发表机构
Institute of High Energy Physics, Chinese Academy of Sciences; University of Chinese Academy of Sciences; College of Physics and Optoelectronic Engineering, Chongqing Normal University（中国科学院高能物理研究所; 中国科学院大学; 重庆师范大学物理与光电工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对微扰QCD中exclusive过程出现负概率的问题，提出振幅级NRQCD因子化恢复正性，并通过NNLO计算验证得到正且收敛更好的预言。
AI 中文摘要
在量子力学中，波函数的模平方是事件发生的概率——正性是自明的。量子场论与量子力学一一对应：波函数对应矩阵元，因此过程的概率应为矩阵元的模平方，由构造保证为正。然而，在微扰量子场论创立时期，费曼、施温格和朝永振一郎在处理量子电动力学中的 inclusive 过程时，由于红外抵消迫使平方振幅截断，且小耦合常数 α≃1/137 使这种处理无害。将这一做法推广到量子色动力学中的 exclusive 过程时，由于耦合常数较大，在次领头阶（NLO）就已产生负的衰变率和产生率，并持续到次次领头阶（NNLO）。我们指出，对于 exclusive 过程，其初态和末态在 QCD 中为无色、在 QED 中为电中性，红外发散逐振幅抵消，KLN 约束不存在，因此截断振幅的完整模平方才是概率的恰当且显式正的定义。我们提出振幅级 NRQCD 因子化作为恢复正性的系统性方案，证明每个振幅级截断可观测量都允许有效表示 Γ^amp=Γ_LO|1+(α_s/π)(c_1+ic_2)+(α_s^2/π^2)(c_3+ic_4)|^2，并通过 J/ψ→3γ、Υ→3γ、e^+e^-→J/ψ+J/ψ 以及 B 工厂中八个 exclusive 粲偶素产生道的完整 NNLO QCD 修正，证明该方案产生正且收敛更好的预言。
英文摘要
In quantum mechanics the modulus square of the wave function is the probability of an event --- positivity is self-evident. Quantum field theory corresponds to quantum mechanics one-to-one: the wave function corresponds to the matrix element, so the probability of a process should be the modulus square of the matrix element, positive by construction. In the founding era of perturbative quantum field theory, however, Feynman, Schwinger and Tomonaga treated inclusive processes in quantum electrodynamics, where the truncation of the squared amplitude was forced by infrared cancellations and rendered harmless by the small coupling $α\simeq1/137$. Carried over to exclusive processes in quantum chromodynamics, where the coupling is large, this practice produced negative decay and production rates already at NLO, persisting at NNLO. We point out that for exclusive processes, whose initial and final states are colorless for QCD and electrically neutral for QED, the infrared divergences cancel amplitude by amplitude and the KLN constraint is absent, so the complete modulus square of the truncated amplitude is the proper, manifestly positive definition of the probability. We formulate amplitude-level NRQCD factorization as the systematic prescription that restores positivity, show that every amplitude-level truncated observable admits the effective representation $Γ^{\mathrm{amp}}=Γ_{\mathrm{LO}}\bigl|1+\frac{α_s}π(c_1+ic_2)+\frac{α_s^2}{π^2}(c_3+ic_4)\bigr|^2$, and demonstrate, with the complete NNLO QCD corrections to $J/ψ\to3γ$, $Υ\to3γ$, $e^+e^-\to J/ψ+J/ψ$ and the eight exclusive charmonium production channels at $B$ factories, that the prescription yields positive and better-converging predictions.
Comments6 pages, 1 table, no figures
