Renormalization of relativistic baryon chiral perturbation theory and power counting

Abstract

We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized diagrams beyond the standard MS scheme of chiral perturbation theory to remove contributions violating the power counting. This is achieved by a suitable renormalization of the parameters of the most general effective Lagrangian. In addition to its simplicity our method has the benefit that it can be easily applied to multiloop diagrams. As an application we discuss the mass of the nucleon and compare the result with the expression of the infrared regularization of Becher and Leutwyler.

One-loop analysis of the interactions between charmed mesons and Goldstone bosons

“…There is a notable power counting breaking (PCB) issue in baryon ChPT [33]: using the dimensional regularization with the modified minimal subtraction (MS) scheme in calculating loop integrals, the naive power counting does not work and all loop diagrams start contributing at O p 2 , with p being a small momentum. There have been several solutions to this problem: heavy baryon (HB) approach [34,35], infrared regularizaion (IR) [36] and extended-on-mass-shell (EOMS) scheme [37] (for a review and a detailed comparison of these approaches, see ref. [38]).…”

Chiral dynamics of/with unstable particles

“…Specifically, we employed the heavy-baryon (HB) formulations utilizing the standard counting of the nucleon mass as m N ∼ Λ b (HB-πN) with Λ b denoting the breakdown scale of the chiral expansion, and the counting scheme with m N ∼ Λ 2 b /Q (HB-NN) employed in few-nucleon studies. We have also performed calculations within a covariant (Cov) formulation of ChPT based on an extended on-mass-shell (EOMS) renormalization scheme [20][21][22]. Our analysis differs in several aspects from the already mentioned earlier studied of this topic.…”

Threshold Neutral Pion Photoproduction on the Proton

“…In addition, the usual divergences of dimensional regularization also have to be dealt with. We opt for the EOMS regularization scheme, where both these problems are addressed simultaneously, by absorbing their fully analytical expressions into the low-energy constants of the corresponding order [28,29]. The success of this renormalization scheme has been thoroughly studied on many physical observables in [30][31][32][33][34][35][36][37][38][39][40][41].…”