WallGo.PotentialTools.effectivePotentialNoResum

Class for the one-loop thermal effective potential.

Defined without high-temperature expansion and without resummation.

Classes

EImaginaryOption(value)

Enums for what to do with imaginary parts in the effective potential.

EffectivePotentialNoResum([integrals, ...])

One-loop thermal effective potential
class EImaginaryOption(value)[source]

Enums for what to do with imaginary parts in the effective potential.

ABS_ARGUMENT = 2

Absolute value of argument of integral

ABS_RESULT = 3

Absolute value of analytically continued integral

ERROR = 1

Throw an error if imaginary part nonzero

PRINCIPAL_PART = 4

Principal part of analytically continued integral

class EffectivePotentialNoResum(integrals=None, useDefaultInterpolation=False, imaginaryOption=EImaginaryOption.ERROR)[source]

One-loop thermal effective potential

Specialization of the abstract EffectivePotential class that implements common functions for computing the 1-loop potential at finite temperature, without any assumptions regarding the temperature (no high- or low-\(T\) approximations). In some literature this would be the 4D effective potential.

Initialisation of EffectivePotentialNoResum

Parameters:

  • integrals (Integrals, optional) – An object of the Integrals class. Default is None in which case the integrals will be done without interpolation. Beware this may be slow.

  • useDefaultInterpolation (bool, optional) – If True the default integration data will be loaded and used for interpolation.

  • imaginaryOption (EImaginaryOption) – Default is EImaginaryOption.ERROR which throws an error if nonzero imaginary parts arise. Alternatives are EImaginaryOption.PRINCIPAL_PART for the principal part of the integrals, EImaginaryOption.ABS_RESULT for taking the absolute part of the result, and EImaginaryOption.ABS_ARGUMENT for taking the absolute part of the argument.

Returns:

cls – An object of the EffectivePotentialNoResum class.

Return type:

EffectivePotentialNoResum

abstractmethod bosonInformation(fields, temperature)[source]

Calculate the boson particle spectrum. Should be overridden by subclasses.

Parameters:

  • fields (array_like) – Field value(s). Either a single point (with length Ndim), or an array of points.

  • temperature (float or array_like) – The temperature at which to calculate the boson masses. Can be used for including thermal mass corrrections. The shapes of fields and temperature should be such that fields.shape[:-1] and temperature.shape are broadcastable (that is, fields[0,…]*T is a valid operation).

Returns:

  • massSq (array_like) – A list of the boson particle masses at each input point X. The shape should be such that massSq.shape == (X[…,0]*T).shape + (Nbosons,). That is, the particle index is the last index in the output array if the input array(s) are multidimensional.

  • degreesOfFreedom (float or array_like) – The number of degrees of freedom for each particle. If an array (i.e., different particles have different d.o.f.), it should have length Ndim.

  • c (float or array_like) – A constant used in the one-loop zero-temperature effective potential. If an array, it should have length Ndim. Generally c = 1/2 for gauge boson transverse modes, and c = 3/2 for all other bosons.

  • rgScale (float or array_like) – Renormalization scale in the one-loop zero-temperature effective potential. If an array, it should have length Ndim. Typically, one takes the same rgScale for all particles, but different scales for each particle are possible.

Return type:

tuple[ndarray, float | ndarray, float | ndarray, float | ndarray]

abstractmethod fermionInformation(fields, temperature)[source]

Calculate the fermion particle spectrum. Should be overridden by subclasses.

Parameters:

  • fields (array_like) – Field value(s). Either a single point (with length Ndim), or an array of points.

  • temperature (float or array_like)

Returns:

  • massSq (array_like) – A list of the fermion particle masses at each input point field. The shape should be such that massSq.shape == (field[…,0]).shape. That is, the particle index is the last index in the output array if the input array(s) are multidimensional.

  • degreesOfFreedom (float or array_like) – The number of degrees of freedom for each particle. If an array (i.e., different particles have different d.o.f.), it should have length Ndim.

  • c (float or array_like) – A constant used in the one-loop zero-temperature effective potential. If an array, it should have length Ndim. Generally c = 3/2 for all fermions.

  • rgScale (float or array_like) – Renormalization scale in the one-loop zero-temperature effective potential. If an array, it should have length Ndim. Typically, one takes the same rgScale for all particles, but different scales for each particle are possible.

Return type:

tuple[ndarray, float | ndarray, float | ndarray, float | ndarray]

static jCW(massSq, degreesOfFreedom, c, rgScale)[source]

Coleman-Weinberg potential

Parameters:

  • msq (array_like) – A list of the boson particle masses at each input point X.

  • degreesOfFreedom (float or array_like) – The number of degrees of freedom for each particle. If an array (i.e., different particles have different d.o.f.), it should have length Ndim.

  • c (float or array_like) – A constant used in the one-loop zero-temperature effective potential. If an array, it should have length Ndim. Generally c = 1/2 for gauge boson transverse modes, and c = 3/2 for all other bosons.

  • rgScale (float or array_like) – Renormalization scale in the one-loop zero-temperature effective potential. If an array, it should have length Ndim. Typically, one takes the same rgScale for all particles, but different scales for each particle are possible.

  • massSq (ndarray)

Returns:

jCW – One-loop Coleman-Weinberg potential for given particle spectrum.

Return type:

float or array_like

potentialOneLoop(bosons, fermions)[source]

One-loop corrections to the zero-temperature effective potential in dimensional regularization.

Parameters:

  • bosons (tuple) – bosonic particle spectrum (here: masses, number of dofs, ci)

  • fermions (tuple) – fermionic particle spectrum (here: masses, number of dofs)

  • RGscale (float) – RG scale of the effective potential

Returns:

potential

Return type:

float or array_like

potentialOneLoopThermal(bosons, fermions, temperature)[source]

One-loop thermal correction to the effective potential without any temperature expansions.

Parameters:

  • bosons (tuple) – bosonic particle spectrum (here: masses, number of dofs, ci)

  • fermions (tuple) – fermionic particle spectrum (here: masses, number of dofs)

  • temperature (float or array_like)

Returns:

potential

Return type:

float or array_like