Renormalization of the unitarized Weinberg-Tomozawa interaction without on-shell factorization and I=0 K¯N–πΣ coupled channels

Osamu Morimatsu,Kazuki Yamada

doi:10.1103/physrevc.100.025201

Abstract

We calculate the scattering $T$-matrix of $I=0$ $\bar K N-\pi \Sigma$ coupled channels taking a ladder sum of the Weinberg-Tomozawa interaction without on-shell factorization, regularizing three types of divergent meson-baryon loop functions by dimensional regularization and renormalizing them by introducing counter terms. We show that not only infinite but also finite renormalization is important in order for the renormalized physical scattering $T$-matrix to have the form of the Weinberg-Tomozawa interaction. The results with and without on-shell factorization are compared. The difference of the scattering $T$-matrix is small near the renormalization point, close to the observed $\Lambda$(1405). The difference, however, increases with the distance from the renormalization point. The scattering $T$-matrix without on-shell factorization has two poles in the complex center-of-mass energy plane as with on-shell factorization, the real part of which is close to the observed $\Lambda$(1405). While the difference is small with and without on-shell factorization in the position of the first pole, closer to the observed $\Lambda$(1405), the difference is considerably large in the position of the second pole: the imaginary part of the center-of-mass energy of the second pole without on-shell factorization is as large as or even larger than twice that with on-shell factorization. Also, we discuss the origin of the contradiction about the second pole between two approaches, the chiral unitary approach with on-shell factorization and the phenomenological approach without on-shell factorization.

Highlights

Chiral perturbation theory [1–4] is a method to describe the dynamics of Goldstone bosons in the framework of an effective field theory
We show that infinite and finite renormalization is important for the renormalized physical scattering T -matrix to have the form of the Weinberg-Tomozawa interaction
In this paper we studied unitarized chiral dynamics without on-shell factorization

Summary

Introduction

Chiral perturbation theory [1–4] is a method to describe the dynamics of Goldstone bosons in the framework of an effective field theory. Writing down the most general effective Lagrangian containing all possible terms compatible with chiral symmetry, one obtains the scattering T -matrix order by order in powers of momenta and quark masses at low center-of-mass energies, where infinities arising from loops are absorbed in a renormalization of the coefficients of the effective Lagrangian. Chiral perturbation theory has been successful in describing low-energy meson-meson and meson-baryon scatterings but cannot describe bound states or resonances due to its very perturbative nature. A nonperturbative method, the chiral unitary approach has been developed [5–8], in which the leading terms of chiral

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Results

Conclusion