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

Abstract

In this project, we will compute the form factors relevant for $B\to K^{\ast }(\to K\ddot{I}€){\ell }^{+}{\ell }^{-}$ decays. To map the finite-volume matrix elements computed on the lattice to the infinite-volume $B\to K\ddot{I}€$ matrix elements, the $K\ddot{I}€$ scattering amplitude needs to be determined using Lüscher'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 $K^{\ast }K\ddot{I}€$ coupling for two different ensembles with pion masses of $317(2)$ and $178(2)$ MeV.

7 pages, 3 figures, Proceedings of the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan State University, East Lansing, Michigan USA