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

TL;DR

This study uses lattice simulations to extract P-wave form factors in B_s to D_s** semileptonic decays, revealing significant radial excitation contributions and providing insights into the Isgur-Wise form factors.

Contribution

It introduces a lattice-based method to extract P-wave form factors from four-point correlators in B_s decays, including all final states, which is a novel approach.

Findings

Radial excitations significantly contribute to the Uraltsev sum rule at zero-recoil.

Numerical results for Isgur-Wise form factors are obtained from lattice data.

The study demonstrates the feasibility of using coarse lattices for such analyses.

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^{**} $ 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.