### Abstract

We determine the leading-order nonrelativistic quantum chromodynamics (NRQCD) matrix element 〈O1〉Υ and the ratio (q^{2})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 〈q^{2}〉Υ, which is the ratio of order-v^{2} matrix element to 〈O_{1}〉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 | |

Publication status | Published - 2011 Feb 21 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**NRQCD matrix elements for S-wave bottomonia and Γ[η _{b}(nS)→γγ] with relativistic corrections.** / Chung, Hee Sok; Lee, Jungil; Yu, Chaehyun.

Research output: Contribution to journal › Article

_{b}(nS)→γγ] with relativistic corrections',

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 697, no. 1, pp. 48-51. https://doi.org/10.1016/j.physletb.2011.01.033

}

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

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

UR - http://www.scopus.com/inward/citedby.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 -