Interactions of πK, ππK and KKπ systems at maximal isospin from lattice QCD

We study the interactions of systems two and three nondegenerate mesons composed pions kaons at maximal isospin using lattice QCD, specifically $\pi^+K^+$, $\pi^+\pi^+K^+$ $K^+K^+\pi^+$. Utilizing stochastic LapH method, we determine spectrum these on CLS $N_f=2+1$ ensembles with pion masses $200$ MeV $340$ MeV, include many levels in different momentum frames. constrain K matrices describing two- three-particle by fitting to results predicted finite-volume formalism, including up $p$ waves. This requires also for $\pi^+\pi^+$ $K^+ K^+$ spectrum, which have been obtained previously same configurations. explore strategies, comparing fits energy shifts energies boosted rest frame, simultaneous global all relevant channels those where first fit two-particle then add information. provide determination matrix K^+ \pi^+$ systems, finding statistically significant nonzero most cases. $s$ waves $\pi^+ scattering, evidence an attractive $p$-wave scattering length. compare our Chiral Perturbation Theory, investigation impact discretization errors, leading order predictions Wilson Theory.