Lattice Study of Spectator Effects in $b$-hadron Decays

TL;DR

This paper presents a lattice QCD calculation of matrix elements related to spectator effects in $b$-hadron decays, providing essential non-perturbative inputs for the Heavy Quark Expansion.

Contribution

It offers the first lattice determination of the bare matrix elements for spectator effects in $b$-hadron decays, focusing on $B^+$, $B_d$, and $ ext{ extLambda}_b$ hadrons.

Findings

Computed bare matrix elements on two lattice spacings

Provided data for $B^+$, $B_d$, and $ ext{ extLambda}_b$

Set the stage for future renormalization and continuum extrapolation

Abstract

The Heavy Quark Expansion (HQE) gives an expansion of inclusive decay rates of $b$-hadrons as a simultaneous series in $\alpha_s$ and $1/m_b$, in terms of perturbatively defined coefficients and non-perturbative matrix elements. Spectator effects arise from the dimension-$6$ operators in the HQE in which along with the heavy quark, a light spectator quark from the hadron participates in the weak decay. In this work, we provide a lattice determination of the bare matrix elements that contribute to the spectator effects for the $B^+$-meson, $B_d$-meson and the $\Lambda_b$-baryon. The computations were performed on two separate lattice spacings of the RBC-UKQCD (2+1)-flavor Domain Wall Fermion ensembles. Renormalization and continuum extrapolation of the matrix elements have not yet been computed, and are left to future work.