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 >_Upsilon and the ratio < q^2>_Upsilon, for Upsilon=Upsilon(nS) with n=1, 2, and 3 by comparing the measured values for Gamma[Upsilon -> 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 >_Upsilon, which is the ratio of order-v^2 matrix element to < O_1 >_Upsilon, are new. They can be used for NRQCD predictions involving Upsilon(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] = 0.512^{+0.096}_{-0.094} keV, Gamma[eta_b(2S) -> gamma gamma] = 0.235^{+0.043}_{-0.043} keV, and Gamma[eta_b(3S) -> gamma gamma] = 0.170^{+0.031}_{-0.031} keV.

11 pages, minor corrections, version published in Phys. Lett. B

References in corpus (14)

• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• Relativistic corrections to $J/\psi$ exclusive and inclusive double charm production at B factories
• Dynamic Properties of Charmonium
• Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c
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• Exclusive heavy quarkonium + gamma production from e+ e- annihilation into a virtual photon
• Which hadronic decay modes are good for ${\eta }_b$ searching: double $J/\psi$ or something else?
• Inclusive Charm Production in Upsilon(nS) Decay
• Two-photon width of eta_b, eta'_b and eta''_b from Heavy-Quark Spin Symmetry
• Order-alpha_s corrections to the quarkonium electromagnetic current at all orders in the heavy-quark velocity
• η_b and η_c radiative decays in the Salpeter model with the AdS/QCD inspired potential
• Observation prospects of leptonic and Dalitz decays of pseudoscalar quarkonia
• Exclusive decays of χ_{bJ} and η_b into two charmed mesons

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