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

TL;DR

The paper addresses meson-baryon scattering lengths without annihilation diagrams using heavy baryon chiral perturbation theory up to $O(p^4)$. It derives threshold $T$-matrices for five channels, leverages SU(3) symmetry to reduce parameter dependence, and includes loop corrections up to $O(p^4)$ with scale-independent renormalization. Low-energy constants are extracted via both conventional least-squares and Bayesian fits to non-physical lattice QCD data, with an additional non-perturbative iteration to improve convergence, and the results are extrapolated to the physical point. Despite convergence challenges in the perturbative SU(3) expansion, the authors obtain robust negative scattering lengths across all channels by combining four fitting approaches, providing predictions with quantified uncertainties that can be tested by future lattice or experimental data. The work highlights the value of iterative non-perturbative treatment and careful statistical analysis in chiral EFT predictions for kaon-baryon interactions.

Abstract

We calculate the threshold $T$ matrices of the meson and baryon processes that have no annihilation diagrams: $π^{+}Σ^{+}$, $π^{+}Ξ^0$, $K^+p$, $K^+n$, and $\bar{K}^0Ξ^0$ 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 $a_{π^+Σ^+}=-0.16\pm 0.07\,\text{fm}$, $a_{π^+Ξ^0}=-0.04\pm0.04\,\text{fm}$, $a_{K^+p}=-0.41\pm 0.11\,\text{fm}$, $a_{K^+n}=-0.19\pm 0.10\,\text{fm}$, and $a_{\bar{K}^0Ξ^0}=-0.30\pm 0.07\,\text{fm}$, where the uncertainties are conservatively estimated by taking the maximum deviation between the median and extreme values of the statistical errors.

Figures (3)

• Figure 1: Nonvanishing one-loop diagrams contributing at chiral order four. The heavy dots refer to vertices from $\mathcal{L}_{\phi B}^{(2)}$. Dashed lines represent Goldstone bosons and solid lines represent octet baryons.
• Figure 2: Comparison between the five-channel fitting results obtained using the least-squares fitting method and the lattice QCD data for scattering lengths reported in ref. Torok:2009dg.
• Figure 3: Comparison between the five-channel fitting results obtained using the Bayesian statistical analysis and the lattice QCD data for scattering lengths reported in ref. Torok:2009dg.