Study on the $P$-wave form factors contributing to $B_s$ to $D_s$ inclusive semileptonic decays from lattice simulations

Abstract

We present a pilot study on extracting the form factors of the semileptonic decay of a $B_s$ meson to the $P$-wave $D_s^{\ast \ast }$ states from $B_s$ four-point correlators. With their inclusive nature, four-point correlators include contributions from all possible final states. From the extracted $P$-wave form factors, we obtain numerical results for the corresponding Isgur-Wise form factors. The results suggest significant contributions from radial excitations to the Uraltsev sum rule at zero-recoil. In this pilot study, a coarse lattice of $24^3\times 64$ with lattice spacing of $0.11\mathrm{fm}$ is used for the analysis.

Comments: 10 pages, 3 figures, Contribution to the 41st International Symposium on Lattice Field Theory (LATTICE2024), 28 July - 3 August 2024, Liverpool, UK