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

Hee Sok Chung; Jungil Lee; Chaehyun Yu

doi:10.1016/j.physletb.2011.01.033

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

Hee Sok Chung, Jungil Lee, Chaehyun Yu

Department of Physics

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	48-51
Number of pages	4
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	697
Issue number	1
DOIs	https://doi.org/10.1016/j.physletb.2011.01.033
Publication status	Published - 2011 Feb 21

Keywords

Bottomonium
NRQCD
NRQCD matrix element
Relativistic correction
Two-photon width

ASJC Scopus subject areas

Nuclear and High Energy Physics

Access to Document

10.1016/j.physletb.2011.01.033

Cite this

@article{f02adca7ace04a46b2b7e5af676b52fd,

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

abstract = "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.",

keywords = "Bottomonium, NRQCD, NRQCD matrix element, Relativistic correction, Two-photon width",

author = "Chung, {Hee Sok} and Jungil Lee and Chaehyun Yu",

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).",

year = "2011",

month = feb,

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doi = "10.1016/j.physletb.2011.01.033",

language = "English",

volume = "697",

pages = "48--51",

journal = "Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics",

issn = "0370-2693",

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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

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