S波和P波重夸克偶素衰变到l⁺l⁻γ的次领头阶QCD修正
Next-to-leading-order QCD corrections to $S$- and $P$-wave heavy quarkonium decay to $l^{+}l^{-} γ$
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中文总结 AI 辅助
该研究在NRQCD框架下计算重夸克偶素辐射Dalitz衰变的次领头阶QCD修正，分析衰变宽度分布特征，给出不同态对光子能量截断的灵敏度，为实验探测形状因子提供理论依据。
中文摘要 AI 辅助
本研究在NRQCD因子化框架下，全面研究辐射Dalitz衰变H→l⁺l⁻γ的总衰变宽度和微分衰变宽度，精度达到QCD次领头阶（NLO）。计算涵盖S波态（η_c、η_b）和P波三重态（J=0,1,2对应的χ_{cJ}、χ_{bJ}）衰变到电子末态（l=e）和μ子末态（l=μ）的情况。为匹配实际实验探测阈值，对末态光子能量实施系统运动学截断。对轻子对不变质量分布的分析显示，不同多重态存在源自轻子对阈值区和软光子区的不同奇异行为，该奇异行为由轻子质量规一化。S波态仅在轻子对阈值区附近出现一个峰；J=0和J=2的P波态在两个区域均出现峰；而J=1的P波态仅在软光子区出现峰。这些特征为重夸克偶素衰变中探测γ*→l⁺l⁻形状因子提供了丰富途径。对有界相空间积分后发现，χ_{QJ}态的理论预言对软光子能量截断的灵敏度存在明显层级，顺序为χ_{Q1}>χ_{Q2}>χ_{Q0}。在χ_{cJ}→l⁺l⁻γ的情况中，当能量截断从100 MeV增加到500 MeV时，QCD次领头阶的理论预言在l=e时分别下降6%（χ_{c0}）、66%（χ_{c1}）、21%（χ_{c2}）；在l=μ时分别下降17%（χ_{c0}）、66%（χ_{c1}）、39%（χ_{c2}）。将理论预言与BESIII即将开展的高精度实验结果对比，必将加深对微扰计算预言能力的理解。
英文摘要
In this work, we comprehensively study the total and differential decay widths of the radiative Dalitz decays $H \to l^+l^-γ$ up to QCD next-to-leading order (NLO) accuracy within the framework of NRQCD factorization. Our calculation includes the decays of $S$-wave states ($η_c, η_b$) and the $P$-wave triplets ($χ_{cJ}, χ_{bJ}$ for $J=0,1,2$) to both electron ($l=e$) and muon ($l=μ$) final states. To match realistic experimental detection thresholds, systematic kinematic cuts are implemented on the final-state photon energy. Our analysis of the lepton-pair invariant mass distribution shows distinct singular behaviors across the multiplets originating from the lepton-pair threshold region, which is regularized by the lepton mass, and the soft-photon region, respectively. For the $S$-wave states, there is only one peak near the lepton-pair threshold region, while for the $J=0$ and $J=2$ $P$-wave states, the peaks show up in both regions. However, for the $J=1$ $P$-wave states, the peak only appears in the soft-photon region. Such features provide a rich venue to probe the $γ^{\ast}\to l^{+}l^{-}$ form factor in heavy quarkonium decay. Integrating over the bounded phase spaces reveals a distinct hierarchy among the $χ_{QJ}$ states in the sensitivity of our theoretical predictions to the soft-photon energy cuts, ordered as $χ_{Q1} >χ_{Q2}>χ_{Q0}$. In the $χ_{cJ}\to l^{+}l^{-}γ$ cases, as the energy cut increases from 100 $\mathrm{MeV}$, to 500 $\mathrm{MeV}$ the theoretical predictions at QCD NLO are reduced by $6\%(χ_{c0})$,$66\%(χ_{c1})$, and $21\%(χ_{c2})$ for $l=e$, and by $17\%(χ_{c0})$,$66\%(χ_{c1})$, and $39\%(χ_{c2})$ for $l=μ$. Comparing our predictions with the upcoming high-precision experimental tests at BESIII will definitely deepen our understanding of the predictive power of perturbative calculations.
