gamma_m.hpp

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#pragma once

#include <array>

#if __cplusplus >= 201402L
#define QCD_CONSTEXPR_AFTER_CXX14 constexpr
#else
#define QCD_CONSTEXPR_AFTER_CXX14
#endif

namespace QCD{

  constexpr unsigned gamma_m_max_order = 4;

  namespace detail{

    namespace gamma_m{
      constexpr double pi = 3.141592653589793238462643383279;
      constexpr double zeta_3 = 1.202056903159594285399738161511449990765;
      constexpr double zeta_4 = pi*pi*pi*pi/90.;
      constexpr double zeta_5 = 1.036927755143369926331365486457034168057;
      constexpr double zeta_6 = 1.017343061984449139714517929790920527902;
      constexpr double zeta_7 = 1.008349277381922826839797549849796759600;

      constexpr auto max_order = gamma_m_max_order;

      // gamma_m = - sum gamma_m_ij nf^j as^(i+1)
      // as = alpha_s/pi
      //taken from Baikov, Chetyrkin, Kuehn arXiv:1402.6611
      constexpr double gamma_m_00 = 1;

      constexpr double gamma_m_10 = 101./24.;
      constexpr double gamma_m_11 = -5./36.;

      constexpr double gamma_m_20 = 1249./64.;
      constexpr double gamma_m_21 = -277./216. - 5./6.*zeta_3;
      constexpr double gamma_m_22 = -35./1296.;

      constexpr double gamma_m_30 =
    4603055./41472. + 530./27.*zeta_3 - 275./8.*zeta_5;
      constexpr double gamma_m_31 =
    -91723./6912. - 2137./144.*zeta_3 + 55./16.*zeta_4 + 575./72.*zeta_5;
      constexpr double gamma_m_32 =
    2621./31104. + 25./72.*zeta_3 - 5./24.*zeta_4;
      constexpr double gamma_m_33 = -83./15552. + zeta_3/108.;

      constexpr double gamma_m_40 =
    + 99512327./165888. + 23201233./124416.*zeta_3 + 3025./32.*zeta_3*zeta_3
    - 349063./4608.*zeta_4 - 28969645./31104.*zeta_5 + 15125./64.*zeta_6
    + 25795./64.*zeta_7
    ;
      constexpr double gamma_m_41 =
    - 150736283./1492992. - 391813./2592.*zeta_3 - 2365./288.*zeta_3*zeta_3
    + 1019371./13824.*zeta_4 + 12469045./62208.*zeta_5 - 39875./576.*zeta_6
    - 56875./864.*zeta_7
    ;
      constexpr double gamma_m_42 =
    + 660371./373248. + 251353./31104.*zeta_3 + 725./432.*zeta_3*zeta_3 -
    41575./6912.*zeta_4 - 33005./10368.*zeta_5 + 2875./864.*zeta_6
    ;
      constexpr double gamma_m_43 =
    91865./1492992. + 803./5184.*zeta_3 + 7./144.*zeta_4 - 5./27.*zeta_5
    ;
      constexpr double gamma_m_44 = -65./62208. - 5./3888.*zeta_3 + zeta_4/432.;

      constexpr auto max_nf_pow =
    std::array<unsigned,1u + max_order>{{0u, 1u, 2u, 3u, 4u}};

      inline QCD_CONSTEXPR_AFTER_CXX14
      unsigned coeffs_start_index(unsigned order){
    return (order == 0)?
      0:
      (1u + max_nf_pow[order-1] + coeffs_start_index(order-1))
      ;
      }

      constexpr auto coeffs = std::array<double,15>{{
      gamma_m_00,
      gamma_m_10, gamma_m_11,
      gamma_m_20, gamma_m_21, gamma_m_22,
      gamma_m_30, gamma_m_31, gamma_m_32, gamma_m_33,
      gamma_m_40, gamma_m_41, gamma_m_42, gamma_m_43, gamma_m_44
    }};

      inline QCD_CONSTEXPR_AFTER_CXX14
      unsigned gamma_m_max_nf_pow(unsigned order){
    // assert(order <= max_order);
    using namespace detail::gamma_m;
    return max_nf_pow[order];
      }

      inline QCD_CONSTEXPR_AFTER_CXX14
      double gamma_m_nf_coeff(unsigned order, unsigned nfpow){
    // assert(order <= max_order);
    // assert(nfpow <= max_nf_pow(order));
    using namespace detail::gamma_m;
    return( coeffs[coeffs_start_index(order) + nfpow] );
      }

      inline QCD_CONSTEXPR_AFTER_CXX14
      double helper(unsigned order, int nf, unsigned nf_pow){
    //assert(nf_pow <= max_nf_pow[order])
    return
      (nf_pow == max_nf_pow[order])?
      gamma_m_nf_coeff(order, nf_pow):
      gamma_m_nf_coeff(order, nf_pow) + nf*helper(order, nf, nf_pow + 1)
      ;
      }

      inline QCD_CONSTEXPR_AFTER_CXX14
      double gamma_m(unsigned order, int nf){
    // assert(order <= max_order);
    using namespace detail::gamma_m;
    return helper(order, nf, 0);
      }

      inline QCD_CONSTEXPR_AFTER_CXX14
      double helper(
      unsigned order,
      int nf,
      double alpha_s,
      unsigned cur_order
      ){
    //assert(order <= max_order)
    return (cur_order == order)?
      gamma_m(order, nf):(
          + gamma_m(cur_order, nf)
          + alpha_s/pi * helper(order, nf, alpha_s, cur_order + 1)
      );
      }
    }
  }


  inline QCD_CONSTEXPR_AFTER_CXX14
  double gamma_m(unsigned order, int nf, double alpha_s){
    // assert(order <= max_order);
    using namespace detail::gamma_m;
    return - alpha_s/pi*helper(order, nf, alpha_s, 0);
  }


  inline QCD_CONSTEXPR_AFTER_CXX14
  double gamma_m(unsigned order, int nf){
    return detail::gamma_m::gamma_m(order, nf);
  }


  inline QCD_CONSTEXPR_AFTER_CXX14
  unsigned gamma_m_max_nf_pow(unsigned order){
    return detail::gamma_m::gamma_m_max_nf_pow(order);
  }

  inline QCD_CONSTEXPR_AFTER_CXX14
  double gamma_m_nf_coeff(unsigned order, unsigned nfpow){
    return detail::gamma_m::gamma_m_nf_coeff(order, nfpow);
  }


  // the following functions are just defined for safety, e.g.
  // to prevent unintended implicit conversion from negative ints
  // please avoid using them

  inline QCD_CONSTEXPR_AFTER_CXX14
  double gamma_m_nf_coeff(int order, unsigned nfpow){
    // assert(order >= 0);
    return gamma_m_nf_coeff(static_cast<unsigned>(order), nfpow);
  }

  inline QCD_CONSTEXPR_AFTER_CXX14
  double gamma_m_nf_coeff(unsigned order, int nfpow){
    // assert(nfpow >= 0);
    return gamma_m_nf_coeff(order, static_cast<unsigned>(nfpow));
  }

  inline QCD_CONSTEXPR_AFTER_CXX14
  double gamma_m_nf_coeff(int order, int nfpow){
    // assert(order >= 0);
    // assert(nfpow >= 0);
    return
      gamma_m_nf_coeff(static_cast<unsigned>(order), static_cast<unsigned>(nfpow));
  }

}

#undef QCD_CONSTEXPR_AFTER_CXX14