The conventional wisdom in dealing with electromagnetic transition between heavy quarkonia is the multipole expansion, when the emitted photon has a typical energy of order quarkonium binding energy. Nevertheless, in the case when the energy carried by the photon is of order typical heavy quark momentum, the multipole expansion doctrine is expected to break down. In this work, we apply the “hard-scattering” approach originally developed to tackle the strongly hindered magnetic dipole (M1) transition [Y. Jia , ] to the strongly hindered electric dipole (E1) transition between heavy quarkonia. We derive the factorization formula for the strongly hindered E1 transition rates at the lowest order in velocity and αs in the context of the nonrelativistic QCD, and conduct a detailed numerical comparison with the standard predictions for various bottomonia and charmonia E1 transition processes. Published by the American Physical Society 2024

中文翻译：

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重 quarkonia 之间强烈阻碍电偶极子跃迁的硬散射方法


处理重夸科纳之间的电磁跃迁的传统观点是多极展开，当发射的光子具有典型的阶夸科纳结合能时。然而，当光子携带的能量是典型的重夸克动量时，多极子膨胀学说有望被打破。在这项工作中，我们将最初为解决强阻碍磁偶极子 （M1） 跃迁 [Y. Jia ， ] 而开发的 “硬散射” 方法应用于重夸科尼亚之间的强阻碍电偶极子 （E1） 跃迁。在非相对论 QCD 的背景下，我们推导出了速度和 αs 最低阶的强受阻 E1 跃迁速率的因式分解公式，并与各种 bottomonia 和 charmonia E1 跃迁过程的标准预测进行了详细的数值比较。美国物理学会 2024 年出版