Bottomonium decay matrix elements from lattice QCD with two light quarks

Abstract

We calculate the long-distance matrix elements for the decays of the $\ensuremath{\Upsilon}({\ensuremath{\eta}}_{b})$ and ${\ensuremath{\chi}}_{b}{(h}_{b})$ 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 ${\ensuremath{\alpha}}_{s}.$ 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.