Bottomonium Decay Matrix Elements from Lattice QCD with Two Light Quarks

TL;DR

This paper uses lattice QCD with two light quarks to calculate bottomonium decay matrix elements, improving upon quenched estimates and comparing results with phenomenological values, providing insights into decay processes.

Contribution

It presents the first lattice QCD calculations of bottomonium decay matrix elements with two light dynamical quarks, relating them to continuum values and comparing with phenomenology.

Findings

Two-flavor matrix elements are close to phenomenological values.

Color-singlet matrix element is 70% larger than quenched estimate.

Color-octet matrix element is 40% larger than quenched estimate.

Abstract

We calculate the long-distance matrix elements for the decays of the Upsilon (eta_b) and chi_b (h_b) states in lattice QCD with two flavors of light dynamical quarks. We relate the lattice matrix elements to their continuum counterparts through one-loop order in perturbation theory. In the case of the leading S-wave matrix element, we compare our result with a phenomenological value that we extract from the experimental leptonic decay rate by using the theoretical expression for the decay rate, accurate through relative order alpha_s. Whereas estimates of the leading S-wave matrix element from quenched QCD are 40--45% lower than the phenomenological value, the two-flavor estimate of the same matrix element is close to the phenomenological value. Extrapolating to the real world of 2+1 light flavors, we find that this matrix element is approximately 6% higher than the phenomenological value, but that the phenomenological value lies within our error bars. We also compute the color-singlet and color-octet matrix elements for P-wave decays. We find the value of the color-singlet matrix element for 2+1 flavors to be approximately 70% larger than the quenched value and the value of the color-octet matrix element for 2+1 flavors to be approximately 40% larger than the quenched value.