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 -