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In this paper we report on results for the s-wave scattering length of the$\pi$-$K$ system in the $I=3/2$ channel from $N_f=2+1+1$ Lattice QCD. Thecalculation is based on gauge configurations generated by the European TwistedMass Collaboration with pion masses ranging from about $230$ to$450\,\text{MeV}$ at three values of the lattice spacing. Our main result reads$M_{\pi}\,a_0^{3/2,\text{phys}} = -0.059(2)$. Using chiral perturbation theorywe are also able to estimate $M_{\pi}\,a_0^{1/2,\text{phys}} = 0.163(3)$. Theerror includes statistical and systematic uncertainties, and for the latter inparticular errors from the chiral and continuum extrapolations.

Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length