Lambda-nucleon scattering in baryon chiral perturbation theory

TL;DR

This paper computes lambda-nucleon scattering phase shifts using relativistic baryon chiral perturbation theory, highlighting the importance of nonperturbative treatment for certain channels and comparing results with non-relativistic and lattice QCD data.

Contribution

It introduces a relativistic formulation for lambda-nucleon scattering in baryon chiral perturbation theory and discusses nonperturbative effects in specific partial waves.

Findings

Relativistic approach yields milder ultraviolet behavior.

Some higher-order contributions require nonperturbative treatment.

Results are consistent with non-relativistic and lattice QCD phase shifts.

Abstract

We calculate the lambda-nucleon scattering phase shifts and mixing angles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. Scattering amplitudes are obtained by solving the corresponding coupled-channel integral equations that have a milder ultraviolet behavior compared to their non-relativistic analogs. This allows us to consider the removed cutoff limit in our leading-order calculations also in the $^3P_0$ and $^3P_1$ partial waves. We find that, in the framework we are using, at least some part of the higher-order contributions to the baryon-baryon potential in these channels needs to be treated nonperturbatively and demonstrate how this can be achieved in a way consistent with quantum field theoretical renormalization for the leading contact interactions. We compare our results with the ones of the non-relativistic approach and lattice QCD phase shifts obtained for non-physical pion masses.