论文标题
$ {\ cal o}（α_SV^2）$校正向量Quarkonia
${\cal O}(α_sv^2)$ corrections to hadronic decay of vector quarkonia
论文作者
论文摘要
在非派别QCD（NRQCD）分解框架中，我们计算了$ {\ Mathcal O}（α_sv^2）$校正向量Quarkonia的HADRONIC衰减率，以$ j/ψ$和$购来示例。将重归其化和NRQCD分数量表都设置为$ M_Q $，我们获得$γ（j/ψ\ to {\ rm lh}）= 0.0716 \ frac {α_s^3} {m_c^2} \ langle \ Mathcal {O} _1（{}^3S_1）\ rangle_ {J/ψ} [1-1.19α_s+（ - 5.32+3.03α_s）\ langle v^2 \ rangle_ \ rangle_ {J/ψ}] 0.0716 \ frac {α_s^3} {m_b^2} \ langle \ mathcal {o} _1（{}^3S_1）\ rangle_管理[1-1.56α_S+（-5.32+4.611α_S）\4.61α_S）\ langle v^2 \ rang_]我们以图表为基础确认$ \ Mathcal {O}（α_s）$校正的先前计算，其精度显着提高。对于$ J/ψ$ HADRONIC衰变，我们发现$ {\ Mathcal O}（α_SV^2）$校正是中等且积极的，但是无法抵消巨大的负面校正。另一方面，$ {\ mathcal o}（α_sv^2）$ chorkions $υ（ns）$的效果对$ \ narccal {o}（v^2）$ nrqccd matrix元素很敏感。通过适当选择NRQCD矩阵元素，我们对衰减率的理论预测可能与$υ（1s，2s）\ to {\ rm LH} $的实验数据一致。作为副产品，我们还介绍了$ j/ψ（υ）\3γ$精确度为$ \ MATHCAL {O}（α_Sv^2）$的分支比例的理论预测。
Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\mathcal O}(α_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/ψ$ and $Υ$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $Γ(J/ψ\to {\rm LH})= 0.0716\frac{α_s^3}{m_c^2} \langle \mathcal{O}_1({}^3S_1)\rangle_{J/ψ} [1-1.19α_s+(-5.32+3.03α_s)\langle v^2\rangle_{J/ψ}]$ and $Γ(Υ\to {\rm LH})= 0.0716\frac{α_s^3}{m_b^2}\langle\mathcal{O}_1({}^3S_1)\rangle_Υ[1-1.56α_s+(-5.32+4.61α_s)\langle v^2\rangle_Υ]$. We confirm the previous calculation of $\mathcal{O}(α_s)$ corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For $J/ψ$ hadronic decay, we find that the ${\mathcal O}(α_sv^2)$ corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of ${\mathcal O}(α_sv^2)$ corrections for $Υ(nS)$ is sensitive to the $\mathcal{O}(v^2)$ 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 $Υ(1S,2S)\to {\rm LH}$. As a byproduct, we also present the theoretical predictions for the branching ratio of $J/ψ(Υ)\to 3γ$ accurate up to $\mathcal{O}(α_s v^2)$.
