Related papers: Revisiting RGEs for general gauge theories
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
The one-loop renormalization-group equations (RGEs) running behavior of quark and lepton mass matrices with general structures are studied simultaneously. Suppose the non-linear terms of RGEs are dominated by the Yukawa couplings of top…
The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature…
The scalar mass is determined in the simplest scalar-fermion Yukawa-model in the whole range of stability of the scalar potential. Two versions of the Functional Renormalisation Group (FRG) equations are solved, where also composite…
In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $ \beta $-functions are known to the 3-2-2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply…
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective potential and the study of Dynamical Symmetry Breaking (DSB) in an Gross-Neveu (GN) model with N fermions fields…
We present four-loop results for the gauge beta-function and the fermion mass anomalous dimension for a gauge theory with a general gauge group and a multiplet of fermions transforming according to an arbitrary representation, calculated…
Recently, Poole & Thomsen have presented the Renormalization Group Equations (RGEs) in the $\overline{\mathrm{MS}}$ scheme for dimensionless parameters of a general renormalizable gauge theory in a new formalism based on the Local…
We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $\lambda$ and Yukawa…
Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art…
Quantum field theories containing scalar fields with equal quantum numbers allow for a mixed kinetic term in the Lagrangian. It has been argued that this mixing must be taken into consideration when performing renormalization group (RG)…
We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields $\varphi_a$, general Yukawa couplings and a $\mathbb{Z}_4$ symmetry that forbids linear and trilinear terms in the scalar potential. Moreover,…
The MFA approach for simulations with dynamical fermions in lattice gauge theories allows in principle to explore the parameters space of the theory (e.g. the $\beta, m$ plane for the study of chiral condensate in QED) without the need of…
We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel…
We derive the renormalization group equations (RGE) for the flavour coupling matrices of the effective dimension-five operators which yield Majorana neutrino masses in the multi-Higgs-doublet Standard Model; in particular, we consider the…
Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of…
Improving the effective action by the renormalization group (RG) with several mass scales is an important problem in quantum field theories. A method based on the decoupling theorem was proposed in \cite{Bando:1992wy} and systematically…
We discuss renormalization in a toy model with one fermion field and one real scalar field phi, featuring a spontaneously broken discrete symmetry which forbids a fermion mass term and a phi^3 term in the Lagrangian. We employ a…