ThermalFunctions.h File Reference

#include <BSMPT/utility/spline/spline.h>

Go to the source code of this file.

Namespaces
namespace	BSMPT
	This classes calculates the Bounce action of the potential with a set temperature.

Functions
double	BSMPT::ThermalFunctions::JbosonIntegrand (const double &x, const double &k, int diff=0)
double	BSMPT::ThermalFunctions::JbosonNumericalIntegration (const double &x, int diff=0)
double	BSMPT::ThermalFunctions::JbosonInterpolatedLow (const double &x, const int &n, int diff=0)
double	BSMPT::ThermalFunctions::JbosonInterpolatedNegative (const double &x, int diff=0)
double	BSMPT::ThermalFunctions::JbosonInterpolated (const double &x, int diff=0)
double	BSMPT::ThermalFunctions::JfermionIntegrand (const double &x, const double &k, int diff=0)
double	BSMPT::ThermalFunctions::JfermionNumericalIntegration (const double &x, int diff=0)
double	BSMPT::ThermalFunctions::JfermionInterpolatedLow (const double &x, const int &n, int diff=0)
double	BSMPT::ThermalFunctions::JfermionInterpolated (const double &x, int diff=0)
double	BSMPT::ThermalFunctions::JInterpolatedHigh (const double &x, const int &n, int diff=0)

Variables
const double	BSMPT::ThermalFunctions::C_FermionTheta = 2.216079120
const double	BSMPT::ThermalFunctions::C_FermionShift = -0.01560316619
const double	BSMPT::ThermalFunctions::C_BosonTheta = 9.469230596
const double	BSMPT::ThermalFunctions::C_BosonShift = 0.0063108787
const double	BSMPT::ThermalFunctions::C_euler_gamma = 0.5772156649015328606065
	C_euler_gamma Euler gamma constant.

Function Documentation

JbosonIntegrand()

double BSMPT::ThermalFunctions::JbosonIntegrand	(	const double &	x,
		const double &	k,
		int	diff = 0
	)

Integrand of the thermic integral for the bosons \( J_-(x) = \int\limits_{0}^{\infty} \,\mathrm{d}k \, k^2 \log\left[ 1 - \exp\left( -\sqrt{k^2+x} \right) \right] \)

Parameters

x	The ratio m^2/T^2
k	The integration variable
diff	Returns the integrand of J_- for diff = 0 and for the dJ_-/dx for diff = 1

JbosonInterpolated()

double BSMPT::ThermalFunctions::JbosonInterpolated	(	const double &	x,
		int	diff = 0
	)

Puts together the separate interpolations for J_-

Parameters

x	The ratio m^2/T^2
diff	Returns the interpolation of J_- for diff = 0 and for dJ_-/dx for diff = 1

JbosonInterpolatedLow()

double BSMPT::ThermalFunctions::JbosonInterpolatedLow	(	const double &	x,
		const int &	n,
		int	diff = 0
	)

Taylor expansion of J_- for small x=m^2/T^2, \( J_{_,s}(x,n) = -\frac{\pi^4}{45} + \frac{\pi}{12} x - \frac{\pi}{6} x^{3/2} - \frac{x^2}{32}(\log x - c_-) + \pi^2 x \sum\limits_{l=2}^{n} \left( - \frac{x}{4\pi^2} \right)^l \frac{(2l-3)!!\zeta(2l-1)}{(2l)!! (l+1)} \) , c.f. Eq. (2.38) in the manual

Parameters

x	The ratio m^2/T^2
n	The order of the taylor expansion
diff	Returns the expansion for diff = 0 and its derivative for diff = 1

JbosonInterpolatedNegative()

double BSMPT::ThermalFunctions::JbosonInterpolatedNegative	(	const double &	x,
		int	diff = 0
	)

Using linear interpolation with data points to interpolate the thermal integral for bosons for x=m^2/T^2 < 0

Parameters

x	The ratio m^2/T^2
diff	Returns the interpolation of J_- for diff = 0 and for dJ_-/dx for diff = 1

JbosonNumericalIntegration()

double BSMPT::ThermalFunctions::JbosonNumericalIntegration	(	const double &	x,
		int	diff = 0
	)

Numerical integration of the thermical integral for the bosons \( J_-(x) = \int\limits_{0}^{\infty} \,\mathrm{d}k \, k^2 \log\left[ 1 - \exp\left( -\sqrt{k^2+x} \right) \right] \)

Parameters

x	The ratio m^2/T^2
diff	Returns the numerical integration of J_- for diff = 0 and J_-/dx for diff = 1

JfermionIntegrand()

double BSMPT::ThermalFunctions::JfermionIntegrand	(	const double &	x,
		const double &	k,
		int	diff = 0
	)

Integrand of the thermic integral for the fermions \( J_+(x) = \int\limits_{0}^{\infty} \,\mathrm{d}k \, k^2 \log\left[ 1 + \exp\left( -\sqrt{k^2+x} \right) \right] \)

Parameters

x	The ratio m^2/T^2
k	The integration variable
diff	Returns the integrand of J_+ for diff = 0 and for the dJ_+/dx for diff = 1

JfermionInterpolated()

double BSMPT::ThermalFunctions::JfermionInterpolated	(	const double &	x,
		int	diff = 0
	)

Puts together the separate interpolations for J_+, see Eq. (2.44) in the manual

Parameters

x	The ratio m^2/T^2
diff	Returns the interpolation of J_+ for diff = 0 and dJ_+/dx for diff = 1

JfermionInterpolatedLow()

double BSMPT::ThermalFunctions::JfermionInterpolatedLow	(	const double &	x,
		const int &	n,
		int	diff = 0
	)

Taylor expansion of J_+ for small x=m^2/T^2, \( J_{+,s}(x,n) = -\frac{7\pi^4}{360} + \frac{\pi^2}{24} x + \frac{x^2}{32}\left( \log x - c_+ \right) - \pi^2 x \sum\limits_{l=2}^{n} \left( - \frac{x}{4\pi^2} \right)^l \frac{(2l-3)!!\zeta(2l-1)}{(2l)!! (l+1)} \left( 2^{2l-1} - 1\right) \) , see J_{+,s} in Eq. (2.37) in the manual

Parameters

x	The ratio m^2/T^2
n	The order of the taylor expansion
diff	Returns the expansion for diff = 0 and dJ_+/dx for diff = 1

JfermionNumericalIntegration()

double BSMPT::ThermalFunctions::JfermionNumericalIntegration	(	const double &	x,
		int	diff = 0
	)

Numerical integration of the thermical integral for the fermions \( J_+(x) = \int\limits_{0}^{\infty} \,\mathrm{d}k \, k^2 \log\left[ 1 + \exp\left( -\sqrt{k^2+x} \right) \right] \)

Parameters

x	The ratio m^2/T^2
diff	Returns the integrand of J_+ for diff = 0 and for the dJ_+/dx for diff = 1

JInterpolatedHigh()

double BSMPT::ThermalFunctions::JInterpolatedHigh	(	const double &	x,
		const int &	n,
		int	diff = 0
	)

Expansion for large x = m^2/T^2 of the thermal integrals, \( J_{\pm,l}(x,n) = -\exp\left(x^{1/2}\right) \left( \frac{\pi}{2} x^{3/2} \right)^{1/2} \sum\limits_{l=0}^{n} \frac{1}{2^l l!} \frac{\Gamma(5/2+l)}{\Gamma(5/2-l)} x^{-l/2} \), cf. Eq. (2.41) in the manual

Parameters

x	The ratio m^2/T^2
n	The order of the expansion
diff	Returns the expansion for diff = 0 and for its derivative for diff = 1

Variable Documentation

C_BosonShift

const double BSMPT::ThermalFunctions::C_BosonShift = 0.0063108787

constant shift to the polynomial to make the expansions continuous, see delta_- in Eq. (2.43) in the manual

C_BosonTheta

const double BSMPT::ThermalFunctions::C_BosonTheta = 9.469230596

Value for m^2/T^2 at which the interpolated is changed between the two polynomials, see x_-^2 in Eq. (2.43) in the manual

C_FermionShift

const double BSMPT::ThermalFunctions::C_FermionShift = -0.01560316619

constant shift to the polynomial to make the expansions continuous, see delta_+ in Eq. (2.42) in the manual

C_FermionTheta

const double BSMPT::ThermalFunctions::C_FermionTheta = 2.216079120

Value for m^2/T^2 at which the interpolated is changed between the two polynomials, see x_+^2 in Eq. (2.42) in the manual