$K\pi$ scattering and the $K^{\ast }(892)$ resonance in 2+1 flavor QCD

In this project, we will compute the form factors relevant for $B \to K^*(\to K \pi)\ell^+\ell^-$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B\to K\pi$ matrix elements, the $K \pi$ scattering amplitude needs to be determined using L"uscher’s method. Here we present preliminary results from our calculations with $2+1$ flavors of dynamical clover fermions. We extract the $P$-wave scattering phase shifts and determine the $K^{\ast }$ resonance mass and the $K^{\ast }K\pi$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.