NRQCD matrix elements for S-wave bottomonia and Γ[ηb(nS)→γγ] with relativistic corrections

Hee Sok Chung, Jungil Lee, Chaehyun Yu

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41 Citations (Scopus)


We determine the leading-order nonrelativistic quantum chromodynamics (NRQCD) matrix element 〈O1〉Υ and the ratio (q2)Υ, for Υ=Υ(nS) with n=1, 2, and 3 by comparing the measured values for Γ[Υ→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 〈q2〉Υ, which is the ratio of order-v2 matrix element to 〈O1〉Υ, are new. They can be used for NRQCD predictions involving Υ(nS) and ηb(nS) with relativistic corrections. As an application, we predict the two-photon decay rates for the spin-singlet states: Γ[ηb(1S)→γγ]=0.512-0.094+0.096 keV, Γ[ηb(2S)→γγ]=0.235-0.043+0.043 keV, and ηb(3S)→γγ=0.170-0.031+0.031 keV.

Original languageEnglish
Pages (from-to)48-51
Number of pages4
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number1
Publication statusPublished - 2011 Feb 21

Bibliographical note

Funding Information:
This work was supported by the Basic Science Research Program through NRF of Korea funded by the MEST under contracts 2010-0015682 (HSC) and 2010-0028228 (JL) and 2009-0072689 (CY).


  • Bottomonium
  • NRQCD matrix element
  • Relativistic correction
  • Two-photon width

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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