TY - JOUR

T1 - NRQCD matrix elements for S-wave bottomonia and Γ[ηb(nS)→γγ] with relativistic corrections

AU - Chung, Hee Sok

AU - Lee, Jungil

AU - Yu, Chaehyun

N1 - 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).

PY - 2011/2/21

Y1 - 2011/2/21

N2 - 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.

AB - 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.

KW - Bottomonium

KW - NRQCD

KW - NRQCD matrix element

KW - Relativistic correction

KW - Two-photon width

UR - http://www.scopus.com/inward/record.url?scp=79551498249&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2011.01.033

DO - 10.1016/j.physletb.2011.01.033

M3 - Article

AN - SCOPUS:79551498249

VL - 697

SP - 48

EP - 51

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1

ER -