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sigofunctionsDM.hh
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sigofunctionsDM.hh
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#include <gsl/gsl_integration.h>
#include <gsl/gsl_math.h>
#include <string>
#include <sstream>
#include <iostream>
#include <ctime>
#include <cmath>
#include <fstream>
using namespace std;
/*==============================================================================================================
==== Emperical Nuclear parameters - working in units of MeV and fm^-1 for energies and fm for distances ========
==============================================================================================================*/
const double pi = M_PI; // Pie (yummm)
const double MeVtoinvFM = 0.0008065*(2*pi); // approximate conversion factor
const double rho0 = 0.153; // staturation density (fm^-3)
double Kompress = 200*MeVtoinvFM; // Compression modulus (fm^-1)
double mass = 938*MeVtoinvFM; // nucleon mass (fm^-1)
double massOmega = 783*MeVtoinvFM; // omega mass (fm^-1)
double massSigma = 550*MeVtoinvFM; // approximate sigma mass (fm^-1)
double mstar = 0.75*mass; // effective mass
const double asymm = 32.5*MeVtoinvFM; // symmetry energy coefficient (fm^-1)
const double BperA = -16.3*MeVtoinvFM; // Binding energy (fm^-1)
const double MPI = 90e3*MeVtoinvFM;
/*===============================================================================================================
================================== Constant parameters at saturation ============================================
===============================================================================================================*/
double Gomega2(double RHO, double kF){
double E = sqrt(kF*kF + mstar*mstar);
double fieldstrength = (mass + BperA - E)/RHO;
return fieldstrength;
}
double Grho2(double RHO, double kF){
double fieldstrength = 8*(asymm - kF*kF/(6*sqrt(kF*kF + mstar*mstar)))/RHO;
return fieldstrength;
}
double alpha1(double RHO, double kF){
double a1 = Kompress - Gomega2(RHO, kF)*6*pow(kF, 3)/(pi*pi) - 3 * kF*kF/sqrt(kF*kF + mstar*mstar);
return a1;
}
double beta1(double RHO, double kF){
double b1 = 2*mass*(mass - mstar)*alpha1(RHO,kF);
return b1;
}
double gamma1(double RHO, double kF){
double g1 = 3*pow((mass - mstar),2) * alpha1(RHO, kF);
return g1;
}
double del1(double RHO, double IONE, double kF){
double d1 = -alpha1(RHO, kF)*IONE - 6 * pow(kF,3)/(pi*pi) * (mstar*mstar/(kF*kF + mstar*mstar));
return d1;
}
double alpha3 = (mass - mstar);
double beta3 = mass * pow((mass - mstar),2);
double gamma3 = pow((mass - mstar),3);
double del3(double ITHREE){
double d3 = ITHREE;
return ITHREE;
}
double alpha2 = 0.5 * pow((mass - mstar),2);
double beta2 = (1./3.) * mass * pow((mass - mstar),3);
double gamma2 = 0.25 * pow((mass - mstar),4);
double del2(double RHO, double ITWO, double kF){
double d2 = RHO* (mass + BperA) - ITWO - 0.5 * Gomega2(RHO, kF) * RHO*RHO;
return d2;
}
/*===============================================================================================================
====================================== variable parameters ======================================================
===============================================================================================================*/
double C(double RHO, double IONE, double ITWO, double ITHREE, double kF){
double ag21 = ( alpha2*gamma1(RHO, kF) - alpha1(RHO, kF)*gamma2 );
double ag31 = ( alpha3*gamma1(RHO, kF) - alpha1(RHO, kF)*gamma3 );
double ad31 = ( alpha3*del1(RHO, IONE, kF) - alpha1(RHO, kF)*del3(ITHREE) );
double ad21 = ( alpha2*del1(RHO, IONE, kF) - alpha1(RHO, kF)*del2(RHO, ITWO, kF) );
double ab31 = ( alpha3*beta1(RHO, kF) - alpha1(RHO, kF)*beta3 );
double ab21 = ( alpha2*beta1(RHO, kF) - alpha1(RHO, kF)*beta2 );
double cnumerator = -ab21*ad31 + ab31*ad21;
double cdenominator = -ab21*ag31 + ab31*ag21;
double c = cnumerator/cdenominator;
//c = 0;
return c;
}
double B(double RHO, double IONE, double ITWO, double ITHREE, double kF){
double ag21 = ( alpha2*gamma1(RHO, kF) - alpha1(RHO, kF)*gamma2 );
double ag31 = ( alpha3*gamma1(RHO, kF) - alpha1(RHO, kF)*gamma3 );
double ad31 = ( alpha3*del1(RHO, IONE, kF) - alpha1(RHO, kF)*del3(ITHREE) );
double ad21 = ( alpha2*del1(RHO, IONE, kF) - alpha1(RHO, kF)*del2(RHO, ITWO, kF) );
double ab31 = ( alpha3*beta1(RHO, kF) - alpha1(RHO, kF)*beta3 );
double ab21 = ( alpha2*beta1(RHO, kF) - alpha1(RHO, kF)*beta2 );
double bnumerator = -ad31 + ag31*C(RHO, IONE, ITWO, ITHREE, kF);
double bdenominator = -ab31;
double b = bnumerator/bdenominator;
// b = 0;
return b;
}
double Gsigma2(double RHO, double CONSTB, double CONSTC, double IONE, double kF){
double sigmanumerator = alpha1(RHO, kF);
double sigmadenominator = del1(RHO, IONE, kF) - beta1(RHO, kF)*CONSTB - gamma1(RHO, kF)*CONSTC;
double fieldstrength = sigmanumerator/sigmadenominator;
return fieldstrength;
}
/*===============================================================================================================
================================= functions to be integrated ====================================================
===============================================================================================================*/
double rhoS(double k, void *param){ //Scalar density Integrand
double Integrand = 0;
double MEFF = *(double *) param;
double k2 = k*k;
double E = sqrt(k2 + MEFF*MEFF);
Integrand = 2*k2*MEFF/(pi*pi * E);
return Integrand;
}
double I1(double k, void *param){ //relevant integral for solving set of eqns
double Integrand = 0;
double m = *(double *) param;
double E = sqrt(k*k + m*m);
Integrand = (2/(pi*pi)) * pow(k,4) / pow(E,3);
return Integrand;
}
double I2(double k, void *param){ //relevant integral for solving set of eqns
double Integrand = 0;
double m = *(double *) param;
double k2 = k*k; //squared cuz ima lazy
double E = sqrt(k2 + m*m);
Integrand = (2/(pi*pi)) * k2* E;
return Integrand;
}
double I3(double k, void *param){ //relevant integral for solving set of eqns
double Integrand = 0;
double m = *(double *) param;
double k2 = k*k; //squared cuz ima lazy
double E = sqrt(k2 + m*m);
Integrand = (2/(pi*pi)) * k2* m / E;
return Integrand;
}
double P1(double k, void *param){ //relevant integral for solving set of eqns
double Integrand = 0;
double m = *(double *) param;
double E = sqrt(k*k + m*m);
Integrand = (2/(pi*pi)) * pow(k,4) / E;
return Integrand;
}
double EKIN(double k, void *param){ //Kinetic Energy Integrand-same form as I3
//so use it in the integratori to solve for del3
double Integrand = 0;
double m = *(double *) param;
double k2 = k*k; //squared cuz ima lazy
double E = sqrt(k2 + m*m);
Integrand = (2/(pi*pi)) * k2* E;
return Integrand;
}
/* =================== ANALYTIC APPROXIMATIONS FOR NUMERICAL INTEGRALS =========================*/
double eye1(double kF, double m){
double x = kF/m;
double t = sqrt(1 + x*x);
return 2/(pi*pi) * m*m*(0.5*x*t + x/t - (1.5)*log(x+t));
}
double eye3(double kF, double m){
double x = kF/m;
double t = sqrt(1 + x*x);
return 1./(pi*pi) * pow(m, 3)*(x*t - log(x+t));
}
double eye2(double kF, double m){
double x = kF/m;
double t = sqrt(1 + x*x);
return 1./(2*pi*pi) * pow(m, 4)*(-0.5*x*t + x*pow(t, 3) - 0.5*log(x+t));
}
/*=================================== DM CONSTRAINED PARAMETERS ===========================================*/
double Gchi(double sigchi2, double mchi, double mpi){
double arg = sqrt(sigchi2) * mpi*mpi/( sqrt(20.)* mchi);
return sqrt(arg);
}
double Gpi(double sigchin, double mn, double mchi, double mpi, double gchi){
double arg = sqrt(sigchin)* (mn + mchi)*mpi*mpi/( sqrt(3.)*gchi*mn*mchi);
return sqrt(arg);
}