Rigorous Roy-Steiner equation analysis of $\pi K$ scattering at unphysical quark masses

Abstract

We perform a rigorous analysis of the $\pi K$ scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the $\pi K$ lattice data in the inelastic region, the lattice data from the crossed $\pi\pi \to K\bar{K}$ channels, the masses of $f_0(500)$ and $K^*$ at the same pion mass from previous study, and the Regge model. Predictions on the elastic $\pi K$ scattering phase shifts and the $K_0^*(700)$ pole content are made. Contrary to the virtual pole scenario obtained using the $K$-matrix method in the literature, we find that lightest strange scalar meson $K_0^*(700)$ remains a broad resonance at $m_\pi=391$ MeV. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.