Related papers: General scalar renormalisation group equations at …
We present analytical five-loop results for the quark mass and quark field anomalous dimensions, for a general gauge group and in the MSbar scheme. We confirm the values known for the gauge group SU(3) from an independent calculation, and…
We compute the contributions of the dimension-6 SMEFT operators involving four third-generation quarks to the two-loop renormalisation of the quark fields and masses. We perform the computations in both the Naive Dimensional Regularisation…
We derive an algorithm for automatic calculation of perturbative $\beta$-functions and anomalous dimensions in any local quantum field theory with canonical kinetic terms. The infrared rearrangement is performed by introducing a common mass…
We present the three-loop QCD+QED mixed corrections to the on-shell quark mass and wave-function renormalization constants through orders $\mathcal{O}(\alpha_s^m\alpha^n)$ with $m+n=3$. We further derive the three-loop relation between the…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
We extend the ${\cal O}(\alpha_s^5)$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
A two-loop calculation of the renormalization group $\beta$--function in a momentum subtraction scheme with massive quarks is presented using the background field formalism. The results have been obtained by using a set of new generalized…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\Gamma_k$. The ordinary effective action $\Gamma_0$ can be obtained by integrating the flow equation from…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of quantum gravity in arbitrary dimensions. Renormalization group flow diagrams are presented for the three-dimensional and four-dimensional…