Bottomonium Decay Matrix Elements from Lattice QCD with Two Light Quarks

We calculate the long-distance matrix elements for the decays of the Υ (ηb) and χb (hb) 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. Whereas estimates of the leading Swave matrix element from quenched QCD are 40–45% lower than the experimental value extracted from the leptonic decay rate in order αs, the two-flavor estimate of the same matrix element is close to the experimental value. Extrapolating to the real world of 2 + 1 light flavors, we find that this matrix element is approximately 6% higher than the experimental value, but that the experimental value lies within our error bars. We also compute the colorsinglet 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%