Related papers: Renormalization Group Summation with Heavy Fields
The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…
We consider logarithmic contributions to the free energy, instanton effective action and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all…
We propose a simple derivation of renormalization group equations and Callan-Symanzik equations as decoupling theorems of the structures underlying effective field theories.
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
New proves of decoupling of massive fields in several quantum field theories are derived in the effective Lagrangian approach based on Wilson renormalization group. In the most interesting case of gauge theories with spontaneous symmetry…
Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a $\phi^4$-type scalar field theory involving two real scalar fields (one is heavy with mass $M$ and the other light). Then, to all orders…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
Using the renormalisation group and a conjecture concerning the perturbation series for the effective potential, the leading logarithms in the effective potential are exactly summed for $O(N)$ scalar and Yukawa theories.
We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge…
We introduce a systematic approach for the resummation of perturbative series which involve large logarithms not only due to large invariant mass ratios but large rapidities as well. Series of this form can appear in a variety of gauge…
For any perturbative series that is known to $k$-subleading orders of perturbation theory, we utilise the process-appropriate renormalization-group (RG) equation in order to obtain all-orders summation of series terms proportional to…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We use renormalization group summed perturbation theory (RGSPT) to improve perturbation series in quantum chromodynamics in the determination of some of the standard model parameters.
Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log…
I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian…
Analytic continuation of the perturbative series from spacelike to timelike regions is performed using renormalization group summed perturbation theory (RGSPT). This method provides an all-order summation of kinematic ``$\pi^2$-terms''…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder-Schrader formulation of quantum field theory. To this end, we devise a very general regularisation…
The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on…