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Merge remote-tracking branch 'organization/development' into feature-2.0
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Conflicts:
	test/test_threshold_loop_functions.cpp
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Alexander Voigt authored and Alexander Voigt committed Jan 30, 2017
2 parents b84211e + 62ef427 commit 75c8f85
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4 changes: 2 additions & 2 deletions ChangeLog
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Expand Up @@ -112,8 +112,8 @@ FlexibleSUSY-1.7.3 [not released yet]
strings (not symbols).
Thanks to Joshua Ellis.

* Bugfix (commit 7b4ab95): Implement missing limits of F8 and F9 for
x1 -> x2 from arXiv:1407.4081.
* Bugfix: Implement missing limits of threshold correction functions
from arXiv:1407.4081.

FlexibleSUSY-1.7.2 [December, 15 2016]

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184 changes: 154 additions & 30 deletions src/threshold_loop_functions.cpp
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Expand Up @@ -27,7 +27,7 @@ namespace flexiblesusy {
namespace threshold_loop_functions {

namespace {
double sqr(double x) { return x*x; }
template <typename T> T sqr(T 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; }
Expand Down Expand Up @@ -472,6 +472,34 @@ static double f5_1_r2(double r1, double r2)
*lr22))/(pow7(-1. + r2)*sqr(1. + r2));
}

/// f5(r1,r2) in the limit r1 -> r2
static double f5_r1_r2(double r1, double r2)
{
const double r22 = sqr(r2);
const double lr22 = std::log(r22);

return ((r1 - r2)*(11*r2 + 3*cube(r2) - 15*pow5(r2) + pow7(r2) +
3*r2*lr22 + 18*cube(r2)*lr22 +
3*pow5(r2)*lr22))/quad(-1 + r22)\
+ (sqr(r1 - r2)*(-17 - 116*r22 + 90*quad(r2) +
44*pow6(r2) - pow8(r2) - 3*lr22 -
75*r22*lr22 -
105*quad(r2)*lr22 -
9*pow6(r2)*lr22))/
(3.*pow5(-1 + r22)) +
(-1 - 5*r22 + 5*quad(r2) + pow6(r2) -
3*r22*lr22 -
6*quad(r2)*lr22 + pow6(r2)*lr22)
/cube(-1 + r22) +
(cube(r1 - r2)*(3 + 273*r22 + 314*quad(r2) -
498*pow6(r2) - 93*pow8(r2) + pow10(r2) +
90*r22*lr22 +
510*quad(r2)*lr22 +
342*pow6(r2)*lr22 +
18*pow8(r2)*lr22))/
(6.*r2*pow6(-1 + r22));
}

double f5(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
Expand All @@ -483,12 +511,16 @@ double f5(double r1, double r2)
if (is_equal(r2, 1., 0.01))
return f5_1_r2(r2, r1);

if (is_equal(r1, r2, 0.0001))
return 0.75 * f5_r1_r2(r2, r1);

const double r12 = sqr(r1);
const double r22 = sqr(r2);

const double result
= (1+sqr(r1+r2)-r12*sqr(r2))/((r12-1)*(sqr(r2)-1))
= (1+sqr(r1+r2)-r12*r22)/((r12-1)*(r22-1))
+ (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));
- (cube(r2)*(r22+1)*std::log(r22))/((r1-r2)*sqr(r22-1));

return 0.75 * result;
}
Expand All @@ -515,30 +547,58 @@ static double f6_1_1(double r1, double 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)
const double r22 = sqr(r2);

return ((-1 + r22)*(
-3 + 16*r2 + 33*r22 - 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)
8 - 49*r2 + 121*r22 - 129*cube(r2)
- 99*quad(r2) + 28*pow5(r2))
+ quad(r1)*(
3 - 18*r2 + 43*sqr(r2) - 42*cube(r2)
3 - 18*r2 + 43*r22 - 42*cube(r2)
- 47*quad(r2) + pow6(r2))
- 2*r1*(-8 + 10*r2 + 106*sqr(r2) - 359*cube(r2)
- 2*r1*(-8 + 10*r2 + 106*r22 - 359*cube(r2)
+ 211*quad(r2) - 101*pow5(r2)
+ 21*pow6(r2))
- 2*sqr(r1)*(-15 + 98*r2 - 264*sqr(r2)
- 2*sqr(r1)*(-15 + 98*r2 - 264*r22
+ 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)
- 10*r2 + 10*r22 - 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)))
10 - 5*r2 + r22)
+ r1*(-10 + 10*r2 - 5*r22
+ cube(r2)))*std::log(r22))
/(70.*pow7(-1 + r2)*sqr(1 + r2));
}

// f6(r1,r2) in the limit r1 -> r2
static double f6_r1_r2(double r1, double r2)
{
const double r22 = sqr(r2);
const double lr22 = std::log(r22);

return ((r1 - r2)*(3*r2 + 7*cube(r2) - 11*pow5(r2) + pow7(r2) +
10*cube(r2)*lr22 +
2*pow5(r2)*lr22))/quad(-1 + r22)\
+ (sqr(r1 - r2)*(-3 - 62*r22 + 36*quad(r2) +
30*pow6(r2) - pow8(r2) -
30*r22*lr22 -
60*quad(r2)*lr22 -
6*pow6(r2)*lr22))/
(3.*pow5(-1 + r22)) +
(-3*r22 + 2*quad(r2) + pow6(r2) -
5*quad(r2)*lr22 + pow6(r2)*lr22)
/cube(-1 + r22) +
(cube(r1 - r2)*(107*r2 + 206*cube(r2) - 252*pow5(r2) -
62*pow7(r2) + pow9(r2) + 30*r2*lr22 +
240*cube(r2)*lr22 +
198*pow5(r2)*lr22 +
12*pow7(r2)*lr22))/
(6.*pow6(-1 + r22));
}

double f6(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
Expand All @@ -550,6 +610,9 @@ double f6(double r1, double r2)
if (is_equal(r2, 1., 0.01))
return f6_1_r2(r2, r1);

if (is_equal(r1, r2, 0.0001))
return 6./7. * f6_r1_r2(r2, r1);

const double r12 = sqr(r1);
const double r22 = sqr(r2);

Expand All @@ -564,44 +627,74 @@ double f6(double r1, double r2)
/// 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)
const double r22 = sqr(r2);

return (15700 - 14411*r2 + 7850*r22 - 2498*cube(r2)
+ 355*quad(r2)
+ sqr(r1)*(7850 - 2558*r2 - 750*sqr(r2) + 940*cube(r2)
+ sqr(r1)*(7850 - 2558*r2 - 750*r22 + 940*cube(r2)
- 235*quad(r2))
+ quad(r1)*(355 + 65*r2 - 235*sqr(r2) + 142*cube(r2)
+ quad(r1)*(355 + 65*r2 - 235*r22 + 142*cube(r2)
- 30*quad(r2))
+ r1*(-14411 + 8375*r2 - 2558*sqr(r2) + 180*cube(r2)
+ r1*(-14411 + 8375*r2 - 2558*r22 + 180*cube(r2)
+ 65*quad(r2))
+ cube(r1)*(-2498 + 180*r2 + 940*sqr(r2)
+ cube(r1)*(-2498 + 180*r2 + 940*r22
- 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));
const double r22 = sqr(r2);
const double lr22 = std::log(r22);

return (-10*(-1 + r1)*cube(-1 + r2)*(
2 - 5*r2 - 4*sqr(r2) + 4*cube(r2) + 2*quad(r2)
2 - 5*r2 - 4*r22 + 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)
1 - 2*r2 - 2*r22 + 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)
-1 + 3*r2 + 3*r22 - 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)
-2 + 6*r2 + 18*r22 + 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)
-1 + 48*r22 + 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));
}

/// f7(r1,r2) in the limit r1 -> r2
static double f7_r1_r2(double r1, double r2)
{
const double r22 = sqr(r2);
const double lr22 = std::log(r22);

return (-1 - 2*r22 + 3*quad(r2) -
3*r22*lr22 - quad(r2)*lr22)
/cube(-1 + r22) +
((r1 - r2)*(8*r2 - 4*cube(r2) - 4*pow5(r2) +
3*r2*lr22 + 8*cube(r2)*lr22 +
pow5(r2)*lr22))/quad(-1 + r22) +
(sqr(r1 - r2)*(-14 - 54*r22 + 54*quad(r2) +
14*pow6(r2) - 3*lr22 -
45*r22*lr22 -
45*quad(r2)*lr22 -
3*pow6(r2)*lr22))/
(3.*pow5(-1 + r22)) +
(cube(r1 - r2)*(3 + 166*r22 + 108*quad(r2) -
246*pow6(r2) - 31*pow8(r2) +
60*r22*lr22 +
270*quad(r2)*lr22 +
144*pow6(r2)*lr22 +
6*pow8(r2)*lr22))/
(6.*r2*pow6(-1 + r22));
}

double f7(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
Expand All @@ -613,6 +706,9 @@ double f7(double r1, double r2)
if (is_equal(r2, 1., 0.01))
return f7_1_r2(r2, r1);

if (is_equal(r1, r2, 0.0001))
return 6. * f7_r1_r2(r2, r1);

const double r12 = sqr(r1);
const double r22 = sqr(r2);

Expand Down Expand Up @@ -646,30 +742,55 @@ static double f8_1_1(double r1, double 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));
const double r22 = sqr(r2);
const double lr22 = std::log(r22);

return (30*quad(-1 + r2)*(
-1 + 4*sqr(r2) - 3*quad(r2)
-1 + 4*r22 - 3*quad(r2)
+ 2*quad(r2)*lr22)
+ 10*sqr(-1 + r1)*sqr(-1 + r2)*(
1 - 4*r2 + 4*sqr(r2) + 8*cube(r2)
1 - 4*r2 + 4*r22 + 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)
1 - 4*r2 + 4*r22 + 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)
3 - 14*r2 + 18*r22 + 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)
3 - 16*r2 + 24*r22 + 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));
}

/// f8(r1,r2) in the limit r1 -> r2
static double f8_r1_r2(double r1, double r2)
{
const double r22 = sqr(r2);
const double lr22 = std::log(r22);

return (2*(-r2 + pow5(r2) - 2*cube(r2)*lr22))/
cube(-1 + r22) +
((r1 - r2)*(1 + 9*r22 - 9*quad(r2) - pow6(r2) +
6*r22*lr22 +
6*quad(r2)*lr22))/quad(-1 + r22)\
+ (2*sqr(r1 - r2)*(-19*r2 - 9*cube(r2) +
27*pow5(r2) + pow7(r2) - 6*r2*lr22 -
30*cube(r2)*lr22 -
12*pow5(r2)*lr22))/
(3.*pow5(-1 + r22)) +
(cube(r1 - r2)*(31 + 246*r22 - 108*quad(r2) -
166*pow6(r2) - 3*pow8(r2) + 6*lr22 +
144*r22*lr22 +
270*quad(r2)*lr22 +
60*pow6(r2)*lr22))/
(6.*pow6(-1 + r22));
}

double f8(double r1, double r2)
{
if (is_equal(r1, 1., 0.01) && is_equal(r2, 1., 0.01))
Expand All @@ -681,6 +802,9 @@ double f8(double r1, double r2)
if (is_equal(r2, 1., 0.01))
return f8_1_r2(r2, r1);

if (is_equal(r1, r2, 0.0001))
return 1.5 * f8_r1_r2(r2, r1);

const double r12 = sqr(r1);
const double r22 = sqr(r2);

Expand Down

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