AI 中文总结
研究电弱$2 + J \to 2$跃迁振幅，通过微扰处理电弱流插入、全阶处理强子相互作用，推导壳上表示，分离奇点贡献，为约束重夸克领域相关系统形状因子迈出重要一步。
AI 中文摘要
我们推导了一个壳上表示，用于电弱$2 + J \to 2$跃迁振幅，该过程涉及初末态均有两个强子的系统，其中存在由轻粒子交换产生的左手奇点，例如单π介子交换。推导过程微扰地处理电弱流的插入，仅保留外场中的领头阶贡献，而强子相互作用则处理到所有阶，包括单粒子交换效应。我们发现，在此类过程中，由于这些交换，振幅会有对数奇点以及单粒子极点奇点。我们分离出这些贡献以及先前确定的三角形奇点。结果用纯强子振幅、交换流核、三角形函数以及一类在未计入的阈值以下是实且光滑的短程跃迁函数表示。虽然我们仅考虑无自旋粒子的跃迁，但这项工作是朝着约束重夸克领域中涉及核子或矢量介子系统的形状因子迈出的重要一步，其中单π介子交换奇点非常接近阈值。
英文摘要
We derive an on-shell representation for electroweak $2+J\to2$ transition amplitudes involving two hadrons in both the initial and final state for systems where there are left-hand singularities generated by light-particle exchange, e.g. one-pion exchange. The derivation treats the insertion of the electroweak current perturbatively, keeping only the leading-order contribution in the external field, while the hadronic interactions are treated to all orders, including one-particle exchange effects. We find that, in such processes, the amplitude can have logarithmic singularities, as well as one-particle pole singularities, due to these exchanges. We isolate those contributions, as well as previously identified triangle singularities. The result is expressed in terms of the purely hadronic amplitude, exchange-current kernels, triangle functions, and a class of short-distance transition functions that are real and smooth below unaccounted-for thresholds. While we consider only transitions with spinless particles, this work is an important step toward constraining form factors of systems involving nucleons or vector mesons in the heavy quark sector, where the one-pion-exchange singularity is quite close to threshold.
Comments35 pages, 10 figures
