πKscattering in full QCD with domain-wall valence quarks

We calculate the ${\pi }^{+}{K}^{+}$ scattering length in fully-dynamical lattice QCD with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of $b=0.125\mathrm{fm}$, lattice spatial size of $L=2.5\mathrm{fm}$ and at pion masses of $m_{\pi }\sim 290$, 350, 490 and 600 MeV. The lattice data, analyzed at next-to-leading order in chiral perturbation theory, allows an extraction of the full $\pi K$ scattering amplitude at threshold. Extrapolating to the physical point gives $m_{\pi }{a}_{3/2}=-0.0574\pm {0.0016}_{-0.0058}^{+0.0024}$ and $m_{\pi }{a}_{1/2}=0.1725\pm {0.0017}_{-0.0156}^{+0.0023}$ for the $I=3/2$ and $I=1/2$ scattering lengths, respectively, where the first error is statistical and the second error is an estimate of the systematic due to truncation of the chiral expansion.