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666 lines (623 loc) · 21.8 KB
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/*
potential.cpp
Copyright (c) Michael Strickland
GNU General Public License (GPLv3)
See detailed text in license directory
*/
#include <cmath>
#include <iostream>
#include <fstream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <complex>
using namespace std;
#include "mpisolve.h"
#include "grid.h"
#include "specialfunctions.h"
#include "potential.h"
#include "intde2.h"
#define Power(a,b) pow((double)a,(double)b)
#define Sqrt(a) sqrt((double)a)
// used for numerical integration when necessary
int lenaw=LENAW;
double aw[LENAW];
// global variable useful for subroutines
double dx,dy,dz;
double r;
double md;
double mdp;
// determines x distance to center of simulation volume in lattice units
double distx(int sx)
{
return sx - ((double)NUMX+1.)/2. + ( ((double)nodeID) - ((double)numNodes)/2. )*NUMX;
}
// determines y distance to center of simulation volume in lattice units
double disty(int sy)
{
return sy - ((double)NUM+1.)/2.;
}
// determines z distance to center of simulation volume in lattice units
double distz(int sz)
{
return sz - ((double)NUM+1.)/2.;
}
// determines square of distance to center of simulation volume in lattice units
double distsq(int sx,int sy, int sz)
{
double dx,dy,dz,r2;
// coordinate system is centered in simulation volume
dx = sx - ((double)NUMX+1.)/2. + ( ((double)nodeID) - ((double)numNodes)/2. )*NUMX;
dy = sy - ((double)NUM+1.)/2.;
dz = sz - ((double)NUM+1.)/2.;
r2 = (dx*dx+dy*dy+dz*dz);
return r2;
}
dcomp potential(int sx,int sy, int sz)
{
double temp,iV,rV;
double res,err;
double m12,B,wc,e,rho;
// coordinate system is centered in simulation volume
dx = ((double) sx) - ((double)NUMX+1.)/2. + ( ((double)nodeID) - ((double)numNodes)/2. )*NUMX;
dy = ((double) sy) - ((double)NUM+1.)/2.;
dz = ((double) sz) - ((double)NUM+1.)/2.;
r = A*sqrt(dx*dx+dy*dy+dz*dz);
rho = A*sqrt(dx*dx+dy*dy);
switch(POTENTIAL) {
case 0:
// none
return 0.;
break;
case 1:
// cubic well
if ( (sx>NUM/4 && sx<=3*NUM/4) && (sy>NUM/4 && sy<=3*NUM/4) && (sz>NUM/4 && sz<=3*NUM/4) )
return -10.0;
else
return 0.0;
break;
case 2:
// quadrilateral-well in center of cube with short side in z direction
if ( (sx>NUM/4 && sx<=3*NUM/4) && (sy>NUM/4 && sy<=3*NUM/4) && (sz>3*NUM/8 && sz<=5*NUM/8) )
return -10.0;
else
return 0.0;
break;
case 3:
// 3d periodic
temp = sin(2*M_PI*(sx-1)/(NUM-1))*sin(2*M_PI*(sx-1)/(NUM-1));
temp *= sin(2*M_PI*(sy-1)/(NUM-1))*sin(2*M_PI*(sy-1)/(NUM-1));
temp *= sin(2*M_PI*(sz-1)/(NUM-1))*sin(2*M_PI*(sz-1)/(NUM-1));
return -temp+1;
break;
case 4:
// coulomb
if (r < A)
return 0.0;
else
return -1./r + 1./A;
break;
case 5:
// elliptical coulomb
dz *= 2;
r = A*sqrt(dx*dx+dy*dy+dz*dz);
if (r < A)
return 0.0;
else
return -1./r + 1./A;
break;
case 6:
// cornell plus spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4);
if (r < A)
return 4*MASS;
if (r>5.5745)
r = 5.5745;
//return -0.385/r + SIGMA*r + 4*MASS;
return -0.385/r + SIGMA*r - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 7:
// screened cornell
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4);
if (r < A)
return 4*MASS;
else
return -alphas(2*M_PI*T)*(4./3.)*exp(-md*r)/r + SIGMA*(1. - exp(-md*r))/md + 4*MASS;
break;
case 8:
// screened cornell + spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4);
if (r < A)
return 4*MASS;
else
return -alphas(2*M_PI*T)*(4./3.)*exp(-md*r)/r + SIGMA*(1. - exp(-md*r))/md - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 9:
// anisotropically screened short distance piece + isotropic cornell + spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4)*(1 + 0.07*pow(XI,0.2)*(1-A*A*dz*dz/(r*r)))*pow(1+XI,-0.29);
if (r < A)
return 4*MASS;
else
return -alphas(2*M_PI*T)*(4./3.)*exp(-md*r)/r + SIGMA*(1. - exp(-mu(T,1.4)*r))/mu(T,1.4) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 10:
// anisotropically screened cornell + spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4)*(1 + 0.07*pow(XI,0.2)*(1-A*A*dz*dz/(r*r)))*pow(1+XI,-0.29);
if (r < A)
return 4*MASS;
else
return -alphas(2*M_PI*T)*(4./3.)*exp(-md*r)/r + SIGMA*(1. - exp(-md*r))/mu(T,1.4) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 11:
// fully anisotropic screened cornell + spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4)*(1 + 0.07*pow(XI,0.2)*(1-A*A*dz*dz/(r*r)))*pow(1+XI,-0.29);
if (r < A)
return 4*MASS;
else
return -alphas(2*M_PI*T)*(4./3.)*exp(-md*r)/r + SIGMA*(1. - exp(-md*r))/md - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 12:
// fully anisotropic screened cornell using small xi expression for mu + spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4)*(1 - 0.125*XI*(A*A*dz*dz/(r*r)+1));
if (r < A)
return 4*MASS;
else
return -alphas(2*M_PI*T)*(4./3.)*exp(-md*r)/r + SIGMA*(1. - exp(-md*r))/md - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 13:
// modified fully anisotropic screened cornell + spin correction
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(T,1.4)*(pow(1+1.85*pow(XI,1.27),-0.20)+(pow(1+0.74*pow(XI,1.20),-0.23)-pow(1+1.85*pow(XI,1.27),-0.20))*(1-A*A*dz*dz/(r*r)));
if (r < A)
return 4*MASS;
else
return -0.385*exp(-md*r)/r*(1.0 + md*r) + 2.* SIGMA*(1. - exp(-md*r))/md - SIGMA*r*exp(-md*r) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 14:
// newpotential add entropy contribution
// units here are GeV for energy/momentum and GeV^(-1) for distance
md = mu(3,1.4)*(1 - 0.125*XI*(A*A*dz*dz/(r*r)+1))*T/3;
if (r < A)
return 4*MASS;
else
return -0.385*exp(-md*r)/r*(1.0 + md*r) + 2.* SIGMA*(1. - exp(-md*r))/md - SIGMA*r*exp(-md*r) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 15:
// 3d harmonic oscillator
return r*r/2;
break;
case 16:
// Mickey Mouse's Head
double Dx, Dy, Dz, R;
if (r/A <= NUM/4) return -100.0; // head
Dx = ((double) sx) - ((double)NUMX+1.)/2. + ( ((double)nodeID) - ((double)numNodes)/2. )*NUMX;
Dy = sy - ((double)NUM+1.)/2. - (1/sqrt(2.)+0.25)*NUM/4;
Dz = sz - ((double)NUM+1.)/2. - (1/sqrt(2.)+0.25)*NUM/4;
R = sqrt(4*Dx*Dx+Dy*Dy+Dz*Dz);
if (R < NUM/8) return -105.0; // ear
Dy = sy - ((double)NUM+1.)/2. + (1/sqrt(2.)+0.25)*NUM/4;
Dz = sz - ((double)NUM+1.)/2. - (1/sqrt(2.)+0.25)*NUM/4;
R = sqrt(4*Dx*Dx+Dy*Dy+Dz*Dz);
if (R < NUM/8) return -105.0; // ear
Dx = ((double) sx) - ((double)NUMX+1.)/2. - ((double)NUM/8.)+ ( ((double)nodeID) - ((double)numNodes)/2. )*NUMX;
Dy = sy - ((double)NUM+1.)/2.;
Dz = sz - ((double)NUM+1.)/2.;
R = sqrt(Dx*Dx+Dy*Dy+Dz*Dz);
if (R < NUM/6) return -100.0; // nose
return 0;
break;
case 17:
// Dodecahedron
double x, y, z;
x = dx/((NUM-1)/2);
y = dy/((NUM-1)/2);
z = dz/((NUM-1)/2);
if (12.70820393249937 + 11.210068307552588*x >= 14.674169922690343*z && 11.210068307552588*x <= 12.70820393249937 + 14.674169922690343*z && 5.605034153776295*(3.23606797749979*x - 1.2360679774997896*z) <= 6.*(4.23606797749979 + 5.23606797749979*y) && 18.1382715378281*x + 3.464101615137755*z <= 12.70820393249937 && 9.06913576891405*x + 15.70820393249937*y <= 12.70820393249937 + 3.464101615137755*z && 9.70820393249937*y <= 12.70820393249937 + 5.605034153776294*x + 14.674169922690343*z && 12.70820393249937 + 5.605034153776294*x + 9.70820393249937*y + 14.674169922690343*z >= 0. && 15.70820393249937*y + 3.464101615137755*z <= 12.70820393249937 + 9.06913576891405*x && 5.605034153776295*(-6.47213595499958*x - 1.2360679774997896*z) <= 25.41640786499874 && 3.464101615137755*z <= 9.06913576891405*x + 3.*(4.23606797749979 + 5.23606797749979*y) && 1.7320508075688772*(3.23606797749979*x + 8.47213595499958*z) <= 3.*(4.23606797749979 + 3.23606797749979*y) && 5.605034153776294*x + 9.70820393249937*y + 14.674169922690343*z <= 12.70820393249937) return -100.0;
else
return 0.;
case 18:
// Complex 3d harmonic oscillator
return dcomp(1.,1.)*dcomp(r*r/2,0.);
break;
case 19:
// complex coulomb
if (r < A)
return dcomp(0.,1.)*dcomp(-1./A,0.);
else
return dcomp(0.,1.)*dcomp(-1./r,0.);
break;
case 20:
// Complex Dodecahedron
// double x, y, z;
x = dx/((NUM-1)/2);
y = dy/((NUM-1)/2);
z = dz/((NUM-1)/2);
if (12.70820393249937 + 11.210068307552588*x >= 14.674169922690343*z && 11.210068307552588*x <= 12.70820393249937 + 14.674169922690343*z && 5.605034153776295*(3.23606797749979*x - 1.2360679774997896*z) <= 6.*(4.23606797749979 + 5.23606797749979*y) && 18.1382715378281*x + 3.464101615137755*z <= 12.70820393249937 && 9.06913576891405*x + 15.70820393249937*y <= 12.70820393249937 + 3.464101615137755*z && 9.70820393249937*y <= 12.70820393249937 + 5.605034153776294*x + 14.674169922690343*z && 12.70820393249937 + 5.605034153776294*x + 9.70820393249937*y + 14.674169922690343*z >= 0. && 15.70820393249937*y + 3.464101615137755*z <= 12.70820393249937 + 9.06913576891405*x && 5.605034153776295*(-6.47213595499958*x - 1.2360679774997896*z) <= 25.41640786499874 && 3.464101615137755*z <= 9.06913576891405*x + 3.*(4.23606797749979 + 5.23606797749979*y) && 1.7320508075688772*(3.23606797749979*x + 8.47213595499958*z) <= 3.*(4.23606797749979 + 3.23606797749979*y) && 5.605034153776294*x + 9.70820393249937*y + 14.674169922690343*z <= 12.70820393249937) return dcomp(-100.,-100.);
else
return 0.;
case 21:
// Anisotropically Screened Quarkonium Potential with Imaginary Part
if (r < A)
return dcomp(4*MASS,0.);
// real part
md = mu(3,1.4)*(1 - 0.125*XI*(A*A*dz*dz/(r*r)+1))*T/3;
rV = -0.385*exp(-md*r)/r*(1.0 + md*r) + 2.* SIGMA*(1. - exp(-md*r))/md - SIGMA*r*exp(-md*r) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
// imaginary part
md = mu(3,1.4); // do not include angular modification of md for imaginary part since this is already acctd for!
iV = ImV(r*md,acos(A*dz/r),XI); // ImV defined in specialfunctions.cpp
iV *= 0.385*T*TC;
return dcomp(rV,iV);
break;
case 22:
// Include Large-XI Behavior of md
x = A*dz/r; // Cos(theta)
double b;
b = 9./16.; // phenomenological value
md = mu(3,1.4)*Power(1 + XI*(1 + Power(2,1 + b)*(-1 + Power(x,2))*Power(1 + XI,2)*Power(2 + XI,-2 - b)),-0.25)*T/3;
if (r < A)
return 4*MASS;
else
return -0.385*exp(-md*r)/r*(1.0 + md*r) + 2.*SIGMA*(1. - exp(-md*r))/md - SIGMA*r*exp(-md*r) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 23:
// Real Part
// Include Large-XI Behavior of md - PRL
x = A*dz/r; // Cos(theta)
b = 9./16.; // phenomenological value
md = mu(3,1.4)*Power(1 + XI*(1 + Power(2,1 + b)*(-1 + Power(x,2))*Power(1 + XI,2)*Power(2 + XI,-2 - b)),-0.25)*T/3;
if (r < A)
rV = 4*MASS;
else
rV = -0.385*exp(-md*r)/r*(1.0 + md*r) + 2.*SIGMA*(1. - exp(-md*r))/md - SIGMA*r*exp(-md*r) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
// imaginary part
md = mu(3,1.4); // do not include angular modification of md for imaginary part since this is already acctd for! // this choice also fixes md to md @ 3 Tc. :|
iV = ImV(r*md,acos(A*dz/r),XI); // ImV defined in specialfunctions.cpp
iV *= 0.385*T*TC;
return dcomp(rV,iV);
break;
case 24:
// Real Part
// Include new model of Large-XI Behavior of md -- NPA B
// Running Coupling
x = A*dz/r; // Cos(theta)
md = mu(T,1.4)*Power(1. + XI*(1. - (0.0944049*(2.16919 - 29.6088*Power(x,2))*Power(1. + XI,1.5))/(3. + Power(XI,2)))*(1.62114 - (1.*(0.878423 + Power(1. + XI,0.125)))/Sqrt(3. + XI)),-0.25);
if (r < A)
rV = 4*MASS;
else
rV = -0.385*exp(-md*r)/r*(1.0 + md*r) + 2.*SIGMA*(1. - exp(-md*r))/md - SIGMA*r*exp(-md*r) - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
// imaginary part
md = mu(T,1.4); // do not include angular modification of md for imaginary part since this is already acctd for!
iV = ImV(r*md,acos(A*dz/r),XI); // ImV defined in specialfunctions.cpp
iV *= 4*alphas(2*M_PI*T)*T*TC/3;
return dcomp(rV,iV);
break;
case 25:
// Real Part
// Include new model of Large-XI Behavior of md -- NPA A
// Running Coupling
x = A*dz/r; // Cos(theta)
md = mu(T,1.4)*Power(1. + XI*(1. - (0.0944049*(2.16919 - 29.6088*Power(x,2))*Power(1. + XI,1.5))/(3. + Power(XI,2)))*(1.62114 - (1.*(0.878423 + Power(1. + XI,0.125)))/Sqrt(3. + XI)),-0.25);
if (r < A)
rV = 4*MASS;
else
rV = -0.385*exp(-md*r)/r + SIGMA*(1. - exp(-md*r))/md - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
// imaginary part
md = mu(T,1.4); // do not include angular modification of md for imaginary part since this is already acctd for!
iV = ImV(r*md,acos(A*dz/r),XI); // ImV defined in specialfunctions.cpp
iV *= 4*alphas(2*M_PI*T)*T*TC/3;
return dcomp(rV,iV);
break;
case 26:
// cornell + magnetic field
// units here are GeV for energy/momentum and GeV^(-1) for distance
m12 = 4.2048; // m1 + m2 for B0 meson
wc = eB/MASS/3; // factor of 1/3 due to charge of bottom quark
if (r < A)
return m12;
//return b;
else
return -0.385/r + SIGMA*r + MASS*wc*wc*rho*rho/8 + m12;
break;
case 27:
// 3d harmonic oscillator + magnetic field - w0 = 1 - shifted
wc = eB/MASS;
double a,bb,c,d,kx,ky;
kx = Kx;
ky = 0;
a = MASS*(1+wc*wc/4);
bb = wc*ky/4;
c = wc*kx/4;
d = MASS;
return a*rho*rho/2 + d*A*A*dz*dz/2;
case 28:
// 3d harmonic oscillator + magnetic field - w0 = 1 - not shifted
wc = eB/MASS;
kx = Kx;
ky = 0;
a = MASS*(1+wc*wc/4);
bb = wc*ky/4;
c = wc*kx/4;
d = MASS;
return a*rho*rho/2 -bb*dx*A + c*dy*A + d*A*A*dz*dz/2;
case 29:
// coulomb + magnetic field
// units here are GeV for energy/momentum and GeV^(-1) for distance
wc = eB/MASS;
kx = Kx;
ky = 0;
bb = wc*ky/4;
c = wc*kx/4;
return -bb*dx*A + c*dy*A - 1./r + MASS*wc*wc*rho*rho/8.;
break;
case 30:
// cornell + magnetic field (no tune)
// units here are GeV for energy/momentum and GeV^(-1) for distance
wc = eB/MASS/3;
kx = Kx;
ky = 0;
bb = wc*ky/4;
c = wc*kx/4;
return -bb*dx*A + c*dy*A - 0.385/r + SIGMA*r + MASS*wc*wc*rho*rho/8.;
break;
case 31:
// cornell + magnetic field + spin-spin interaction : J/Psi (J/Psi tuned)
// units here are GeV for energy/momentum and GeV^(-1) for distance
wc = 2*eB/MASS/3; // J/Psi
kx = Kx;
ky = 0;
bb = wc*ky/4;
c = wc*kx/4;
a = 2.06; // J/Psi
d = 1.982; // J/Psi
return -bb*dx*A + c*dy*A - 0.312/r + SIGMA*r + MASS*wc*wc*rho*rho/8. + SPINEXP*a*exp(-d*r);
break;
case 32:
// cornell + magnetic field + spin-spin interaction : J/Psi (Upsilon tuned)
// units here are GeV for energy/momentum and GeV^(-1) for distance
wc = 2*eB/MASS/3; // J/Psi
kx = Kx;
ky = 0;
bb = wc*ky/4;
c = wc*kx/4;
a = 0.825; // J/Psi
d = 1.982; // J/Psi
return -bb*dx*A + c*dy*A - 0.42059/r + SIGMA*r + MASS*wc*wc*rho*rho/8. + SPINEXP*a*exp(-d*r);
break;
case 33:
// cornell + magnetic field + spin-spin interaction : Upsilon (Upsilon tuned)
// units here are GeV for energy/momentum and GeV^(-1) for distance
wc = -eB/MASS/3; // Upsilon
kx = Kx;
ky = 0;
bb = wc*ky/4;
c = wc*kx/4;
a = 0.318; // Upsilon
d = 1.982; // Upsilon
return -bb*dx*A + c*dy*A - 0.42059/r + SIGMA*r + MASS*wc*wc*rho*rho/8. + SPINEXP*a*exp(-d*r);
break;
case 34:
// cornell + magnetic field + spin-spin interaction : J/Psi -- SHIFTED ALONG Y AXIS (Upsilon tuned)
// units here are GeV for energy/momentum and GeV^(-1) for distance
wc = 2*eB/MASS/3; // J/Psi
kx = Kx;
ky = 0;
bb = wc*ky/4;
c = wc*kx/4;
a = 0.825; // J/Psi
d = 1.982; // J/Psi
double y0;
y0 = round((4*SIGMA*MASS - 2*kx*eB/3)/(4*eB*eB/9)/A);
dy += y0;
r = A*sqrt(dx*dx+dy*dy+dz*dz);
rho = A*sqrt(dx*dx+dy*dy);
return -bb*dx*A + c*dy*A - 0.42059/r + SIGMA*r + MASS*wc*wc*rho*rho/8. + SPINEXP*a*exp(-d*r);
break;
default:
return 0.;
break;
}
}
// returns value of potential which should be subtracted when computing binding energies
dcomp potentialSub(int sx, int sy, int sz)
{
double iV,rV;
// coordinate system is centered in simulation volume
dx = ((double) sx) - ((double)NUMX+1.)/2. + ( ((double)nodeID) - ((double)numNodes)/2. )*NUMX;
dy = ((double) sy) - ((double)NUM+1.)/2.;
dz = ((double) sz) - ((double)NUM+1.)/2.;
r = A*sqrt(dx*dx+dy*dy+dz*dz);
switch(POTENTIAL) {
case 0:
case 1:
case 2:
case 3:
return 0.;
break;
case 4:
case 5:
return 1./A;
break;
case 6:
r = 5.5745;
//return -0.385/r + SIGMA*r + 4*MASS;
return -0.385/r + SIGMA*r - 0.8*SIGMA/(4*MASS*MASS*r) + 4*MASS;
break;
case 7:
case 8:
case 9:
case 10:
return SIGMA/mu(T,1.4) + 4*MASS;
break;
case 11:
md = mu(T,1.4)*(1 + 0.07*pow(XI,0.2)*(1-A*A*dz*dz/(r*r)))*pow(1+XI,-0.29);
return SIGMA/md + 4*MASS;
break;
case 12:
md = mu(T,1.4)*(1 - 0.125*XI*(A*A*dz*dz/(r*r)+1));
//cout << SIGMA << ", " << md << ", " << MASS << endl;
return SIGMA/md + 4*MASS;
break;
case 13:
md = mu(T,1.4)*(pow(1+1.85*pow(XI,1.27),-0.20)+(pow(1+0.74*pow(XI,1.20),-0.23)-pow(1+1.85*pow(XI,1.27),-0.20))*(1-A*A*dz*dz/(r*r)));
return SIGMA/md + 4*MASS;
break;
case 14:
md = mu(3,1.4)*(1 - 0.125*XI*(A*A*dz*dz/(r*r)+1))*T/3;
break;
case 15:
return 0.;
break;
case 16:
return 0.;
break;
case 17:
return 0.;
break;
case 18:
return 0.;
break;
case 19:
return 0.;
break;
case 20:
return 0.;
break;
case 21:
md = mu(3,1.4)*(1 - 0.125*XI*(A*A*dz*dz/(r*r)+1))*T/3;
rV = 2*SIGMA/md + 4*MASS;
//iV = -1 + XI/6;
//iV *= 0.385*T*TC;
iV = 0;
return dcomp(rV,iV);
break;
case 22:
double x,b;
x = A*dz/r; // Cos(theta)
b = 9./16.; // phenomenological value
md = mu(3,1.4)*Power(1 + XI*(1 + Power(2,1 + b)*(-1 + Power(x,2))*Power(1 + XI,2)*Power(2 + XI,-2 - b)),-0.25)*T/3;
return 2*SIGMA/md + 4*MASS;
break;
case 23:
x = A*dz/r; // Cos(theta)
b = 9./16.; // phenomenological value
md = mu(3,1.4)*Power(1 + XI*(1 + Power(2,1 + b)*(-1 + Power(x,2))*Power(1 + XI,2)*Power(2 + XI,-2 - b)),-0.25)*T/3;
rV = 2*SIGMA/md + 4*MASS;
iV = 0;
return dcomp(rV,iV);
break;
case 24:
x = A*dz/r; // Cos(theta)
md = mu(T,1.4)*Power(1. + XI*(1. - (0.0944049*(2.16919 - 29.6088*Power(x,2))*Power(1. + XI,1.5))/(3. + Power(XI,2)))*(1.62114 - (1.*(0.878423 + Power(1. + XI,0.125)))/Sqrt(3. + XI)),-0.25);
rV = 2*SIGMA/md + 4*MASS;
iV = 0;
return dcomp(rV,iV);
break;
case 25:
x = A*dz/r; // Cos(theta)
md = mu(T,1.4)*Power(1. + XI*(1. - (0.0944049*(2.16919 - 29.6088*Power(x,2))*Power(1. + XI,1.5))/(3. + Power(XI,2)))*(1.62114 - (1.*(0.878423 + Power(1. + XI,0.125)))/Sqrt(3. + XI)),-0.25);
rV = SIGMA/md + 4*MASS;
iV = 0;
return dcomp(rV,iV);
break;
case 26:
return 0.;
break;
case 27:
return 0.;
break;
case 28:
return 0.;
break;
case 29:
return 0.;
break;
case 30:
return 0.;
break;
case 31:
return 0.;
break;
case 32:
return 0.;
break;
case 33:
return 0.;
break;
case 34:
return 0.;
break;
default:
return 0.;
break;
}
return 0.;
}
// phir integrand
double phir(double z)
{
return 2*z*(1-sin(z*r*md)/(z*r*md))/(z*z+1)/(z*z+1);
}
// utility function for ps1 and ps2
double psig(double r, double z)
{ // note r here is rhat
return (r*z*cos(r*z)-sin(r*z))/(r*r*r*z*z*z);
}
// psi1 integrand
double psi1(double z)
{
double cos2theta = A*A*dz*dz/(r*r);
double sin2theta = 1. - cos2theta;
return z*(1 - 1.5*(sin2theta*sin(z*md*r)/(z*md*r) + (1-3*cos2theta)*psig(r*md, z)))/(z*z+1)/(z*z+1);
}
// psi2 integrand
double psi2(double z)
{
double cos2theta = A*A*dz*dz/(r*r);
double sin2theta = 1. - cos2theta;
return -4*z*(1 - 3*((2./3. - cos2theta)*sin(z*md*r)/(z*md*r) + (1-3*cos2theta)*psig(r*md, z)))/(z*z+1)/(z*z+1)/(z*z+1)/3;
}
// three loop running coupling
// mu is assumed to be in units of TC
double alphas(double mu)
{
double b0,b1,b2,L,R,nc,nf,lambda_ms,t;
nc = 3;
nf = (double) NF;
b0 = (11*nc-2*nf)/(12*M_PI);
b1 = (17*nc*nc-nf*(10*nc+6*(nc*nc-1)/(2*nc))/2)/(24*M_PI*M_PI);
b2 = (2857 - 5033*nf/9 + 325*nf*nf/27)/(128*M_PI*M_PI*M_PI);
lambda_ms = 0.344;
t = 2*log(mu*TC/lambda_ms);
return (1 - (b1*log(t))/(Power(b0,2)*t) + (b0*b2 + Power(b1,2)*(-1 - log(t) + Power(log(t),2)))/(Power(b0,4)*Power(t,2)) - (3*b0*b1*b2*log(t) + Power(b1,3)*(0.5 - 2*log(t) - (5*Power(log(t),2))/2. + Power(log(t),3)))/(Power(b0,6)*Power(t,3)))/(b0*t);
}
// derivative of three loop running coupling with respect to mu
// mu is assumed to be in units of TC
double alphasp(double mu)
{
double b0,b1,b2,L,R,nc,nf,lambda_ms,t;
nc = 3;
nf = (double) NF;
b0 = (11*nc-2*nf)/(12*M_PI);
b1 = (17*nc*nc-nf*(10*nc+6*(nc*nc-1)/(2*nc))/2)/(24*M_PI*M_PI);
b2 = (2857 - 5033*nf/9 + 325*nf*nf/27)/(128*M_PI*M_PI*M_PI);
lambda_ms = 0.344;
t = 2*log(mu*TC/lambda_ms);
return ((-2*(-4*Power(b1,3) + 3*b0*b1*b2 + b1*log(t)*(3*(Power(b1,2) - 4*b0*b2) + Power(b1,2)*(13 - 4*log(t))*log(t)) + Power(b0,2)*t*(-2*Power(b1,2) + 3*b0*b2 + Power(b1,2)*log(t)*(-5 + 3*log(t)) + Power(b0,2)*t*(b1 + Power(b0,2)*t - 2*b1*log(t)))))/(Power(b0,7)*mu*Power(t,5)));
}
// debye screening mass
double mu(double t, double fac)
{
return fac*sqrt( (1+((double)NF)/6)*4*M_PI*alphas(2*M_PI*t) )*t*TC;
}
// derivative of debye screening mass wrt T
double mup(double t, double fac)
{
return (fac*(6 + NF)*Sqrt((2*M_PI)/3.)*(alphas(2*M_PI*t) + M_PI*t*alphasp(2*M_PI*t)))/Sqrt((6 + NF)*alphas(2*M_PI*t));
}