VectorSingletDM.cpp

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//   GAMBIT: Global and Modular BSM Inference Tool
//   *********************************************

#include "gambit/Elements/gambit_module_headers.hpp"
#include "gambit/Elements/virtual_higgs.hpp"
#include "gambit/DarkBit/DarkBit_rollcall.hpp"
#include "gambit/Utils/ascii_table_reader.hpp"
#include "boost/make_shared.hpp"
#include "gambit/DarkBit/DarkBit_utils.hpp"

namespace Gambit
{

  namespace DarkBit
  {

    class VectorSingletDM
    {
      public:
        VectorSingletDM(
            TH_ProcessCatalog* const catalog,
            double gammaH,
            double vev,
            double alpha_strong)
        : Gamma_mh(gammaH), v0 (vev),
          alpha_s (alpha_strong)
        {
          mh   = catalog->getParticleProperty("h0_1").mass;
          mb   = catalog->getParticleProperty("d_3").mass;
          mc   = catalog->getParticleProperty("u_2").mass;
          mtau = catalog->getParticleProperty("e-_3").mass;
          mt   = catalog->getParticleProperty("u_3").mass;
          mZ0  = catalog->getParticleProperty("Z0").mass;
          mW   = catalog->getParticleProperty("W+").mass;
        };
        ~VectorSingletDM() {}

        double Dh2 (double s)
        {
          return 1/((s-mh*mh)*(s-mh*mh)+mh*mh*Gamma_mh*Gamma_mh);
        }

        double sv(std::string channel, double lambda, double mass, double v)
        {
          // Note: Valid for mass > 45 GeV
          double s = 4*mass*mass/(1-v*v/4);
          double sqrt_s = sqrt(s);
          if ( sqrt_s < 90 )
          {
            piped_invalid_point.request(
                "VectorSingletDM sigmav called with sqrt_s < 90 GeV.");
            return 0;
          }

          if ( channel == "hh" )
          {
            if ( sqrt_s > mh*2 )
            {
              return sv_hh(lambda, mass, v);
            }
            else return 0;
          }

          if ( channel == "bb" and sqrt_s < mb*2 ) return 0;
          if ( channel == "cc" and sqrt_s < mc*2  ) return 0;
          if ( channel == "tautau" and sqrt_s < mtau*2 ) return 0;
          if ( channel == "tt" and sqrt_s < mt*2 ) return 0;
          if ( channel == "ZZ" and sqrt_s < mZ0*2) return 0;
          if ( channel == "WW" and sqrt_s < mW*2) return 0;

          if ( sqrt_s < 300 )
          {
            double br = virtual_SMHiggs_widths(channel,sqrt_s);
            double Gamma_s = virtual_SMHiggs_widths("Gamma",sqrt_s);
            double GeV2tocm3s1 = gev2cm2*s2cm;
            double y = s/pow(mass, 2);

            // Explicitly close channel for off-shell top quarks
            if ( channel == "tt" and sqrt_s < mt*2) return 0;

            double res = 2*lambda*lambda*v0*v0*(1-y/3 + pow(y,2)/12)/3/
              sqrt_s*Dh2(s)*Gamma_s*GeV2tocm3s1*br;
            return res;
          }
          else
          {
            if ( channel == "bb" ) return sv_ff(lambda, mass, v, mb, true);
            if ( channel == "cc" ) return sv_ff(lambda, mass, v, mc, true);
            if ( channel == "tautau" ) return sv_ff(lambda, mass, v, mtau, false);
            if ( channel == "tt" ) return sv_ff(lambda, mass, v, mt, true);
            if ( channel == "ZZ" ) return sv_ZZ(lambda, mass, v);
            if ( channel == "WW" ) return sv_WW(lambda, mass, v);
          }
          return 0;
        }

        // Annihilation into W bosons.
        double sv_WW(double lambda, double mass, double v)
        {
          double s = 4*mass*mass/(1-v*v/4);
          double x = pow(mW,2)/s;
          double y = s/pow(mass, 2);
          double GeV2tocm3s1 = gev2cm2*s2cm;
          return pow(lambda,2)*s/24/M_PI*sqrt(1-4*x)*(1-y/3 + pow(y,2)/12)*
          Dh2(s)*(1-4*x+12*pow(x,2))*GeV2tocm3s1;
        }

        // Annihilation into Z bosons.
        double sv_ZZ(double lambda, double mass, double v)
        {
          double s = 4*mass*mass/(1-v*v/4);
          double x = pow(mZ0,2)/s;
          double y = s/pow(mass, 2);
          double GeV2tocm3s1 = gev2cm2*s2cm;
          return pow(lambda,2)*s/48/M_PI*sqrt(1-4*x)*(1-y/3 + pow(y,2)/12)*
          Dh2(s)*(1-4*x+12*pow(x,2))*GeV2tocm3s1;
        }

        // Annihilation into fermions
        double sv_ff(
            double lambda, double mass, double v, double mf, bool is_quark)
        {
          double s = 4*mass*mass/(1-v*v/4);
          double vf = sqrt(1-4*pow(mf,2)/s);
          double y = s/pow(mass, 2);
          double Xf = 1;
          if ( is_quark ) Xf = 3 *
            (1+(3/2*log(pow(mf,2)/s)+9/4)*4*alpha_s/3/M_PI);
          double GeV2tocm3s1 = gev2cm2*s2cm;
          return pow(lambda,2)*(1-y/3 + pow(y,2)/12)*
            pow(mf,2)/12/M_PI*Xf*pow(vf,3) * Dh2(s) *GeV2tocm3s1;
        }

        double sv_hh(double lambda, double mass, double v)
        {
          // Hardcode lower limit for velocity to avoid nan results.
          v = std::max(v, 1e-6);
          double GeV2tocm3s1 = gev2cm2*s2cm;
          double s = 4*mass*mass/(1-v*v/4);  // v is relative velocity
          double xV = mass*mass/s;
          double xH = mh*mh/s;
          double xG = Gamma_mh*mh/s;
          double beta =  (s - 2*pow(mh,2))/sqrt((s - 4*pow(mh,2))*(s - 4*pow(mass,2)));
          double vH = sqrt(1-4*xH);

          return GeV2tocm3s1*(vH*pow(lambda,2)*pow(s,-3)*pow(xV,-4)*pow(pow(xG,2) + pow(-1 + xH,2),-1)*
          ((4*lambda*s*xV*(1 - 6*xV + xH*(2 + 4*xV))*pow(v0,2)*(1 + xH + pow(xG,2) - 2*pow(xH,2))*(xV - 4*xH*xV + pow(xH,2)) +
          4*(1 + 4*xV*(-1 + 3*xV))*pow(s,2)*(xV - 4*xH*xV + pow(xH,2))*(pow(xG,2) + pow(1 + 2*xH,2))*pow(xV,2) +
          pow(lambda,2)*pow(v0,4)*(pow(xG,2) + pow(-1 + xH,2))*(xV + (1 + 12*xV*(-1 + 4*xV))*pow(xH,2) + (4 - 32*xV)*pow(xH,3) + 6*pow(xH,4) - 64*xH*pow(xV,3) +
          96*pow(xV,4)))*pow(xV - 4*xH*xV + pow(xH,2),-1) - 8*beta*lambda*(-1 + 4*xH)*atanh(1/beta)*pow(v0,2)*pow(1 - 2*xH,-1)*
          (2*s*(-1 + 2*xH)*xV*((-1 + xH)*(1 + 2*xH) - pow(xG,2))*(2*xV*pow(-1 + xH,2) + pow(xH,2) - 4*(1 + 2*xH)*pow(xV,2) + 24*pow(xV,3)) -
          lambda*pow(v0,2)*(pow(xG,2) + pow(-1 + xH,2))*(-8*xV*pow(xH,3) + 3*pow(xH,4) - pow(xH,2)*(1 + 8*pow(xV,2)) + 4*xH*(xV + 8*pow(xV,3)) -
          2*xV*(1 - 2*xV + 24*pow(xV,3))))*pow(1 - 6*xH + 8*pow(xH,2),-1)))/(2304*M_PI);
        }

      private:
        double Gamma_mh, mh, v0, alpha_s, mb, mc, mtau, mt, mZ0, mW;
    };

    void DarkMatter_ID_VectorSingletDM(std::string& result) { result = "V"; }
    void DarkMatterConj_ID_VectorSingletDM(std::string& result) { result = "V"; }

    void DD_couplings_VectorSingletDM_Z2(DM_nucleon_couplings &result)
    {
      using namespace Pipes::DD_couplings_VectorSingletDM_Z2;
      const Spectrum& spec = *Dep::VectorSingletDM_Z2_spectrum;
      const SubSpectrum& he = spec.get_HE();
      double mass = spec.get(Par::Pole_Mass,"V");
      double lambda = he.get(Par::dimensionless,"lambda_hV");
      double mh = spec.get(Par::Pole_Mass,"h0_1");

      // Expressions taken from Cline et al. (2013, PRD 88:055025, arXiv:1306.4710)
      double fp = 2./9. + 7./9.*(*Param["fpu"] + *Param["fpd"] + *Param["fps"]);
      double fn = 2./9. + 7./9.*(*Param["fnu"] + *Param["fnd"] + *Param["fns"]);

      result.gps = lambda*fp*m_proton/pow(mh,2)/mass/2;
      result.gns = lambda*fn*m_neutron/pow(mh,2)/mass/2;
      result.gpa = 0;  // Only SI cross-section
      result.gna = 0;

      logger() << LogTags::debug << "Vector DM DD couplings:" << std::endl;
      logger() << " gps = " << result.gps << std::endl;
      logger() << " gns = " << result.gns << std::endl;
      logger() << " gpa = " << result.gpa << std::endl;
      logger() << " gna = " << result.gna << EOM;

    } // function DD_couplings_VectorSingletDM_Z2

    void TH_ProcessCatalog_VectorSingletDM_Z2(DarkBit::TH_ProcessCatalog &result)
    {
      using namespace Pipes::TH_ProcessCatalog_VectorSingletDM_Z2;
      using std::vector;
      using std::string;

      // Initialize empty catalog
      TH_ProcessCatalog catalog;
      TH_Process process_ann("V", "V");

      // Explicitly state that Vector DM is self-conjugate
      process_ann.isSelfConj = true;

      // Import particle masses and couplings

      // Convenience macros
      #define getSMmass(Name, spinX2)                                           \
       catalog.particleProperties.insert(std::pair<string, TH_ParticleProperty> \
       (Name , TH_ParticleProperty(SM.get(Par::Pole_Mass,Name), spinX2)));
      #define addParticle(Name, Mass, spinX2)                                   \
       catalog.particleProperties.insert(std::pair<string, TH_ParticleProperty> \
       (Name , TH_ParticleProperty(Mass, spinX2)));

      // Import Spectrum objects
      const Spectrum& spec = *Dep::VectorSingletDM_Z2_spectrum;
      const SubSpectrum& he = spec.get_HE();
      const SubSpectrum& SM = spec.get_LE();
      const SMInputs& SMI   = spec.get_SMInputs();

      // Import couplings
      double lambda = he.get(Par::dimensionless,"lambda_hV");
      double v = he.get(Par::mass1,"vev");
      double alpha_s = SMI.alphaS;      // alpha_s(mZ)^MSbar

      // Get SM pole masses
      getSMmass("e-_1",     1)
      getSMmass("e+_1",     1)
      getSMmass("e-_2",     1)
      getSMmass("e+_2",     1)
      getSMmass("e-_3",     1)
      getSMmass("e+_3",     1)
      getSMmass("Z0",     2)
      getSMmass("W+",     2)
      getSMmass("W-",     2)
      getSMmass("g",      2)
      getSMmass("gamma",  2)
      getSMmass("u_3",      1)
      getSMmass("ubar_3",   1)
      getSMmass("d_3",      1)
      getSMmass("dbar_3",   1)

      // Pole masses not available for the light quarks.
      addParticle("u_1"   , SMI.mU,  1) // mu(2 GeV)^MS-bar, not pole mass
      addParticle("ubar_1", SMI.mU,  1) // mu(2 GeV)^MS-bar, not pole mass
      addParticle("d_1"   , SMI.mD,  1) // md(2 GeV)^MS-bar, not pole mass
      addParticle("dbar_1", SMI.mD,  1) // md(2 GeV)^MS-bar, not pole mass
      addParticle("u_2"   , SMI.mCmC,1) // mc(mc)^MS-bar, not pole mass
      addParticle("ubar_2", SMI.mCmC,1) // mc(mc)^MS-bar, not pole mass
      addParticle("d_2"   , SMI.mS,  1) // ms(2 GeV)^MS-bar, not pole mass
      addParticle("dbar_2", SMI.mS,  1) // ms(2 GeV)^MS-bar, not pole mass

      // Masses for neutrino flavour eigenstates. Set to zero.
      // (presently not required)
      addParticle("nu_e",     0.0, 1)
      addParticle("nubar_e",  0.0, 1)
      addParticle("nu_mu",    0.0, 1)
      addParticle("nubar_mu", 0.0, 1)
      addParticle("nu_tau",   0.0, 1)
      addParticle("nubar_tau",0.0, 1)

      // Higgs-sector masses
      double mV = spec.get(Par::Pole_Mass,"V");
      double mH = spec.get(Par::Pole_Mass,"h0_1");
      addParticle("V",        mV, 2)  // Vector DM
      addParticle("h0_1",     mH, 0)  // SM-like Higgs
      addParticle("pi0",   meson_masses.pi0,       0)
      addParticle("pi+",   meson_masses.pi_plus,   0)
      addParticle("pi-",   meson_masses.pi_minus,  0)
      addParticle("eta",   meson_masses.eta,       0)
      addParticle("rho0",  meson_masses.rho0,      1)
      addParticle("rho+",  meson_masses.rho_plus,  1)
      addParticle("rho-",  meson_masses.rho_minus, 1)
      addParticle("omega", meson_masses.omega,     1)

      // Get rid of convenience macros
      #undef getSMmass
      #undef addParticle

      // Import Decay information

      // Import decay table from DecayBit
      const DecayTable* tbl = &(*Dep::decay_rates);

      // Save Higgs width for later
      double gammaH = tbl->at("h0_1").width_in_GeV;

      // Set of imported decays
      std::set<string> importedDecays;

      // Minimum branching ratio to include
      double minBranching = 0;

      // Import relevant decays (only Higgs and subsequent decays)
      using DarkBit_utils::ImportDecays;
      // Notes: Virtual Higgs decays into offshell W+W- final states are not
      // imported.  All other channels are correspondingly rescaled.  Decay
      // into VV final states is accounted for, leading to zero photons.
      ImportDecays("h0_1", catalog, importedDecays, tbl, minBranching,
          daFunk::vec<std::string>("Z0", "W+", "W-", "e+_2", "e-_2", "e+_3", "e-_3"));

      // Instantiate new VectorSingletDM_Z2 object
      auto vectorDM = boost::make_shared<VectorSingletDM>(&catalog, gammaH, v, alpha_s);

      // Populate annihilation channel list and add thresholds to threshold
      // list.
      // (remark: the lowest threshold is here = 2*mV, whereas in DS-internal
      // conventions, this lowest threshold is not listed)
      process_ann.resonances_thresholds.threshold_energy.push_back(2*mV);
      auto channel =
        daFunk::vec<string>("bb", "WW", "cc", "tautau", "ZZ", "tt", "hh");
      auto p1 =
        daFunk::vec<string>("d_3",   "W+", "u_2",   "e+_3", "Z0", "u_3",   "h0_1");
      auto p2 =
        daFunk::vec<string>("dbar_3","W-", "ubar_2","e-_3", "Z0", "ubar_3","h0_1");
      {
        for ( unsigned int i = 0; i < channel.size(); i++ )
        {
          double mtot_final =
            catalog.getParticleProperty(p1[i]).mass +
            catalog.getParticleProperty(p2[i]).mass;
          // Include final states that are open for T~m/20
          if ( mV*2 > mtot_final*0.5 )
          {
            daFunk::Funk kinematicFunction = daFunk::funcM(vectorDM,
                &VectorSingletDM::sv, channel[i], lambda, mV, daFunk::var("v"));
            TH_Channel new_channel(
                daFunk::vec<string>(p1[i], p2[i]), kinematicFunction
                );
            process_ann.channelList.push_back(new_channel);
          }
          if ( mV*2 > mtot_final )
          {
            process_ann.resonances_thresholds.threshold_energy.
              push_back(mtot_final);
          }
        }
      }

      // Populate resonance list
      if ( mH >= mV*2 ) process_ann.resonances_thresholds.resonances.
          push_back(TH_Resonance(mH, gammaH));

      catalog.processList.push_back(process_ann);

      // Validate
      catalog.validate();

      result = catalog;

    } // function TH_ProcessCatalog_VectorSingletDM_Z2
  }
}