For theories with multiple couplings the perturbative $β$-functions for scalar, Yukawa couplings are expressible in terms of contributions corresponding to one particle irreducible graphs and also contributions which are one particle reducible depending on the anomalous dimension. Here we discuss redefinitions, or changes of scheme, which preserve this structure. The redefinitions allow for IPR contributions of a specific form, as is necessary to encompass the relation between MS and momentum subtraction renormalisation schemes. Many multiply 1PR terms in the transformed $β$-function are generated but these can all be absorbed into antisymmetric contributions to the anomalous dimensions which are essentially arbitrary and can be discarded. As an illustration the results are applied to the scheme dependence of the anomalous dimension, which determines the $β$-function, for ${\cal N}=1$ supersymmetric scalar fermion theories in four dimensions up to four loops.
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa theory show that when this kind of redundancy exists, different renormalization schemes may lead to different expressions for the renormalization group $β$-functions, even at only one-loop order. However, the renormalization group scaling of physically observable quantities appears not to share this kind of scheme dependence.
Within the refined Gribov-Zwanziger scenario for four-dimensional Yang-Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that simply adding a gluon mass term to the usual Faddeev-Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in good agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization…
Investigation of the factorization scheme dependence of finite order perturbative QCD calculations: searching for approximately ZERO factorization scheme
We investigate the dependence of the $ρ$ meson-nucleon coupling constant on the temperature of the medium using the soft-wall model of AdS/QCD. The finite temperature profile functions for the vector and fermion fields are applied to the model having a thermal dilaton field. The interaction Lagrangian in the bulk between these fields is written as in zero temperature case and includes minimal- and magnetic-type interactions. The temperature dependence of the $g_{ρNN}(T)$ coupling constant and its terms are plotted. We observe that the coupling constant and its separate terms become zero at the…
The resummed thermodynamics of ${\cal N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions ($\text{SYM}_{4,4}$) has been calculated previously to two loop order within hard thermal loop perturbation theory (HTLpt) using the canonical dimensional regularization (DRG) scheme. Herein, we revisit this calculation using the regularization by dimensional reduction (RDR) scheme. Since the RDR scheme manifestly preserves supersymmetry it is the preferred scheme, however, it is important to assess if and by how much the resummed perturbative results depend on the regularization scheme u…
The least squares method: application to analysis of the flavor dependence of the QCD relation between pole and $\rm{\overline{MS}}$-scheme running heavy quark masses
We investigate the renormalization group flow of the field-dependent Yukawa coupling in the framework of the three flavor quark-meson model. In a conventional perturbative calculation, given that the field rescaling is trivial, the Yukawa coupling does not get renormalized at the one-loop level if it is coupled to an equal number of scalar and pseudoscalar fields. Its field-dependent version, however, does flow with respect to the scale. Using the functional renormalization group technique, we show that it is highly nontrivial how to extract the actual flow of the Yukawa coupling as there are …
A common feature of recent functional renormalization group investigations of effective low-energy QCD is the appearance of a back-bending behavior of the chiral phase transition line at low temperatures together with a negative entropy density in the symmetric regime. The regulator scheme dependence of this phenomenon and the necessary modifications at finite densities are analyzed within a two-flavor quark-meson model. The flows at finite densities for three different regulators of three- or four-dimensional momenta are confronted to each other. It is found that the back-bending behavior and…
