Triangle and box diagrams in coupled-channel systems from the chiral Lagrangian

TL;DR

This paper develops a systematic method to compute triangle and box loop contributions in coupled-channel scattering of Goldstone bosons and charmed mesons, ensuring power-counting consistency and avoiding singularities.

Contribution

It introduces an extended set of Passarino--Veltman functions for manifest power-counting conserving one-loop calculations in coupled-channel systems.

Findings

Provides compact, order three and four expressions for loop contributions.

Ensures absence of power-counting violating terms in loop calculations.

Offers a formalism applicable to other meson-baryon scattering systems.

Abstract

We perform an analysis of triangle- and box-loop contributions to the generalized potential in the scattering of Goldstone bosons off the J^P= 0^- and 1^- charmed mesons. Particular emphasis is put on the use of on-shell mass parameters in such contributions in terms of a renormalization scheme that ensures the absence of power-counting violating terms. This is achieved with a systematically extended set of Passarino--Veltman basis functions, that leads to manifest power-counting conserving one-loop expressions and avoids the occurrence of superficial kinematical singularities. Compact expressions to chiral order three and four are presented that are particularly useful in coding such coupled-channel systems. Our formal results are generic and prepare analogous computations for other systems, like meson-baryon scattering from the chiral Lagrangian.