# The quark-mass dependence of elastic $\pi K$ scattering from QCD

## TL;DR

This study uses lattice QCD to analyze how the elastic πK scattering amplitudes depend on quark mass, revealing the evolution of resonances and bound states as pion and kaon masses vary.

## Contribution

First lattice QCD determination of πK scattering amplitudes across multiple quark masses, providing insights into resonance behavior and analytic continuation limitations.

## Key findings

- P-wave amplitude shows a pole evolving from bound state to resonance.
- S-wave amplitude indicates a possible κ/K0*(700)-like resonance.
- Lattice results highlight challenges in model-independent resonance extraction.

## Abstract

We present a determination of the isospin-1/2 elastic $\pi K$ scattering amplitudes in S and P partial waves using lattice Quantum Chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV. Below the first inelastic threshold, the P-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound-state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the S-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $\kappa$/$K_0^\star(700)$-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely-determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.