The oneloop.ghost module

Library of functions and routines for the one-loop ghost propagator computed in the Screened Massive Expansion.

Contents:

Note

  1. Where not otherwise specified, s is the adimensional Euclidean momentum squared s=p^{2}/m^{2}.

  2. Most functions are defined modulo factors of the coupling constant. If the ren parameter is available, such factors become irrelevant when renormalization is enabled using ren=True.

The one-loop ghost dressing function, propagator and spectral function

ghost_chi_inv(s, xi=0, G0=0.14524)

Inverse ghost dressing function \chi^{-1}(s).

Modulo a factor of \alpha.

Parameters:

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

ghost_chi(s, xi=0, G0=0.14524)

Ghost dressing function \chi(s).

Modulo a factor of \alpha^{-1}.

Parameters:

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

ghost_prop(s, xi=0, G0=0.14524, ren=True, Z=None, mu0=6.099699589795203, dimensionful=False, m=0.65577)

Ghost propagator \mathcal{G}(p^{2}).

Modulo a factor of \alpha^{-1}.

Parameters:

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

  • ren – if True, multiplicatively renormalize the propagator

  • Z – if None, renormalize the propagator in the MOM scheme at the scale mu0, else use Z as the multiplicative renormalization factor (only if ren=True)

  • mu0 – adimensional renormalization scale \mu_{0} for the renormalization of the propagator in the MOM scheme (only if ren=True)

  • dimensionful – if False, adimensionalize the propagator by multiplying it by m2; if True, s is the dimensionful momentum squared p^{2}

  • m – gluon mass parameter m (only if dimensionful=True)

ghost_spectral(s, xi=0, G0=0.14524, ren=True, Z=None, mu0=6.099699589795203, dimensionful=False, m=0.65577)

Ghost spectral function \rho_{\mathcal{G}}(p^{2}) in Minkowski space.

Modulo a factor of \alpha^{-1}. The \varepsilon for the difference across the branch cut is defined in the PySmeQcd.settings module.

Parameters:

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

  • ren – if True, multiplicatively renormalize the spectral function

  • Z – if None, renormalize the spectral function in the MOM scheme at the scale mu0, else use Z as the multiplicative renormalization factor (only if ren=True)

  • mu0 – adimensional renormalization scale \mu_{0} for the renormalization of the spectral function in the MOM scheme (only if ren=True)

  • dimensionful – if False, adimensionalize the spectral function by multiplying it by m2; if True, s is the dimensionful Minkowski momentum squared p^{2}_{M}

  • m – gluon mass parameter m (only if dimensionful=True)

Note

s is the adimensional Minkowski momentum squared p_{M}^{2}/m^{2}, or the dimensionful Minkowski momentum squared p_{M}^{2} if dimensionful=True.

dghost_chi_inv(s, xi=0)

Derivative of ghost_chi_inv with respect to s.

Parameters:

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

Plots

ghost_chi_plot(s=[0.001, 25], N_s=1000, xi=0, G0=0.14524, inverse=False, ren=True, Z=None, mu0=6.099699589795203, dimensionful=False, m=0.65577, scale='log', title=False, outf=None)

Plots the ghost dressing function in Euclidean space.

Modulo a factor of \alpha^{-1}.

Parameters:

  • s – a two-element list containing the minimum and maximum momentum squared for the plot (see below for dimensions)

  • N_s – an integer specifying the number of plot points

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

  • inverse – if True, plot the inverse dressing function

  • ren – if True, multiplicatively renormalize the dressing function

  • Z – if None, renormalize the dressing function in the MOM scheme at the scale mu0, else use Z as the multiplicative renormalization factor (only if ren=True)

  • mu0 – adimensional renormalization scale \mu_{0} for the renormalization of the dressing function in the MOM scheme (only if ren=True)

  • dimensionful – if False, adimensionalize the dressing function by multiplying it by m2; if True, s is the dimensionful momentum squared p^{2}

  • m – gluon mass parameter m (only if dimensionful=True)

  • scale – if set to 'log', switch to a log-lin scale

  • title – if True, show a title for the plot

  • outf – if not None, save the output to the file specified by outf rather than printing it out

ghost_prop_plot(s=[0.001, 25], N_s=1000, xi=0, G0=0.14524, ren=True, Z=None, mu0=6.099699589795203, dimensionful=False, m=0.65577, scale='log', title=False, outf=None)

Plots the ghost propagator in Euclidean space.

Modulo a factor of \alpha^{-1}.

Parameters:

  • s – a two-element list containing the minimum and maximum momentum squared for the plot (see below for dimensions)

  • N_s – an integer specifying the number of plot points

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

  • ren – if True, multiplicatively renormalize the propagator

  • Z – if None, renormalize the propagator in the MOM scheme at the scale mu0, else use Z as the multiplicative renormalization factor (only if ren=True)

  • mu0 – adimensional renormalization scale \mu_{0} for the renormalization of the propagator in the MOM scheme (only if ren=True)

  • dimensionful – if False, adimensionalize the propagator by multiplying it by m2; if True, s is the dimensionful momentum squared p^{2}

  • m – gluon mass parameter m (only if dimensionful=True)

  • scale – if set to 'log', switch to a log-lin scale

  • title – if True, show a title for the plot

  • outf – if not None, save the output to the file specified by outf rather than printing it out

ghost_spectral_plot(s=[0.001, 25], N_s=1000, xi=0, G0=0.14524, ren=True, Z=None, mu0=6.099699589795203, dimensionful=False, m=0.65577, scale='log', title=False, outf=None)

Plots the ghost spectral function in Minkowski space.

Modulo a factor of \alpha^{-1}.

Parameters:

  • s – a two-element list containing the minimum and maximum Minkowski momentum squared for the plot (see below for dimensions)

  • N_s – an integer specifying the number of plot points

  • xi – gauge parameter \xi

  • G0 – additive renormalization constant G_{0}

  • ren – if True, multiplicatively renormalize the spectral function

  • Z – if None, renormalize the spectral function in the MOM scheme at the scale mu0, else use Z as the multiplicative renormalization factor (only if ren=True)

  • mu0 – adimensional renormalization scale \mu_{0} for the renormalization of the spectral function in the MOM scheme (only if ren=True)

  • dimensionful – if False, adimensionalize the spectral function by multiplying it by m2; if True, s is the dimensionful Minkowski momentum squared p^{2}_{M}

  • m – gluon mass parameter m (only if dimensionful=True)

  • scale – if set to 'log', switch to a log-lin scale

  • title – if True, show a title for the plot

  • outf – if not None, save the output to the file specified by outf rather than printing it out

Note

s is the adimensional Minkowski momentum squared p_{M}^{2}/m^{2}, or the dimensionful Minkowski momentum squared p_{M}^{2} if dimensionful=True.