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threshold_loop_functions.cpp
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threshold_loop_functions.cpp
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// ====================================================================
// This file is part of FlexibleSUSY.
//
// FlexibleSUSY is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published
// by the Free Software Foundation, either version 3 of the License,
// or (at your option) any later version.
//
// FlexibleSUSY is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with FlexibleSUSY. If not, see
// <http://www.gnu.org/licenses/>.
// ====================================================================
#include "threshold_loop_functions.hpp"
#include "pv.hpp"
#include "numerics.h"
#include <cmath>
#include <limits>
namespace flexiblesusy {
namespace threshold_loop_functions {
namespace {
double sqr(double x) { return x*x; }
template <typename T> T cube(T x) { return x*x*x; }
template <typename T> T quad(T x) { return x*x*x*x; }
template <typename T> T pow5(T x) { return x*x*x*x*x; }
template <typename T> T pow6(T x) { return x*x*x*x*x*x; }
template <typename T> T pow7(T x) { return x*x*x*x*x*x*x; }
template <typename T> T pow8(T x) { return x*x*x*x*x*x*x*x; }
template <typename T> T pow9(T x) { return x*x*x*x*x*x*x*x*x; }
template <typename T> T pow10(T x) { return x*x*x*x*x*x*x*x*x*x; }
template <typename T>
bool is_zero(T a, T prec = std::numeric_limits<T>::epsilon())
{
return std::fabs(a) < prec;
}
template <typename T>
bool is_equal(T a, T b, T prec = std::numeric_limits<T>::epsilon())
{
return is_zero(a - b, prec);
}
template <typename T>
bool is_equal_rel(T a, T b, T prec = std::numeric_limits<T>::epsilon())
{
if (is_equal(a, b, std::numeric_limits<T>::epsilon()))
return true;
if (std::fabs(a) < std::numeric_limits<T>::epsilon())
return is_equal(a, b, prec);
return std::fabs((a - b)/a) < prec;
}
}
double F1(double x)
{
const double x2 = sqr(x);
if (is_equal(x, 1., 0.01))
return (16 + 41*x - 44*x2 + 21*cube(x) - 4*quad(x))/30.;
return x*std::log(x2)/(x2-1);
}
double F2(double x)
{
const double x2 = sqr(x);
if (is_equal(x, 1., 0.01))
return (-5 + 216*x - 226*x2 + 104*cube(x) - 19*quad(x))/70.;
return 6*x2*(2-2*x2+(1+x2)*std::log(x2))/cube(x2-1);
}
double F3(double x)
{
const double x2 = sqr(x);
if (is_equal(x, 1., 0.01))
return (-27 + 218*x - 142*x2 + 48*cube(x) - 7*quad(x))/90.;
return 2*x*(5*(1-x2)+(1+4*x2)*std::log(x2))/(3*sqr(x2-1));
}
double F4(double x)
{
const double x2 = sqr(x);
if (is_equal(x, 1., 0.01))
return (31 + 22*x - 42*x2 + 24*cube(x) - 5*quad(x))/30.;
return 2*x*(x2-1-std::log(x2))/sqr(x2-1);
}
double F5(double x)
{
const double x2 = sqr(x);
const double x4 = quad(x);
if (is_equal(x, 1., 0.01))
return (13 + 165*x - 174*x2 + 81*cube(x) - 15*x4)/70.;
return 3*x*(1-x4+2*x2*std::log(x2))/cube(1-x2);
}
double F6(double x)
{
const double x2 = sqr(x);
if (is_equal(x, 1., 0.01))
return (-103 + 128*x - 26*x2 + quad(x))/120.;
return (x2-3)/(4*(1-x2)) + x2*(x2-2)/(2*sqr(1.-x2))*std::log(x2);
}
double F7(double x)
{
const double x2 = sqr(x);
const double x4 = quad(x);
if (is_equal(x, 1., 0.01))
return -1.8642857142857139 + 2.057142857142856*x
+ 1.7142857142857153*x2 - 1.1428571428571432*cube(x)
+ 0.2357142857142858*x4;
return (-3*(x4-6*x2+1.))/(2*sqr(x2-1))
+ (3*x4*(x2-3.))/(cube(x2-1.))*std::log(x2);
}
/// F8(x1,x2) in the limit x1 -> 1 and x2 -> 1
static double F8_1_1(double x1, double x2)
{
return (-2.7015873015872867 + 13.815873015872924*x2
- 28.54761904761879*sqr(x2) + 29.898412698412283*cube(x2)
- 15.82222222222179*quad(x2)
+ 2.9904761904758974*pow5(x2)
+ 0.7031746031747295*pow6(x2)
- 0.39365079365082534*pow7(x2)
+ 0.05714285714286069*pow8(x2)
+ sqr(x1)*(-0.2999999999999769 + 5.352380952380799*x2
- 23.09047619047574*sqr(x2)
+ 47.08571428571352*cube(x2)
- 54.404761904761074*quad(x2)
+ 38.03809523809467*pow5(x2)
- 16.18571428571403*pow6(x2)
+ 3.923809523809459*pow7(x2)
- 0.41904761904761173*pow8(x2))
+ quad(x1)*(0.057142857142858015 + 0.050793650793644535*x2
- 1.193650793650774*sqr(x2)
+ 3.352380952380916*cube(x2)
- 4.534920634920595*quad(x2)
+ 3.511111111111082*pow5(x2)
- 1.6095238095237963*pow6(x2)
+ 0.41269841269840923*pow7(x2)
- 0.04603174603174563*pow8(x2))
+ cube(x1)*(-0.16507936507937204 - 1.0158730158729674*x2
+ 7.961904761904614*sqr(x2)
- 19.555555555555294*cube(x2)
+ 24.926984126983836*quad(x2)
- 18.590476190475986*pow5(x2)
+ 8.292063492063399*pow6(x2)
- 2.0825396825396587*pow7(x2)
+ 0.22857142857142587*pow8(x2))
+ x1*(3.009523809523779 - 17.269841269841073*x2
+ 43.13650793650738*sqr(x2)
- 61.71428571428479*cube(x2)
+ 55.83492063491965*quad(x2)
- 33.01587301587234*pow5(x2)
+ 12.533333333333038*pow6(x2)
- 2.793650793650719*pow7(x2)
+ 0.279365079365071*pow8(x2)))/quad(-1. + x2);
}
/// F8(x1,x2) in the limit x1 -> 1
static double F8_1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));
return -2. + (4.*(-1. + x1)*(-0.5 + 2.*sqr(x2) - 1.5*quad(x2)
+ quad(x2)*lx22))
/cube(-1. + sqr(x2))
+ (2. - 2.*sqr(x2) + 2.*quad(x2)*lx22)
/sqr(-1. + sqr(x2))
- (1.3333333333333333*cube(-1. + x1)*(
-sqr(x2) - 9.*quad(x2) + 9.*pow6(x2)
+ pow8(x2)
+ (-6.*quad(x2) - 6.*pow6(x2))*lx22))
/pow5(-1. + sqr(x2))
+ (2.*sqr(-1. + x1)*(
-0.16666666666666666 + 1.5*sqr(x2) + 1.5*quad(x2)
- 2.8333333333333335*pow6(x2)
+ (3.*quad(x2) + pow6(x2))*lx22))
/quad(-1. + sqr(x2))
+ (0.26666666666666666*quad(-1. + x1)*(
0.25 + 2.5*sqr(x2) + 80.*quad(x2) - 47.5*pow6(x2)
- 36.25*pow8(x2) + pow10(x2)
+ (37.5*quad(x2) + 75.*pow6(x2)
+ 7.5*pow8(x2))*lx22))
/pow6(-1. + sqr(x2));
}
// F8(x1,x2) in the limit x1 -> x2
static double F8_x1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));
return -2. + (2.*(x1 - x2)*(3.*x2 - 4.*cube(x2) + pow5(x2) +
2.*x2*lx22))/cube(-1. + sqr(x2)) +
(2.*sqr(x2)*(-1. + sqr(x2) - 2.*lx22 +
sqr(x2)*lx22))/sqr(-1. + sqr(x2)) -
(0.33333333333333326*sqr(x1 - x2)*
(17.000000000000007 - 9.000000000000007*sqr(x2) -
9.*quad(x2) + pow6(x2) +
6.000000000000002*lx22 +
18.000000000000004*sqr(x2)*lx22))/
quad(-1. + sqr(x2)) -
(1.333333333333333*cube(x1 - x2)*
(-1. - 9.000000000000002*sqr(x2) +
9.000000000000002*quad(x2) + pow6(x2) -
6.*sqr(x2)*lx22 -
6.000000000000003*quad(x2)*lx22))/
(x2*pow5(-1. + sqr(x2)));
}
double F8(double x1, double x2)
{
if (is_equal(x1, 1., 0.01) && is_equal(x2, 1., 0.01))
return F8_1_1(x1, x2);
if (is_equal(x1, 1., 0.01))
return F8_1_x2(x1, x2);
if (is_equal(x2, 1., 0.01))
return F8_1_x2(x2, x1);
if (is_equal(x1, x2, 0.00001))
return F8_x1_x2(x1, x2);
const double x12 = sqr(x1);
const double x22 = sqr(x2);
return -2. + 2./(x12-x22)
*(quad(x1)/(x12-1.)*std::log(x12)
-quad(x2)/(x22-1.)*std::log(x22));
}
/// F9(x1,x2) in the limit x1 -> 1 and x2 -> 1
static double F9_1_1(double x1, double x2)
{
return 8.223809523809523 - 12.863492063492064*x2
+ 10.580952380952382*sqr(x2) - 4.609523809523809*cube(x2)
+ 0.8349206349206348*quad(x2)
+ x1*(-12.863492063492064 + 26.260317460317456*x2
- 24.609523809523807*sqr(x2) + 11.530158730158728*cube(x2)
- 2.184126984126984*quad(x2))
+ cube(x1)*(-4.60952380952381 + 11.53015873015873*x2
- 11.961904761904762*sqr(x2)
+ 5.942857142857143*cube(x2)
- 1.1682539682539683*quad(x2))
+ quad(x1)*(0.8349206349206351 - 2.1841269841269844*x2
+ 2.3190476190476197*sqr(x2)
- 1.1682539682539685*cube(x2)
+ 0.23174603174603178*quad(x2))
+ sqr(x1)*(10.580952380952379 - 24.609523809523804*x2
+ 24.6047619047619*sqr(x2)
- 11.96190476190476*cube(x2)
+ 2.319047619047619*quad(x2));
}
/// F9(x1,x2) in the limit x1 -> 1
static double F9_1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));
return (-2.*(-1. + x1)*cube(-1. + sqr(x2))*(
-1. + quad(x2) - 2.*sqr(x2)*lx22)
+ 2.*quad(-1. + sqr(x2))*(
1. - sqr(x2) + sqr(x2)*lx22)
- 1.3333333333333333*cube(-1. + x1)*(
-1. + sqr(x2))*(
-1. - 9.*sqr(x2) + 9.*quad(x2) + pow6(x2)
+ (-6.*sqr(x2) - 6.*quad(x2))*lx22)
+ 0.3333333333333333*sqr(-1. + x1)*sqr(-1. + sqr(x2))
*(5. + 15.*sqr(x2) - 21.*quad(x2) + pow6(x2)
+ (18.*sqr(x2) + 6.*quad(x2))*lx22)
- 0.06666666666666667*quad(-1. + x1)*(
-16. - 305.*sqr(x2) + 170.*quad(x2) + 160.*pow6(x2)
- 10.*pow8(x2) + pow10(x2)
+ (-150.*sqr(x2) - 300.*quad(x2)
- 30.*pow6(x2))*lx22))
/pow6(-1. + sqr(x2));
}
/// F9(x1,x2) in the limit x1 -> x2
static double F9_x1_x2(double x1, double x2)
{
const double lx22 = std::log(sqr(x2));
return (2.*(-1. + sqr(x2) - lx22))/
sqr(-1. + sqr(x2)) -
(2.*(x1 - x2)*(-1. + quad(x2) -
2.*sqr(x2)*lx22))/
(x2*cube(-1. + sqr(x2))) -
(1.3333333333333333*cube(x1 - x2)*
(-1.0000000000000002 - 9.*sqr(x2) + 9.*quad(x2) +
pow6(x2) - 6.*sqr(x2)*lx22 -
6.*quad(x2)*lx22))/
(x2*pow5(-1. + sqr(x2))) +
(1.6666666666666665*sqr(x1 - x2)*
(0.2000000000000001 - 4.200000000000001*sqr(x2) +
3.000000000000001*quad(x2) + pow6(x2) -
1.2000000000000002*sqr(x2)*lx22 -
3.6000000000000005*quad(x2)*lx22))/
(sqr(x2)*quad(-1. + sqr(x2)));
}
double F9(double x1, double x2)
{
if (is_equal(x1, 1., 0.01) && is_equal(x2, 1., 0.01))
return F9_1_1(x1, x2);
if (is_equal(x1, 1., 0.01))
return F9_1_x2(x1, x2);
if (is_equal(x2, 1., 0.01))
return F9_1_x2(x2, x1);
if (is_equal(x1, x2, 0.00001))
return F9_x1_x2(x1, x2);
const double x12 = sqr(x1);
const double x22 = sqr(x2);
return 2./(x12-x22)*(x12/(x12-1.)*std::log(x12)-x22/(x22-1.)*std::log(x22));
}
double f(double r)
{
return F5(r);
}
double g(double r)
{
return F7(r);
}
double f1(double r)
{
if (is_equal(r, 1., 0.01))
return (-81 + 464*r + 270*sqr(r)
- 208*cube(r) + 45*quad(r))/490.;
const double r2 = sqr(r);
return (6*(r2+3)*r2)/(7*sqr(r2-1))
+ (6*(r2-5)*quad(r)*std::log(r2))/(7*cube(r2-1));
}
double f2(double r)
{
if (is_equal(r, 1., 0.01))
return (-285 + 1616*r + 1230*sqr(r)
- 848*cube(r) + 177*quad(r))/1890.;
const double r2 = sqr(r);
return (2*(r2+11)*r2)/(9*sqr(r2-1))
+ (2*(5*r2-17)*quad(r)*std::log(r2))/(9*cube(r2-1));
}
double f3(double r)
{
if (is_equal(r, 1., 0.01))
return (849 - 1184*r + 1566*sqr(r)
- 736*cube(r) + 135*quad(r))/630.;
const double r2 = sqr(r);
const double r4 = quad(r);
return (2*(r4+9*r2+2))/(3*sqr(r2-1))
+ (2*(r4-7*r2-6)*r2*std::log(r2))/(3*cube(r2-1));
}
double f4(double r)
{
const double r2 = sqr(r);
const double r4 = quad(r);
if (is_equal(r, 1., 0.01))
return (2589 - 3776*r + 4278*r2 - 1984*cube(r) + 363*r4)/1470.;
return (2*(5*r4+25*r2+6))/(7*sqr(r2-1))
+ (2*(r4-19*r2-18)*r2*std::log(r2))/(7*cube(r2-1));
}
/// f5(r1,r2) in the limit r1 -> 1 and r2 -> 1
static double f5_1_1(double r1, double r2)
{
return 0.772943722943723
- 0.5524891774891774*r2
+ 0.7870670995670994*sqr(r2)
- 0.3316558441558441*cube(r2)
+ 0.056277056277056266*quad(r2)
+ r1*(-0.5524891774891774
+ 1.0700757575757573*r2
- 0.6625541125541123*sqr(r2)
+ 0.22483766233766228*cube(r2)
- 0.03344155844155843*quad(r2))
+ cube(r1)*(-0.33165584415584404
+ 0.22483766233766223*r2
- 0.08755411255411245*sqr(r2)
+ 0.01650432900432896*cube(r2)
- 0.0007034632034631958*quad(r2))
+ quad(r1)*(0.05627705627705626
- 0.03344155844155841*r2
+ 0.010281385281385256*sqr(r2)
- 0.0007034632034631921*cube(r2)
- 0.0002705627705627725*quad(r2))
+ sqr(r1)*(0.7870670995670994 - 0.6625541125541123*r2
+ 0.32061688311688297*sqr(r2)
- 0.08755411255411248*cube(r2)
+ 0.01028138528138527*quad(r2));
}
/// f5(r1,r2) in the limit r1 -> 1
static double f5_1_r2(double r1, double r2)
{
const double lr22 = std::log(sqr(r2));
return (-0.025*cube(-1. + r1)*(
4. - 17.*r2 + 4.*sqr(r2)
- 25.*cube(r2)
- 20.*quad(r2)
+ 41.*pow5(r2)
+ 12.*pow6(r2)
+ pow7(r2)
+ (-30.*cube(r2) - 30.*pow5(r2))
*lr22))/(pow6(-1. + r2)*sqr(1. + r2))
- (0.125*sqr(-1. + r1)*(
1. - 4.*r2 + sqr(r2)
- 4.*cube(r2)
- 5.*quad(r2)
+ 8.*pow5(r2)
+ 3.*pow6(r2)
+ (-6.*cube(r2) - 6.*pow5(r2))
*lr22))/(pow5(-1. + r2)*sqr(1. + r2))
+ (0.75*(-1 + r2 + 2*sqr(r2)
- quad(r2)
- pow5(r2)
+ (cube(r2) + pow5(r2))
*lr22))/(cube(-1 + r2)*sqr(1 + r2))
+ (0.25*(-1. + r1)*(
1. - r2 - 2.*sqr(r2) + 8.*cube(r2)
+ quad(r2) - 7.*pow5(r2)
+ (3.*cube(r2) + 3.*pow5(r2))
*lr22))/(quad(-1. + r2)*sqr(1. + r2))
+ (0.05*quad(-1. + r1)*(
-1. + 4.5*r2 + 2.*sqr(r2)
+ 16.5*cube(r2) - 16.5*pow5(r2) - 2.*pow6(r2)
- 4.5*pow7(r2) + pow8(r2)
+ (15.*cube(r2) + 15.*pow5(r2))
*lr22))/(pow7(-1. + r2)*sqr(1. + r2));
}
double f5(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
return f5_1_1(r1, r2);
if (is_equal(r1, 1., 0.01))
return f5_1_r2(r1, r2);
if (is_equal(r2, 1., 0.01))
return f5_1_r2(r2, r1);
const double r12 = sqr(r1);
const double result
= (1+sqr(r1+r2)-r12*sqr(r2))/((r12-1)*(sqr(r2)-1))
+ (cube(r1)*(r12+1)*std::log(r12))/(sqr(r12-1)*(r1-r2))
- (cube(r2)*(sqr(r2)+1)*std::log(sqr(r2)))/((r1-r2)*sqr(sqr(r2)-1));
return 0.75 * result;
}
/// f6(r1,r2) in the limit r1 -> 1 and r2 -> 1
static double f6_1_1(double r1, double r2)
{
return 1 + (4*(-1 + r1))/7. - (2*sqr(-1 + r1))/35.
- cube(-1 + r1)/70. + (9*quad(-1 + r1))/490.
+ (0.5714285714285714 - (2*(-1 + r1))/35. - sqr(-1 + r1)/70.
+ (9*cube(-1 + r1))/490.
- (3*quad(-1 + r1))/245.)*(-1 + r2)
+ (-0.05714285714285714 + (1 - r1)/70. + (9*sqr(-1 + r1))/490.
- (3*cube(-1 + r1))/245.
+ quad(-1 + r1)/147.)*sqr(-1 + r2)
+ (-0.014285714285714285 + (9*(-1 + r1))/490.
- (3*sqr(-1 + r1))/245. + cube(-1 + r1)/147.
- quad(-1 + r1)/294.)*cube(-1 + r2)
+ (0.018367346938775512 - (3*(-1 + r1))/245. + sqr(-1 + r1)/147.
- cube(-1 + r1)/294.
+ (5*quad(-1 + r1))/3234.)*quad(-1 + r2);
}
/// f6(r1,r2) in the limit r1 -> 1
static double f6_1_r2(double r1, double r2)
{
return ((-1 + sqr(r2))*(
-3 + 16*r2 + 33*sqr(r2) - 332*cube(r2)
+ 573*quad(r2) - 584*pow5(r2) + 297*pow6(r2)
- 60*pow7(r2) - 2*cube(r1)*(
8 - 49*r2 + 121*sqr(r2) - 129*cube(r2)
- 99*quad(r2) + 28*pow5(r2))
+ quad(r1)*(
3 - 18*r2 + 43*sqr(r2) - 42*cube(r2)
- 47*quad(r2) + pow6(r2))
- 2*r1*(-8 + 10*r2 + 106*sqr(r2) - 359*cube(r2)
+ 211*quad(r2) - 101*pow5(r2)
+ 21*pow6(r2))
- 2*sqr(r1)*(-15 + 98*r2 - 264*sqr(r2)
+ 331*cube(r2) + 106*quad(r2)
- 99*pow5(r2) + 23*pow6(r2)))
+ 60*pow5(r2)*(5 + quad(r1) + cube(r1)*(-5 + r2)
- 10*r2 + 10*sqr(r2) - 5*cube(r2)
+ quad(r2) + sqr(r1)*(
10 - 5*r2 + sqr(r2))
+ r1*(-10 + 10*r2 - 5*sqr(r2)
+ cube(r2)))*std::log(sqr(r2)))
/(70.*pow7(-1 + r2)*sqr(1 + r2));
}
double f6(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
return f6_1_1(r1, r2);
if (is_equal(r1, 1., 0.01))
return f6_1_r2(r1, r2);
if (is_equal(r2, 1., 0.01))
return f6_1_r2(r2, r1);
const double r12 = sqr(r1);
const double r22 = sqr(r2);
const double result
= (r12+r22+r1*r2-r12*r22)/((r12-1)*(r22-1))
+ (pow5(r1)*std::log(r12))/(sqr(r12-1)*(r1-r2))
- (pow5(r2)*std::log(r22))/((r1-r2)*sqr(r22-1));
return 6./7. * result;
}
/// f7(r1,r2) in the limit r1 -> 1 and r2 -> 1
static double f7_1_1(double r1, double r2)
{
return (15700 - 14411*r2 + 7850*sqr(r2) - 2498*cube(r2)
+ 355*quad(r2)
+ sqr(r1)*(7850 - 2558*r2 - 750*sqr(r2) + 940*cube(r2)
- 235*quad(r2))
+ quad(r1)*(355 + 65*r2 - 235*sqr(r2) + 142*cube(r2)
- 30*quad(r2))
+ r1*(-14411 + 8375*r2 - 2558*sqr(r2) + 180*cube(r2)
+ 65*quad(r2))
+ cube(r1)*(-2498 + 180*r2 + 940*sqr(r2)
- 645*cube(r2) + 142*quad(r2)))
/2310.;
}
/// f7(r1,r2) in the limit r1 -> 1
static double f7_1_r2(double r1, double r2)
{
const double lr22 = std::log(sqr(r2));
return (-10*(-1 + r1)*cube(-1 + r2)*(
2 - 5*r2 - 4*sqr(r2) + 4*cube(r2) + 2*quad(r2)
+ pow5(r2) - 6*cube(r2)*lr22)
- 30*quad(-1 + r2)*(
1 - 2*r2 - 2*sqr(r2) + 2*cube(r2) + quad(r2)
- 2*cube(r2)*lr22)
+ 10*sqr(-1 + r1)*sqr(-1 + r2)*(
-1 + 3*r2 + 3*sqr(r2) - 3*quad(r2) - 3*pow5(r2)
+ pow6(r2) + 6*cube(r2)*lr22)
+ 2*cube(-1 + r1)*(-1 + r2)*(
-2 + 6*r2 + 18*sqr(r2) + 15*cube(r2) - 30*quad(r2)
- 18*pow5(r2) + 14*pow6(r2) - 3*pow7(r2)
+ 30*cube(r2)*lr22)
+ quad(-1 + r1)*(
-1 + 48*sqr(r2) + 42*cube(r2) - 90*quad(r2)
- 24*pow5(r2) + 40*pow6(r2) - 18*pow7(r2)
+ 3*pow8(r2) + 60*cube(r2)*lr22))
/(10.*pow7(-1 + r2)*sqr(1 + r2));
}
double f7(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
return f7_1_1(r1, r2);
if (is_equal(r1, 1., 0.01))
return f7_1_r2(r1, r2);
if (is_equal(r2, 1., 0.01))
return f7_1_r2(r2, r1);
const double r12 = sqr(r1);
const double r22 = sqr(r2);
const double result
= (1+r1*r2)/((r12-1)*(r22-1))
+ (cube(r1)*std::log(r12))/(sqr(r12-1)*(r1-r2))
- (cube(r2)*std::log(r22))/((r1-r2)*sqr(r22-1));
return 6. * result;
}
/// f8(r1,r2) in the limit r1 -> 1 and r2 -> 1
static double f8_1_1(double r1, double r2)
{
return 1 - sqr(-1 + r1)/10. + (3*cube(-1 + r1))/40.
- (3*quad(-1 + r1))/70.
+ ((1 - r1)/10. + (3*sqr(-1 + r1))/40.
- (3*cube(-1 + r1))/70.
+ (3*quad(-1 + r1))/140.)*(-1 + r2)
+ (-0.1 + (3*(-1 + r1))/40. - (3*sqr(-1 + r1))/70.
+ (3*cube(-1 + r1))/140.
- quad(-1 + r1)/105.)*sqr(-1 + r2)
+ (0.075 - (3*(-1 + r1))/70. + (3*sqr(-1 + r1))/140.
- cube(-1 + r1)/105.
+ quad(-1 + r1)/280.)*cube(-1 + r2)
+ (-0.04285714285714286 + (3*(-1 + r1))/140.
- sqr(-1 + r1)/105. + cube(-1 + r1)/280.
- quad(-1 + r1)/1155.)*quad(-1 + r2);
}
/// f8(r1,r2) in the limit r1 -> 1
static double f8_1_r2(double r1, double r2)
{
const double lr22 = std::log(sqr(r2));
return (30*quad(-1 + r2)*(
-1 + 4*sqr(r2) - 3*quad(r2)
+ 2*quad(r2)*lr22)
+ 10*sqr(-1 + r1)*sqr(-1 + r2)*(
1 - 4*r2 + 4*sqr(r2) + 8*cube(r2)
- 5*quad(r2) - 4*pow5(r2)
+ 6*quad(r2)*lr22)
+ 10*(-1 + r1)*cube(-1 + r2)*(
1 - 4*r2 + 4*sqr(r2) + 8*cube(r2)
- 5*quad(r2) - 4*pow5(r2)
+ 6*quad(r2)*lr22)
+ 2*cube(-1 + r1)*(-1 + r2)*(
3 - 14*r2 + 18*sqr(r2) + 30*cube(r2)
- 15*quad(r2) - 18*pow5(r2) - 6*pow6(r2)
+ 2*pow7(r2) + 30*quad(r2)*lr22)
+ quad(-1 + r1)*(
3 - 16*r2 + 24*sqr(r2) + 48*cube(r2)
- 48*pow5(r2) - 24*pow6(r2) + 16*pow7(r2)
- 3*pow8(r2) + 60*quad(r2)*lr22))
/(40.*pow7(-1 + r2)*sqr(1 + r2));
}
double f8(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
return f8_1_1(r1, r2);
if (is_equal(r1, 1., 0.01))
return f8_1_r2(r1, r2);
if (is_equal(r2, 1., 0.01))
return f8_1_r2(r2, r1);
const double r12 = sqr(r1);
const double r22 = sqr(r2);
const double result
= (r1+r2)/((r12-1)*(r22-1))
+ (quad(r1)*std::log(r12))/(sqr(r12-1)*(r1-r2))
- (quad(r2)*std::log(r22))/((r1-r2)*sqr(r22-1));
return 1.5 * result;
}
/// Iabc(a,a,a)
static double Iaaa(double a, double b, double c)
{
return (151.*quad(a) + 13.*sqr(b)*sqr(c) - 128.*cube(a)*(b + c) - 40.*a*b*c*(b + c)
+ sqr(a)*(37.*sqr(b) + 128.*b*c + 37.*sqr(c))) / (60.*pow6(a));
}
/// Iabc(a,a,c)
static double Iaac(double a, double b, double c)
{
return ((sqr(a) - sqr(c))
* (17.*pow6(a) - 16.*pow5(a)*b - 40.*cube(a)*b*sqr(c)
+ 8.*a*b*quad(c) - sqr(b)*quad(c) + quad(a)*(5.*sqr(b) + 8.*sqr(c))
+ sqr(a)*(20.*sqr(b)*sqr(c) - quad(c)))
- 6.*sqr(a)*sqr(c) * log(sqr(a)/sqr(c))
* (6.*quad(a) - 8.*cube(a)*b + 3.*sqr(a)*(sqr(b) - sqr(c)) + sqr(c)*(sqr(b) + sqr(c))))
/ (6.*sqr(a)*quad(sqr(a) - sqr(c)));
}
/// Iabc(a,a,0)
double Iaa0(double a, double b)
{
return (17.*sqr(a) - 16.*a*b + 5.*sqr(b)) / (6.*quad(a));
}
/// Iabc(0,b,c)
double I0bc(double b, double c)
{
return log(sqr(b/c))/(sqr(b) - sqr(c));
}
double Iabc(double a, double b, double c) {
if ((is_zero(a) && is_zero(b) && is_zero(c)) ||
(is_zero(a) && is_zero(b)) ||
(is_zero(a) && is_zero(c)) ||
(is_zero(b) && is_zero(c)))
return 0.;
if (is_equal_rel(std::abs(a), std::abs(b), 0.01) && is_equal_rel(std::abs(a), std::abs(c), 0.01))
return Iaaa(std::abs(a),std::abs(b),std::abs(c));
if (is_equal_rel(std::abs(a), std::abs(b), 0.01)) {
if (is_zero(c))
return Iaa0(std::abs(a),std::abs(b));
return Iaac(std::abs(a),std::abs(b),c);
}
if (is_equal_rel(std::abs(b), std::abs(c), 0.01)) {
if (is_zero(a))
return Iaa0(std::abs(b),std::abs(c));
return Iaac(std::abs(b),std::abs(c),a);
}
if (is_equal_rel(std::abs(a), std::abs(c), 0.01)) {
if (is_zero(b))
return Iaa0(std::abs(a),std::abs(c));
return Iaac(std::abs(a),std::abs(c),b);
}
if (is_zero(a))
return I0bc(b,c);
if (is_zero(b))
return I0bc(c,a);
if (is_zero(c))
return I0bc(a,b);
return ( (sqr(a * b) * log(sqr(a / b))
+ sqr(b * c) * log(sqr(b / c))
+ sqr(c * a) * log(sqr(c / a)))
/ ((sqr(a) - sqr(b)) * (sqr(b) - sqr(c)) * (sqr(a) - sqr(c))) );
}
/**
* B0 function for zero momentum, arxiv:0901.2065 Eq (130)
*
* @param m1 \f$m_1\f$ (not squared)
* @param m2 \f$m_2\f$ (not squared)
* @param scale \f$Q\f$ (not squared)
*
* @return \f$B_0(p=0,m_1,m_2,Q)\f$
*/
double B0(double m1, double m2, double scale)
{
return passarino_veltman::ReB0(0, m1*m1, m2*m2, scale*scale);
}
/**
* B0' function for zero momentum, arxiv:0901.2065 Eq (130)
*
* @param m1 \f$m_1\f$ (not squared)
* @param m2 \f$m_2\f$ (not squared)
*
* @return \f$B_0'(p=0,m_1,m_2)\f$
*/
double DB0(double m1, double m2)
{
const double m12 = sqr(m1);
const double m14 = sqr(m12);
const double m22 = sqr(m2);
const double m24 = sqr(m22);
if (is_zero(m12) || is_zero(m22))
return 0.;
if (is_equal_rel(m12, m22, 1e-3))
return 1./(6. * m22);
return (m14 - m24 + 2*m12*m22*std::log(m22/m12))/
(2*cube(m12 - m22));
}
/**
* C0 function for zero momentum, arxiv:0901.2065 Eq (130)
*
* \f$C_0(0,m_1,m_2,m_3) = -I_{abc}(m_1,m_2,m_3)\f$
*
* @param m1 \f$m_1\f$ (not squared)
* @param m2 \f$m_2\f$ (not squared)
* @param m3 \f$m_3\f$ (not squared)
*
* @return \f$C_0(p=0,m_1,m_2,m_3)\f$
*/
double C0(double m1, double m2, double m3)
{
return c0(m1, m2, m3);
}
double D0(double m1, double m2, double m3, double m4)
{
return d0(m1,m2,m3,m4);
}
/**
* \f$\tilde{D}_2\f$ for zero momentum, arxiv:0901.2065 Eq (131)
*
* @param m1 \f$m_1\f$ (not squared)
* @param m2 \f$m_2\f$ (not squared)
* @param m3 \f$m_3\f$ (not squared)
* @param m4 \f$m_4\f$ (not squared)
*
* @return \f$\tilde{D}_2(m_1,m_2,m_3,m_4)\f$
*/
double D2t(double m1, double m2, double m3, double m4)
{
return C0(m2, m3, m4) + m1*m1 * D0(m1, m2, m3, m4);
}
/**
* \f$\tilde{D}_4\f$ for zero momentum, arxiv:0901.2065 Eq (131)
*
* @param m1 \f$m_1\f$ (not squared)
* @param m2 \f$m_2\f$ (not squared)
* @param m3 \f$m_3\f$ (not squared)
* @param m4 \f$m_4\f$ (not squared)
* @param scale \f$Q\f$ (not squared)
*
* @return \f$\tilde{D}_4(m_1,m_2,m_3,m_4,Q)\f$
*/
double D4t(double m1, double m2, double m3, double m4, double scale)
{
return B0(m3, m4, scale) + (m1*m1 + m2*m2) * C0(m2, m3, m4)
+ quad(m1) * D0(m1, m2, m3, m4);
}
/**
* \f$W\f$ for zero momentum, arxiv:0901.2065 Eq (130)
*
* @param m1 \f$m_1\f$ (not squared)
* @param m2 \f$m_2\f$ (not squared)
* @param scale \f$Q\f$ (not squared)
*
* @return \f$W(m_1,m_2,Q)\f$
*/
double W(double m1, double m2, double scale)
{
const double m12 = sqr(m1);
const double m14 = sqr(m12);
const double m22 = sqr(m2);
const double m24 = sqr(m22);
const double m26 = m24 * m22;
const double Q2 = sqr(scale);
if (is_zero(m12) || is_zero(m22) || is_zero(Q2))
return 0.;
if (is_equal_rel(m12,m22,1e-3))
return 2./3. - 2. * std::log(Q2/m22);
return (- 2*std::log(Q2/m12)
- std::log(m22/m12)*(2*m26 - 6*m12*m24)/cube(m12 - m22)
- (m14 - 6*m22*m12 + m24)/sqr(m12 - m22));
}
} // namespace threshold_loop_functions
} // namespace flexiblesusy