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We discuss the renormalization of the electric charge at the two-loop level in the Standard Model of the electroweak interactions. We explicitly calculate the expression of the complete on-shell two-loop counterterm using the Background…
The critical exponent corresponding to the renormalization of the composite operator $\bar{\psi}\psi$ is computed in quantum electrodynamics at $O(1/\Nf^2)$ in arbitrary dimensions and covariant gauge at the non-trivial zero of the…
In this thesis we elaborate on two different aspects of the Effective Field Theory (EFT) approach to a Binary Coalescing system in General Relativity (GR). First, we consider the issue of hereditary effects in the Post-Newtonian (PN)…
Chiral EFT yields singular potentials that require regularization and renormalization when implemented in a dynamical equation such as the Lippmann--Schwinger equation. We employ two different approaches, renormalization with contact terms…
The Legendre flow equation, a version of exact Wilsonian renormalization group (WRG) equation, is employed to consider the power counting issues in Nuclear Effective Field Theory. A WRG approach is an ideal framework because it is…
We compute the two-loop effective field theory (EFT) power spectrum of dark matter density fluctuations in $\Lambda$CDM using the recently proposed COBRA method (Bakx. et al, 2025). With COBRA, we are able to evaluate the two-loop matter…
Large scale structure surveys are likely the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a…
Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can…
The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point…
We obtain for the first time the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet…
Using functional renormalization group methods, we study an effective low-energy model describing the Ising-nematic quantum critical point in two-dimensional metals. We treat both gapless fermionic and bosonic degrees of freedom on equal…
We calculate one loop contributions to $\Gamma(h \rightarrow \gamma \, \gamma)$ from higher dimensional operators, in the Standard Model Effective Field Theory (SMEFT). Some technical challenges related to determining Electroweak one loop…
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions…
We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time…
Motivated by the results of the electroweak precision experiments, studies of two-loop self-energy Feynman diagrams are performed. An algebraic method for the reduction of all two-loop self-energies to a set of standard scalar integrals is…
We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of…
Investigating quantum effects arising from high loops in perturbation theory is crucial for the physical applications of any quantum field theory. This paper presents a comprehensive analysis of the two-loop renormalization of CPT-even…
In this article we compute the action of the two loop dilatation operator on restricted Schur polynomials that belong to the su(2) sector, in the displaced corners approximation. In this non-planar large N limit, operators that diagonalize…
A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the…
We present a systematic functional approach to calculating symmetry-restoring counterterms in Effective Field Theories (EFTs) regulated using the Breitenlohner--Maison--'t Hooft--Veltman (BMHV) scheme. Building on a recently developed…