# Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory

## TL;DR

This paper develops a Lorentz-invariant framework for baryon-baryon scattering in SU(3) chiral perturbation theory, deriving integral equations and demonstrating perturbative renormalizability at leading order.

## Contribution

It introduces a coupled-channel integral equation approach with renormalizable potentials in a Lorentz-invariant formulation of baryon chiral perturbation theory.

## Key findings

- Leading-order potentials are perturbatively renormalizable.
- Integral equations have unique solutions in all partial waves.
- Finite subtractions improve ultraviolet convergence.

## Abstract

We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special attention to complications caused by momentum-dependent interactions and propagators of particles with non-zero spin. We define the effective potential as a sum of two-baryon irreducible contributions of time-ordered diagrams and derive a system of integral equations for the scattering amplitude, which provides a coupled-channel generalization of the Kadyshevsky equation. The obtained leading-order baryon-baryon potentials are perturbatively renormalizable, and the corresponding integral equations have unique solutions in all partial waves. We discuss the issue of additional finite subtractions required to improve the ultraviolet convergence of (finite) loop integrals on the example of nucleon-nucleon scattering in the $^3P_0$ partial wave. Assuming that corrections beyond leading order can be treated perturbatively, we obtain a fully renormalizable formalism which can be employed to study baryon-baryon scattering.