Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in N f = 2 + 1 lattice QCD

Preprint number: CP3-Origins-2018-5 DNRF90
Authors: Ruairi Brett (Carnegie Mellon), John Bulava (CP3-Origins & DIAS), Jacob Fallica (U. of Kentucky), Andrew Hanlon (U. of Mainz), Ben Hoerz (U. of Mainz), and Colin Morningstar (Carnegie Mellon)
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The elastic \(I=1/2\), \(s\)- and \(p\)-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with \(N_{\mathrm{f}} = 2+1\) flavors of dynamical Wilson-clover fermions at \(m_{\pi} = 230\mathrm{MeV}\). A large spatial extent of \(L = 3.7\mathrm{fm}\) enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly.The \(p\)-wave amplitude is well described by a Breit-Wigner shape with parameters \(m_{K^{*}}/m_{\pi} = 3.808(18)\) and \(g^{\mathrm{BW}}_{K^{*}K\pi} = 5.33(20)\) which are insensitive to the inclusion of \(d\)-wave mixing and variation of the \(s\)-wave parametrization. An effective range description of the near-threshold \(s\)-wave amplitude yields \(m_{\pi}a_0 = -0.353(25)\).