Related papers: Six-loop beta functions in general scalar theory
We study the $\phi_{\star}^4$ model for a scalar field in a linearization of the Snyder model, using the methods of the Worldline Formalism. Our main result is a master equation for the 1-loop n-point function. From this we derive the…
We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the $\beta$-functions of the dimensionful…
We set up a bootstrap problem for renormalization. Working in the massless four-dimensional O$(N)$ model and the $\lambda \phi^4$ theory, we prove that unitarity leads to all-loop recursion relations between coefficients of scattering…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We consider the problem of determining the beta-functions for any reduced effective field theory. Even though not all the Green's functions of a reduced effective field theory are renormalizable, unlike the full effective field theory,…
We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $\phi^3$ theory and compute the $\beta$ function, the wave function anomalous dimension as well as the mass anomalous dimension…
We investigate the renormalization structure of scalar Galileons in flat spacetime. We explicitly calculate the ultraviolet divergent one-loop contributions to the 2-point, 3-point, 4-point, and 5-point functions. We discuss the structure…
The two-loop anomalous dimension of the chiral matter superfields is calculated for a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $\beta$ function and the anomalous dimension of the quark…
We discuss general one and two-loops banana diagrams with arbitrary masses on the de Sitter spacetime by using direct methods of dS quantum field theory in the dimensional regularization approach. In the one-loop case we also compute the…
We investigate a family of four-dimensional quantum field theories with weakly interacting ultraviolet fixed points up to four loop order in perturbation theory. Key new ingredients are the three loop gauge contributions to quartic scalar…
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $\phi$ with…
We investigate the renormalisation of Einstein gravity using a novel subtraction scheme in dimensional regularisation. The one-loop beta function for Newton's constant receives contributions from poles in even dimensions and can be mapped…
Higher-order vertices at zero external momenta for the scalar field theory describing the critical behaviour of the Ising model are studied within the field-theoretical renormalization group (RG) approach in three dimensions. Dimensionless…
Using the superspace formalism, we compute for the two-dimensional N=1 supersymmetric non-linear $\sigma$-model, the order $(\alpha^{\prime})^{2}$ $(R_{mnpq})^2$ (three-loop) correction to the central charge via the operator product…
Within the framework of QCD we compute renormalization constants for the strong coupling and the quark masses to four-loop order. We apply the DR-bar scheme and put special emphasis on the additional couplings which have to be taken into…
In this paper we continue the study of perturbative renormalizations in an $\mathcal{N}=(0,2)$ supersymmetric model. Previously we analyzed one-loop graphs in the heterotically deformed CP$(N-1)$ models. Now we extend the analysis of the…
We report about the computation of three-loop corrections to the gauge coupling beta functions in the Standard Model.
The loop-expansion of the effective potential in the $O(N)$-symmetric $\phi^4$-model contains generically two types of large logarithms. To resum those systematically a new minimal two-scale subtraction scheme $\tMS$ is introduced in an…