegin()+4,q); return (i!=p.second.rbegin()+4);}
  if (isTetraquark(p)) { auto i = std::find(p.second.rbegin() + 1,p.second.rbegin()+5,q); return (i!=p.second.rbegin()+5);}
  if (isPentaquark(p)) { auto i = std::find(p.second.rbegin() + 1,p.second.rbegin()+6,q); return (i!=p.second.rbegin()+6);}
  if (isNucleus(p) && std::abs(p.pid()) != PROTON) { return (q == 1 || q == 2 || (q==3 && p(2) > 0));}
  if (isSUSY(p)) { // APID SUSY case
    auto pp = p.shift(1);
    if ( pp.ndigits() == 1 ) { return false; } // Handle squarks
    if ( pp.ndigits() == 3 ) { return (pp(1) == q); } // Handle ~q qbar pairs
    if ( pp.ndigits() == 4 ) { return (pp(1) == q || pp(2) == q); } // Ignore gluinos and squarks
    if ( pp.ndigits() == 5 ) {  return (pp(1) == q || pp(2) == q || pp(3) == q); } // Ignore gluinos and squarks
    if ( pp.ndigits() > 5 ) { pp = pp.shift(1); } // Drop gluinos and squarks
    return hasQuark(pp, q); }
  return false;
}
template<> inline bool hasQuark(const int& p, const int& q){ auto value_digits = DecodedPID(p); return hasQuark(value_digits, q);}
 
template<class T> inline bool hasStrange(const T& p) { return  hasQuark(p,SQUARK); }
template<class T> inline bool hasCharm(const T& p) { return  hasQuark(p,CQUARK); }
template<class T> inline bool hasBottom(const T& p) { return  hasQuark(p,BQUARK); }
template<class T> inline bool hasTop(const T& p) { return  hasQuark(p,TQUARK); }
 
 
// APID: The baryon number is defined as:
// B = (1/3)*( n_q - n_{qbar} )
// where n_q⁠ is the number of quarks, and ⁠n_{qbar} is the number of
// antiquarks. By convention, squarks have the same quantum numbers as
// the corresponding quarks (modulo spin and R), so have baryon number
// 1/3.
template<class T> inline int baryonNumber3(const T& p) {return baryonNumber3(p->pdg_id());}
template<> inline int baryonNumber3(const DecodedPID& p){
  if (isQuark(p.pid())) { return (p.pid() > 0) ? 1 : - 1;}
  if (isDiquark(p)) { return (p.pid() > 0) ? 2 : -2; }
  if (isMeson(p) || isTetraquark(p)) { return 0; }
  if (isBaryon(p) || isPentaquark(p)){ return (p.pid() > 0) ? 3 : -3; }
  if (isNucleus(p)) {
    const int result = 3*p(8) + 30*p(7) + 300*p(6);
    return (p.pid() > 0) ? result : -result;
  }
  if (isSUSY(p)) {
    auto pp = p.shift(1);
    if (pp.ndigits() < 3 ) { return baryonNumber3(pp); } // super-partners of fundamental particles
    if (pp(0) == COMPOSITEGLUON) {
      if (pp(1) == COMPOSITEGLUON) { return 0; } // R-Glueballs
      if ( pp.ndigits() == 4 ) { return 0; }  // states with gluino-quark-antiquark
      if ( pp.ndigits() == 5) { return (p.pid() > 0) ? 3 : -3; } // states with gluino-quark-quark-quark
    }
    if (pp.ndigits() == 3) { return 0; } // squark-antiquark
    if (pp.ndigits() == 4) { return (p.pid() > 0) ? 3 : -3; } // states with squark-quark-quark
  }
  return 0;
}
template<> inline int baryonNumber3(const int& p){ auto value_digits = DecodedPID(p); return baryonNumber3(value_digits);}
 
template<class T> inline double baryonNumber(const T& p) {return baryonNumber(p->pdg_id());}
template<> inline double baryonNumber(const DecodedPID& p){ return static_cast<double>(baryonNumber3(p))/3.0;}
template<> inline double baryonNumber(const int& p){ auto value_digits = DecodedPID(p);  return static_cast<double>(baryonNumber3(value_digits))/3.0;}
 
 
// APID: The strangeness of a particle is defined as:
// S = − ( n_s − n_{sbar} )
// where n_s represents the number of strange quarks and n_{sbar}
// represents the number of strange antiquarks. By convention, strange
// squarks have the same quantum numbers as strange quarks (modulo
// spin and R), so have strangeness -1.
static const std::array<int,10> is_strange = {
  +0, +0, +0, -1, +0, +0, +0, +0, +0, +0 };
template<class T> inline int strangeness(const T& p) {return strangeness(p->pdg_id());}
template<> inline int strangeness(const DecodedPID& p){
  if (isNucleus(p) && p.ndigits() == 10) { return (p.pid() > 0) ? -p(2) : p(2); }
  if (isStrange(p.pid())) { return (p.pid() > 0) ? -1 : 1; }
  if (!hasStrange(p) && !hasSquark(p,SQUARK)) { return 0; }
  if (std::abs(p.pid()) == K0) { return (p.pid() > 0) ? 1 : -1; }
  size_t nq = 0;
  int sign = 1;
  int signmult = 1;
  int result=0;
  bool classified = false;
  if (!classified && isMeson(p)) { classified = true; nq = 2; if ((*(p.second.rbegin()+2)) == 2||(*(p.second.rbegin()+2)) == 4 ) { sign=-1;} signmult =-1; }
  if (!classified && isDiquark(p)) {return is_strange.at(p(0))+is_strange.at(p(1)); }
  if (!classified && isBaryon(p)) { classified = true; nq = 3; }
  if (!classified && isTetraquark(p)){ return is_strange.at(p(3)) + is_strange.at(p(4)) - is_strange.at(p(6)) - is_strange.at(p(7)); }
  if (!classified && isPentaquark(p)){ return is_strange.at(p(3)) + is_strange.at(p(4)) + is_strange.at(p(5)) + is_strange.at(p(6)) - is_strange.at(p(7)); }
  if (!classified && isSUSY(p)) {
    nq = 0;
    auto pp = p.shift(1);
    if (pp.ndigits() < 3 ) { return strangeness(pp); } // super-partners of fundamental particles
    if (pp(0) == COMPOSITEGLUON) {
      if (pp(1) == COMPOSITEGLUON) { return 0; } // R-Glueballs
      if ( pp.ndigits() == 4 || pp.ndigits() == 5) {
        pp = pp.shift(1); // Remove gluino
      }
    }
    if (pp.ndigits() == 3) { classified = true; nq = 2; if (p.last()%2==0) {sign = -1;} signmult = -1; } // states with quark-antiquark or squark-antiquark
    if (pp.ndigits() == 4) { classified = true; nq = 3; } // states with quark-quark-quark or squark-quark-quark
  }
  for (auto r = p.second.rbegin() + 1; r != p.second.rbegin() + 1 + nq; ++r) {
    result += is_strange.at(*r)*sign;
    sign*=signmult;
  }
  return p.pid() > 0 ? result : -result;
}
template<> inline int strangeness(const int& p){ auto value_digits = DecodedPID(p); return strangeness(value_digits);}
 
 
template<class T> inline int numberOfLambdas(const T& p) {return numberOfLambdas(p->pdg_id());}
template<> inline int numberOfLambdas(const DecodedPID& p){
  if (std::abs(p.pid()) == LAMBDA0) { return  (p.pid() > 0) ? 1 : -1; }
  if (isNucleus(p) && p.ndigits() == 10) { return (p.pid() > 0) ? p(2) : -p(2); }
  return 0;
}
template<> inline int numberOfLambdas(const int& p){ auto value_digits = DecodedPID(p); return numberOfLambdas(value_digits);}
 
 
template<class T> inline int numberOfProtons(const T& p) {return numberOfProtons(p->pdg_id());}
template<> inline int numberOfProtons(const DecodedPID& p){
  if (std::abs(p.pid()) == PROTON) { return  (p.pid() > 0) ? 1 : -1; }
  if (isNucleus(p)) {
    const int result = p(5) + 10*p(4) + 100*p(3);
    return (p.pid() > 0) ? result : -result;
  }
  return 0;
}
template<> inline int numberOfProtons(const int& p){ auto value_digits = DecodedPID(p); return numberOfProtons(value_digits);}
 
 
template<class T> inline bool isBSM(const T& p){return isBSM(p->pdg_id());}
template<> inline bool isBSM(const DecodedPID& p){
  if (p.pid() == GRAVITON || std::abs(p.pid()) == MAVTOP || p.pid() == DARKPHOTON) return true;
  if (std::abs(p.pid()) > 16 && std::abs(p.pid()) < 19) return true;
  if (std::abs(p.pid()) > 31 && std::abs(p.pid()) < 39) return true;
  if (std::abs(p.pid()) > 39 && std::abs(p.pid()) < 81) return true;
  if (std::abs(p.pid()) > 6 && std::abs(p.pid()) < 9) return true;
  if (isSUSY(p)) return true;
  if (isNeutrinoRH(p.pid())) return true;
  if (isGenericMultichargedParticle(p)) return true;
  if (isTechnicolor(p)) return true;
  if (isExcited(p)) return true;
  if (isKK(p)) return true;
  if (isHiddenValley(p)) return true;
  if (isMonopole(p)) return true;
  if (isDM(p.pid())) return true;
  return false;
}
template<> inline bool isBSM(const int& p){
  if (p == GRAVITON || std::abs(p) == MAVTOP || p == DARKPHOTON) return true;
  if (std::abs(p) > 16 && std::abs(p) < 19) return true;
  if (std::abs(p) > 31 && std::abs(p) < 38) return true;
  if (std::abs(p) > 39 && std::abs(p) < 81) return true;
  if (std::abs(p) > 6 && std::abs(p) < 9) return true;
  auto value_digits = DecodedPID(p); return isBSM(value_digits);
}
 
template<class T> inline bool isTransportable(const T& p){return isTransportable(p->pdg_id());}
template<> inline bool isTransportable(const DecodedPID& p){ return isPhoton(p.pid()) || isGeantino(p.pid()) || isHadron(p) || isLepton(p.pid()) || p.pid() == DARKPHOTON;}
template<> inline bool isTransportable(const int& p){ auto value_digits = DecodedPID(p); return isTransportable(value_digits);}
 
template<class T> inline bool isValid(const T& p){return isValid(p->pdg_id());}
template<> inline bool isValid(const DecodedPID& p){
  return p.pid() !=0 && ( isQuark(p) || isLepton(p) || isBoson(p) || isGlueball(p) ||
                         isTrajectory(p.pid()) || isGenSpecific(p.pid()) || isDiquark(p) ||
                         isBSM(p) || isHadron(p) || isNucleus(p) || isGeantino(p.pid()) ||
                         isPythia8Specific(p) ); }
template<> inline bool isValid(const int& p){ if (!p) return false; if (std::abs(p) < 42) return true;
  if (isGenSpecific(p)) return true;
  auto value_digits = DecodedPID(p); return isValid(value_digits);
}
 
template<class T> inline int leadingQuark(const T& p) {return leadingQuark(p->pdg_id());}
template<> inline int leadingQuark(const DecodedPID& p){
  if (isQuark(p.pid())) { return std::abs(p.pid());}
  if (isMeson(p)) { return p.max_digit(1,3);}
  if (isDiquark(p)) { return p.max_digit(2,4);}
  if (isBaryon(p)) { return p.max_digit(1,4);}
  if (isTetraquark(p)) { return p.max_digit(1,5);}
  if (isPentaquark(p)) { return p.max_digit(1,6);}
  if (isSUSY(p)) { // APID SUSY case
    auto pp = p.shift(1);
    if ( pp.ndigits() == 1 ) { return 0; } // Handle squarks
    if ( pp.ndigits() == 3 ) { pp = DecodedPID(pp(1)); } // Handle ~q qbar pairs
    if ( pp.ndigits()  > 3 ) { pp = pp.shift(1); } // Drop gluinos and squarks
    return leadingQuark(pp); }
  return 0;
}
 
template<> inline int leadingQuark(const int& p){ auto value_digits = DecodedPID(p); return leadingQuark(value_digits);}
 
template<class T> inline bool isLightHadron(const T& p) { auto lq = leadingQuark(p); return  (lq == DQUARK || lq == UQUARK||lq == SQUARK) && isHadron(p); }
template<class T> inline bool isHeavyHadron(const T& p) {  auto lq = leadingQuark(p); return  (lq == CQUARK || lq == BQUARK || lq == TQUARK ) && isHadron(p); }
template<class T> inline bool isStrangeHadron(const T& p) { return  leadingQuark(p) == SQUARK && isHadron(p); }
template<class T> inline bool isCharmHadron(const T& p) { return  leadingQuark(p) == CQUARK && isHadron(p); }
template<class T> inline bool isBottomHadron(const T& p) { return  leadingQuark(p) == BQUARK && isHadron(p); }
template<class T> inline bool isTopHadron(const T& p) { return  leadingQuark(p) == TQUARK && isHadron(p); }
 
template<class T> inline bool isLightMeson(const T& p) { auto lq = leadingQuark(p); return  (lq == DQUARK || lq == UQUARK||lq == SQUARK) && isMeson(p); }
template<class T> inline bool isHeavyMeson(const T& p) { auto lq = leadingQuark(p); return  (lq == CQUARK || lq == BQUARK || lq == TQUARK) && isMeson(p); }
template<class T> inline bool isStrangeMeson(const T& p) { return  leadingQuark(p) == SQUARK && isMeson(p); }
template<class T> inline bool isCharmMeson(const T& p) { return  leadingQuark(p) == CQUARK && isMeson(p); }
template<class T> inline bool isBottomMeson(const T& p) { return  leadingQuark(p) == BQUARK && isMeson(p); }
template<class T> inline bool isTopMeson(const T& p) { return  leadingQuark(p) == TQUARK && isMeson(p); }
 
template<class T> inline bool isCCbarMeson(const T& p) { return isCCbarMeson(p->pdg_id());}
template<> inline bool isCCbarMeson(const DecodedPID& p) { return leadingQuark(p) == CQUARK && isMeson(p) && (*(p.second.rbegin()+2)) == CQUARK && (*(p.second.rbegin()+1)) == CQUARK; }
template<> inline bool isCCbarMeson(const int& p) { return isCCbarMeson(DecodedPID(p)); }
 
template<class T> inline bool isBBbarMeson(const T& p){ return isBBbarMeson(p->pdg_id());}
template<> inline bool isBBbarMeson(const DecodedPID& p) { return leadingQuark(p) == BQUARK && isMeson(p) && (*(p.second.rbegin()+2)) == BQUARK && (*(p.second.rbegin()+1)) == BQUARK; }
template<> inline bool isBBbarMeson(const int& p) { return isBBbarMeson(DecodedPID(p)); }
 
 
template<class T> inline bool isLightBaryon(const T& p) { auto lq = leadingQuark(p); return  (lq == DQUARK || lq == UQUARK||lq == SQUARK) && isBaryon(p); }
template<class T> inline bool isHeavyBaryon(const T& p) {  auto lq = leadingQuark(p); return  (lq == CQUARK || lq == BQUARK || lq == TQUARK) && isBaryon(p); }
template<class T> inline bool isStrangeBaryon(const T& p) { return  leadingQuark(p) == SQUARK && isBaryon(p); }
template<class T> inline bool isCharmBaryon(const T& p) { return  leadingQuark(p) == CQUARK && isBaryon(p); }
template<class T> inline bool isBottomBaryon(const T& p) { return  leadingQuark(p) == BQUARK && isBaryon(p); }
template<class T> inline bool isTopBaryon(const T& p) { return  leadingQuark(p) == TQUARK && isBaryon(p); }
 
 
// APID: This function selects B-Hadrons which predominantly decay weakly. (Commonly used definition in GeneratorFilters package.)
// 5[1-4]1 L = J = 0, S = 0
// 5[1-5][1-4]2 J = 1/2, n_r = 0, n_L =0
template<class T> inline bool isWeaklyDecayingBHadron(const T& p) {return isWeaklyDecayingBHadron(p->pdg_id());}
template<> inline bool isWeaklyDecayingBHadron(const int& p) {
  const int pid = std::abs(p);
  return ( pid == 511   || // B0
           pid == 521   || // B+
           pid == 531   || // B_s0
           pid == 541   || // B_c+
           pid == 5122  || // Lambda_b0
           pid == 5132  || // Xi_b-
           pid == 5232  || // Xi_b0
           pid == 5112  || // Sigma_b-
           pid == 5212  || // Sigma_b0
           pid == 5222  || // Sigma_b+
           pid == 5332  || // Omega_b-
           pid == 5142  || // Xi_bc0
           pid == 5242  || // Xi_bc+
           pid == 5412  || // Xi'_bc0
           pid == 5422  || // Xi'_bc+
           pid == 5342  || // Omega_bc0
           pid == 5432  || // Omega'_bc0
           pid == 5442  || // Omega_bcc+
           pid == 5512  || // Xi_bb-
           pid == 5522  || // Xi_bb0
           pid == 5532  || // Omega_bb-
           pid == 5542  ); // Omega_bbc0
}
template<> inline bool isWeaklyDecayingBHadron(const DecodedPID& p){ return isWeaklyDecayingBHadron(p.pid()); }
 
 
// APID: This function selects C-Hadrons which predominantly decay weakly. (Commonly used definition in GeneratorFilters package.)
// 4[1-3]1 L = J = 0, S = 0
// 4[1-4][1-3]2 J = 1/2, n_r = 0, n_L =0
// NB Omitting pid = 4322 (Xi'_C+) a this undergoes an EM rather than
// weak decay.  (There was an old version of Herwig that decayed it
// weakly, but this was fixed in Herwig 7.)
template<class T> inline bool isWeaklyDecayingCHadron(const T& p) {return isWeaklyDecayingCHadron(p->pdg_id());}
template<> inline bool isWeaklyDecayingCHadron(const int& p) {
  const int pid = std::abs(p);
  return ( pid == 411   || // D+
           pid == 421   || // D0
           pid == 431   || // Ds+
           pid == 4122  || // Lambda_c+
           pid == 4132  || // Xi_c0
           pid == 4232  || // Xi_c+
           pid == 4212  || // Xi_c0
           pid == 4332  || // Omega_c0
           pid == 4412  || // Xi_cc+
           pid == 4422  || // Xi_cc++
           pid == 4432  ); // Omega_cc+
}
template<> inline bool isWeaklyDecayingCHadron(const DecodedPID& p){ return isWeaklyDecayingCHadron(p.pid()); }
 
 
template<class T> inline int charge3( const T& p){return charge3(p->pdg_id());}
template<class T> inline double fractionalCharge(const T& p){return fractionalCharge(p->pdg_id());}
template<class T> inline double charge( const T& p){
  if (isGenericMultichargedParticle(p)) // BSM multi-charged particles might have a fractional charge that's not a multiple of 1/3
    return fractionalCharge(p);
  else
    return 1.0*charge3(p)/3.0;
}
template<class T> inline double threeCharge( const T& p){ return charge3(p);}
template<class T> inline bool isCharged( const T& p){ return charge3(p) != 0;}
 
 
template<> inline int charge3(const DecodedPID& p) {
  auto ap = std::abs(p.pid());
  if (ap < TABLESIZE ) return p.pid() > 0 ? triple_charge.at(ap) : -triple_charge.at(ap);
  if (ap == K0) return 0;
  if (ap == GEANTINO0) return 0;
  if (ap == GEANTINOPLUS) return p.pid() > 0 ? 3 : -3;
  if (ap == MAVTOP) return p.pid() > 0 ? 2 : -2;
  size_t nq = 0;
  int sign = 1;
  int signmult = 1;
  int result=0;
  bool classified = false;
  if (!classified && isMeson(p)) { classified = true; nq = 2; if ((*(p.second.rbegin()+2)) == 2||(*(p.second.rbegin()+2)) == 4 ) { sign=-1;} signmult =-1; }
  if (!classified && isDiquark(p)) {return triple_charge.at(p(0))+triple_charge.at(p(1)); }
  if (!classified && isBaryon(p)) { classified = true; nq = 3; }
  if (!classified && isTetraquark(p)){ return triple_charge.at(p(3)) + triple_charge.at(p(4)) - triple_charge.at(p(6)) - triple_charge.at(p(7)); }
  if (!classified && isPentaquark(p)){ return triple_charge.at(p(3)) + triple_charge.at(p(4)) + triple_charge.at(p(5)) + triple_charge.at(p(6)) - triple_charge.at(p(7)); }
  if (!classified && isNucleus(p)) { return 3*numberOfProtons(p);}
  if (!classified && isSUSY(p)) {
    nq = 0;
    auto pp = p.shift(1);
    if (pp.ndigits() < 3 ) { return charge3(pp); } // super-partners of fundamental particles
    if (pp(0) == COMPOSITEGLUON) {
      if (pp(1) == COMPOSITEGLUON) { return 0; } // R-Glueballs
      if ( pp.ndigits() == 4 || pp.ndigits() == 5) {
        pp = pp.shift(1); // Remove gluino
      }
    }
    if (pp.ndigits() == 3) { classified = true; nq = 2; if (p.last()%2==0) {sign = -1;} signmult = -1; } // states with squark-antiquark or quark-anti-quark
    if (pp.ndigits() == 4) { classified = true; nq = 3; } // states with squark-quark-quark or quark-quark-quark
  }
  if (!classified && isHiddenValley(p)) { // Hidden Valley particles
    auto pp = p.shift(2);
    if (!classified && isMeson(pp)) { classified = true; nq = 2; if ((*(pp.second.rbegin()+2)) == 2||(*(pp.second.rbegin()+2)) == 4 ) { sign=-1;} signmult =-1; }
    if (!classified && isDiquark(pp)) {return triple_charge.at(pp(0))+triple_charge.at(pp(1)); }
    if (!classified && isBaryon(pp)) { classified = true; nq = 3; }
    
  }
  if (!classified && isKK(p)) { // Kaluza-Klein particles
    auto pp = p.shift(2);
    auto ap = std::abs(pp.pid());
    if (ap < TABLESIZE ) return pp.pid() > 0 ? triple_charge.at(ap) : -triple_charge.at(ap);
 
  }
  if (!classified && isDM(p.pid())) { //Dark Matter Particles
    if (p.ndigits() == 7){ // Determining the charges for the more elaborate, 7-digit DM codes
      auto pp = p.shift(3); // The first two digits indicate the particle is DM, the third indicates left/right-handedness (see 11(j))
      auto ap = std::abs(pp.pid());
      if (ap < TABLESIZE ) return pp.pid() > 0 ? triple_charge.at(ap) : -triple_charge.at(ap);
    }else if (std::abs(p.pid()) < TABLESIZE) return p.pid() > 0 ? triple_charge.at(ap) : -triple_charge.at(ap);  // Just to make sure the correct charge is returned for DM 51-60
  }
  if (!classified && isMonopole(p)) {
    result = 3*(p(3)*100 + p(4)*10 + p(5));
    return ( (p.pid() > 0 && p(2) == 1) ||  (p.pid() < 0 && p(2) == 2) ) ? result : -result;
  }
  if (!classified && isGenericMultichargedParticle(p)) {
    double abs_charge = 0.0;
    if (p(0) == 1) abs_charge = p(3)*100. + p(4)*10. + p(5)*1 + p(6)*0.1; // multi-charged particle PDG ID is +/-100XXXY0, where the charge is XXX.Y
    if (p(0) == 2) abs_charge = (p(3)*10. + p(4))/(p(5)*10.0 + p(6)); // multi-charged particle PDG ID is +/-200XXYY0, where the charge is XX/YY
    int abs_threecharge = static_cast<int>(std::round(abs_charge * 3.)); // the multi-charged particles might have a fractional charge that's not a multiple of 1/3, in that case round to the closest multiple of 1/3 for charge3 and threecharge
    return p.pid() > 0 ? abs_threecharge : -1 * abs_threecharge;
  }
  for (auto r = p.second.rbegin() + 1; r != p.second.rbegin() + 1 + nq; ++r) {
    result += triple_charge.at(*r)*sign;
    sign*=signmult;
  }
  return p.pid() > 0 ? result : -result;
}
template<> inline int charge3(const int& p){
  int ap = std::abs(p);
  if (ap < TABLESIZE) return p > 0 ? triple_charge.at(ap):-triple_charge.at(ap);
  auto value_digits = DecodedPID(p);
  return charge3(value_digits);
}
 
 
template<class T> inline bool isNeutral( const T& p){ return p->pdg_id() != 0 && charge3(p) == 0;}
template<> inline bool isNeutral(const DecodedPID& p){ return p.pid() != 0 && charge3(p) == 0;}
template<> inline bool isNeutral(const int& p){ auto value_digits = DecodedPID(p); return isNeutral(value_digits);}
 
 
template<> inline double fractionalCharge(const DecodedPID& p) {
  if(!isGenericMultichargedParticle(p)) return 1.0*charge3(p)/3.0; // this method is written for multi-charged particles, still make sure other cases are handled properly
  double abs_charge = 0;
  if (p(0) == 1) abs_charge = p(3)*100. + p(4)*10. + p(5)*1 + p(6)*0.1; // multi-charged particle PDG ID is +/-100XXXY0, where the charge is XXX.Y
  if (p(0) == 2) abs_charge = (p(3)*10. + p(4))/(p(5)*10.0 + p(6)); // multi-charged particle PDG ID is +/-200XXYY0, where the charge is XX/YY
  return p.pid() > 0 ? abs_charge : -1 * abs_charge;
}
template<> inline double fractionalCharge(const int& p){auto value_digits = DecodedPID(p); return fractionalCharge(value_digits);}
 
// APID: Including Z' and Z'' as EM interacting.
template<class T> inline bool isEMInteracting(const T& p){return isEMInteracting(p->pdg_id());}
template<> inline bool isEMInteracting(const int& p) {return (isPhoton(p) || isZ(p) || p == ZPRIME || p == ZDBLPRIME || std::abs(charge(p))>std::numeric_limits<double>::epsilon() || isMonopole(p));}
 
template<class T> inline bool isParton(const T& p) { return isQuark(p)||isGluon(p);}
 
// APID: Intended to return 2J
// Useful for G4ParticleDefinition constructor
template<class T> inline int spin2(const T& p) { return spin2(p->pdg_id()); }
template<> inline int spin2(const DecodedPID& p) {
  if (isSUSY(p)) {
    auto pp = p.shift(1);
    auto ap = std::abs(pp.pid());
    if (ap < TABLESIZE ) { return std::abs(double_spin.at(ap)-1); } // sparticles (0->1, 1 -> 0,  2->1,  4->3)
    return p.last()-1; // R-Hadrons (p.last() == 2J +1)
  }
  if (isHiddenValley(p)) { //Hidden Valley spins
    auto pp = p.shift(2);
    if (isHadron(pp)) { return pp.last()-1; } // Hadrons (p.last == 2J+1 - special cases handled above)
  }
  if (isKK(p)) { // Kaluza-Klein spins
    auto pp = p.shift(2);
    auto ap = std::abs(pp.pid());
    if (ap < TABLESIZE ) { return double_spin.at(ap); } // fundamental particles
  }
  if (isDM(std::abs(p.pid()))) { //DM spins
    if (p.ndigits() == 7) { // Determining the spins for the more elaborate, 7-digit DM codes
      auto pp = p.shift(3); // The first two digits indicate the particle is DM, the third indicates left/right-handedness (see 11(j))
      auto ap = std::abs(pp.pid());
      if (ap < TABLESIZE) { return double_spin.at(ap); } // fundamental particles
    }else if (std::abs(p.pid()) < TABLESIZE) { // Just to make sure the correct spin is returned for DM 51-60
      return std::abs(double_spin.at(std::abs(p.pid())));
    }
  }
  auto ap = std::abs(p.pid());
  if (ap == K0S) { return 0; }
  if (ap == K0L) { return 0; }
  if (ap == MAVTOP) { return 1; } // TODO check this
  if (ap == DARKPHOTON) { return 2; } // TODO check this
  if (ap < TABLESIZE ) { return double_spin.at(ap); } // fundamental particles
  if (isHadron(p)) { return p.last()-1; } // Hadrons (p.last == 2J+1 - special cases handled above)
  if (isMonopole(p)) { return 0; } // PDG 11i - For now no spin information is provided. Also matches the definition in the G4Extensions/Monopole package.
  if (isGenericMultichargedParticle(p)) { return 0; } // APID Matches the definition in the G4Extensions/Monopole package.
  if (isNucleus(p)) { return 1; }  // TODO need to explicitly deal with nuclei
  return p.last() > 0 ? 1 : 0; //  Anything else - best guess
}
template<> inline int spin2(const int& p){ auto value_digits = DecodedPID(p); return spin2(value_digits);}
 
template<class T> inline double spin(const T& p) { return spin(p->pdg_id()); }
template<> inline double spin(const DecodedPID& p) { return 1.0*spin2(p)/2.0; }
template<> inline double spin(const int& p){ auto value_digits = DecodedPID(p); return spin(value_digits);}
 
 
// APID: Returns an unordered list of the quarks contained by the current particle
template<class T> inline std::vector<int> containedQuarks(const T& p) { return containedQuarks(p->pdg_id()); }
template<> inline std::vector<int> containedQuarks(const int& p) {
  auto pp = DecodedPID(p);
  std::vector<int> quarks;
  if (isQuark(pp.pid())) { quarks.push_back(std::abs(pp.pid())); }
  else if (isDiquark(pp)) { quarks.push_back(pp(0)); quarks.push_back(pp(1)); }
  else if (isMeson(pp)) { quarks.push_back(*(pp.second.rbegin() + 1)); quarks.push_back(*(pp.second.rbegin()+2)); }
  else if (isBaryon(pp)) { for (size_t digit = 1; digit < 4; ++digit) { quarks.push_back(*(pp.second.rbegin() + digit)); } }
  else if (isTetraquark(pp)) { for (size_t digit = 1; digit < 5; ++digit) { quarks.push_back(*(pp.second.rbegin() + digit)); } }
  else if (isPentaquark(pp)) { for (size_t digit = 1; digit < 6; ++digit) { quarks.push_back(*(pp.second.rbegin() + digit)); } }
  else if (isNucleus(pp)) { const int A = std::abs(baryonNumber3(pp)/3); const int Z = std::abs(numberOfProtons(pp)); const int L = std::abs(numberOfLambdas(pp));
    const int n_uquarks = A + Z; const int n_dquarks = 2*A - Z - L; const int n_squarks = L;
    quarks.reserve(3*A); quarks.insert(quarks.end(), n_dquarks, 1); quarks.insert(quarks.end(), n_uquarks, 2); quarks.insert(quarks.end(), n_squarks, 3); }
  else if (isSUSY(pp)) { // APID SUSY case
    pp = pp.shift(1);
    if ( pp.ndigits() > 1 ) { // skip squarks
      if ( pp.ndigits() == 3 ) { pp = DecodedPID(pp(1)); } // Handle ~q qbar pairs
      if ( pp.ndigits()  > 3 ) { pp = pp.shift(1); } // Drop gluinos and squarks
      return containedQuarks(pp.pid());
    }
  }
  return quarks;
}
template<> inline std::vector<int> containedQuarks(const DecodedPID& p) { return containedQuarks(p.pid()); }
 
template<class T> inline bool isStrongInteracting(const T& p){return isStrongInteracting(p->pdg_id());}
template<> inline bool isStrongInteracting(const int& p) { return (isGluon(p) || isQuark(p) || isDiquark(p) || isGlueball(p) || isLeptoQuark(p) || isHadron(p) || isRHadron(p));} // APID: Glueballs and R-Hadrons are also strong-interacting
 
#endif