Meson-baryon scattering lengths without annihilation diagrams to order $p^4$ in heavy baryon chiral perturbation theory

TL;DR

This paper computes meson-baryon scattering lengths up to order $p^4$ in heavy baryon chiral perturbation theory, fitting lattice QCD data to determine low-energy constants and physical scattering lengths.

Contribution

It provides the first detailed calculation of these scattering lengths at order $p^4$ using both perturbative and non-perturbative methods, with comprehensive fits to lattice data.

Findings

Scattering lengths for five channels are provided with uncertainties.

Convergence issues are observed in the perturbative approach.

Median values from multiple fits yield the final scattering lengths.

Abstract

We calculate the threshold $T$ matrices of the meson and baryon processes that have no annihilation diagrams: $\pi^{+}\Sigma^{+}$, $\pi^{+}\Xi^0$, $K^+p$, $K^+n$, and $\bar{K}^0\Xi^0$ to the fourth order in heavy baryon chiral perturbation theory. By performing least squares and Bayesian fits to the non-physical lattice QCD data, we determine the low-energy constants through both perturbative and non-perturbative iterative methods. By using these low-energy constants, we obtain the physical scattering lengths in these fits. The convergence behavior is not good across all channels in the perturbative method. The scattering lengths for the five channels, obtained by taking the median values from four different fitting approaches, are $a_{\pi^+\Sigma^+}=-0.16\pm 0.07\,\text{fm}$, $a_{\pi^+\Xi^0}=-0.04\pm0.04\,\text{fm}$, $a_{K^+p}=-0.41\pm 0.11\,\text{fm}$, $a_{K^+n}=-0.19\pm 0.10\,\text{fm}$, and $a_{\bar{K}^0\Xi^0}=-0.30\pm 0.07\,\text{fm}$, where the uncertainties are conservatively estimated by taking the maximum deviation between the median and extreme values of the statistical errors.