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

Abstract

The Heavy Quark Expansion (HQE) gives an expansion of inclusive decay rates of $b$-hadrons as a simultaneous series in $\hat{I}{\pm }_s$ 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 $\hat{I}{›}_b$-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.

9 pages, 5 figures, contribution to the proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany