NRQCD matrix elements for S-wave bottomonia and Gamma[eta(b)(nS) -> gamma gamma] with relativistic corrections

Abstract

We determine the leading-order nonrelativistic quantum chromodynamics (NRQCD) matrix element (O-1)(Y) and the ratio (q(2))(Y.) for Y = Y(ns) with n = 1, 2, and 3 by comparing the measured values for Gamma[Y -> e(+)e(-)] with the NRQCD factorization formula in which relativistic corrections are resummed to all orders in the heavy-quark velocity v. The values for < q(2)>(Y), which is the ratio of order-v(2) matrix element to (O-1)(Y), are new. They can be used for NRQCD predictions involving Y(nS) and eta(b)(nS) with relativistic corrections. As an application, we predict the two-photon decay rates for the spin-singlet states: Gamma[eta(b)(1S) -> gamma gamma] = 0.5121(-0.094)(+0.096) keV, Gamma[eta(b) (2S) -> gamma gamma] = 0.2351(-0.043)(+0.043) key, and Gamma[eta(b)(3S) -> gamma gamma] = 0.170(-0.031)(+0.031) keV. (C) 2011 Published by Elsevier B.V.