O(αsv2) corrections to the hadronic decay of vector quarkonia

2020/10/22 by Wen-Long Sang, Feng Feng, Yu Jia
Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Factorization #Hadron #High-Energy Particle Collisions Research #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Renormalization #hep-ex #hep-ph

paper · pdf · doi:10.1103/physrevd.102.094021

published as Phys. Rev. D 102, 094021 (2020) · 21 pages, 5 figures, 3 tables

arxiv created 2020/10/22 · openalex created_date 2020/10/29 · openalex publication_date 2020/11/19 · arxiv updated 2020/11/25 · openalex updated_date 2026/08/05

Abstract

Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the O(\ensuremathα_sv²) corrections to the hadronic decay rate of vector quarkonia, exemplified by J/\ensuremathψ and \mathrm\ensuremathΥ. Setting both the renormalization and NRQCD factorization scales to be m_Q, we obtain \mathrm\ensuremathΓ(J/\ensuremathψ\ensuremath→LH)=0.0716\frac\ensuremathα_s³m_c²⟨O₁(³S₁)⟩_J/\ensuremathψ[1\ensuremath-1.19\ensuremathα_s+(\ensuremath-5.32+3.03\ensuremathα_s)⟨v²⟩_J/\ensuremathψ] and \mathrm\ensuremathΓ(\mathrm\ensuremathΥ\ensuremath→LH)=0.0716\frac\ensuremathα_s³m_b²⟨O₁(³S₁)⟩_\mathrm\ensuremathΥ[1\ensuremath-1.56\ensuremathα_s+(\ensuremath-5.32+4.61\ensuremathα_s)⟨v²⟩_\mathrm\ensuremathΥ]. We confirm the previous calculation of O(\ensuremathα_s) corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For J/\ensuremathψ hadronic decay, we find that the O(\ensuremathα_sv²) corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of O(\ensuremathα_sv²) corrections for \mathrm\ensuremathΥ(nS) is sensitive to the O(v²) NRQCD matrix elements. With the appropriate choice of the NRQCD matrix elements, our theoretical predictions for the decay rates may be consistent with the experimental data for \mathrm\ensuremathΥ(1S,2S)\ensuremath→LH. As a by-product, we also present the theoretical predictions for the branching ratio of J/\ensuremathψ(\mathrm\ensuremathΥ)\ensuremath→3\ensuremathγ accurate up to O(\ensuremathα_sv²).

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