Related papers: Renormalization Scheme Dependence and Renormalizat…
Starting from a well defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to…
The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function beta, the next-to-leading-log (NLL)…
The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of…
Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories.…
We prove that the functional renormalization group flow equation admits a perturbative solution and show explicitly the scheme transformation that relates it to the standard schemes of perturbation theory. We then define a universal scheme…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single…
As an alternative to directly integrating their defining equations to find the running coupling $a(\mu)$ and the running mass $m(\mu)$, we expand these quantities in powers of $\ln\left(\frac{\mu}{\mu^\prime}\right)$ and their boundary…
We present a new procedure for improving the effective potential by using renormalization group equation (RGE) in the presence of several mass scales. We propose a modification of the mass-dependent (MD) renormalization scheme, MDbar…
Renormalization group procedure suggests that the low-energy behavior of effective coupling constant in asymptotically free Hamiltonians is connected with the existence of bound states and depends on how the interactions responsible for the…
We examine the perturbative calculation of the inclusive semi-leptonic decay rate $\Gamma$ for the $b$-quark, using mass-independent renormalization. To finite order of perturbation theory the series for $\Gamma$ will depend on the…
When calculating next-to-leading order QCD cross sections, divergences in intermediate steps of the calculation must be regularized. The final result is independent of the regularization scheme used, provided that it is unitary. In this…
The dependence of function renormalization group equation on regulators is investigated. A parameter is introduced to control the suppression of regulators. Functional renormalization group equations will become regulator-independent if…
We reconsider the choice of renormalization schemes in a differential-equation approach to aid the discussion of the renormalization of the unstable particles and the CKM matrix in the Standard Model. Certain mass dependent schemes do not…
Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = sigma(e^+ e^- --> hadrons)/sigma(e^+ e^- --> mu^+ mu^-), as obtained from the…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
Similarity renormalization group procedure identifies the role of bound states in the low-energy rate of change of effective coupling constant in a model Hamiltonian with asymptotic freedom.