### 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 |
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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 |

### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics