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arXiv 2303.18243hep-ph
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来自重靶质量展开的 Rutherford 散射软行为

Soft pattern of Rutherford scattering from heavy target mass expansion

Yu Jia, Jia-Yue Zhang

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11 pages, 1 figure
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AI总结：

本文研究了树级 Rutherford 散射的软行为，分析了两类入射粒子与重复合靶的散射，发现未极化截面在特定展开阶下具有普适性，并利用有效场论方法重现了靶为复合 Dirac 费米子时的微分截面软行为。

摘要：

我们研究了树级 Rutherford 散射过程的软行为。我们考虑了两类 Rutherford 散射：一是低能无质量点状入射粒子（例如自旋为 $1/2$ 或自旋为 $0$ 的电子）撞击携带各种自旋（最高至自旋-$2$）的静态大质量复合靶粒子；二是缓慢运动的轻入射粒子撞击重静态复合靶。对于第一类，在实验室系中发现，未极化截面在 $1/M$ 展开的前两阶表现出普适形式，但在次次领头阶存在差异（尽管该阶的某些项仍是普适的，或以确定方式依赖于靶自旋）。对于第二类，在电子速度展开的最低阶，对 $1/M$ 的所有阶，未极化截面是普适的（也对入射粒子自旋不敏感）。普适性在相对阶 $v^2/M^2$ 处部分失效，尽管该阶的某些项仍是普适的，或以特定方式依赖于靶自旋。我们还采用有效场论方法，重现了靶粒子为复合 Dirac 费米子时微分截面的软行为。

英文摘要：

We investigate the soft behavior of the tree-level Rutherford scattering process. We consider two types of Rutherford scattering, a low-energy massless point-like projectile (say, a spin-${1\over 2}$ or spin-$0$ electron) to hit a static massive composite target particle carrying various spins (up to spin-$2$), and a slowly-moving light projectile hits a heavy static composite target. For the first type, the unpolarized cross sections in the laboratory frame are found to exhibit universal forms in the first two orders of $1/M$ expansion, yet differ at the next-to-next-to-leading order (though some terms at this order still remain to be universal or depend on the target spin in a definite manner). For the second type, at the lowest order in electron velocity expansion, through all orders in $1/M$, the unpolarized cross section is universal (also not sensitive to the projectile spin). The universality partially breaks down at relative order-$v^2/M^2$, though some terms at this order are still universal or depend on the target spin in a specific manner. We also employ the effective field theory approach to reproduce the soft behavior of the differential cross sections for the target particle being a composite Dirac fermion.

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