Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data

Abstract

A comprehensive analysis of $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes at large unphysical pion mass for all important partial waves is presented. A set of crossing-symmetric partial-wave hyperbolic dispersion relations is used to describe lattice QCD data at $m_{\pi }=391$ MeV. In the present analysis, the amplitudes for the $S$- and $P$-waves are formulated by combining the constraints of analyticity, unitarity, and crossing symmetry, fulfilling Roy-Steiner-type equations. We use these results to investigate the low-lying strange-meson resonances and resolve the instability problem tied to analytic continuation in prior lattice QCD studies based on the $K$-matrix formalism. At $m_{\pi }=391$ MeV, the rigorous Roy-Steiner-type equation approach allows us to determine the $S$-wave scattering lengths, $m_{\pi }{a}_0^{1/2}=\left(0.92_{-0.28}^{+0.06}\right)$, $m_{\pi }{a}_0^{3/2}=-\left(0.32_{-0.02}^{+0.05}\right)$, and the $\kappa$ (also known as $K_0^{\ast }(700)$) pole position, $\sqrt{s_{\kappa }}=\left(966_{-24}^{+41}-i198_{-17}^{+38}\right)$ MeV. We also provide a detailed analysis of the complex validity domain of the Roy-Steiner-type equations.

Comments: 66 pages, 19 figures; discussions added; revised version published in Phys.Rev.D