Soft pattern of gravitational Rutherford scattering from heavy target mass expansion

TL;DR

This paper analyzes the soft behavior of gravitational Rutherford scattering, revealing universal patterns in cross sections at various orders of mass and velocity expansions, with some spin-dependent nuances.

Contribution

It provides a detailed expansion-based analysis of gravitational Rutherford scattering, highlighting universality and spin dependence at different orders.

Findings

Unpolarized cross sections show universality at leading orders.

Universality persists at all orders in $1/M$ for slow-moving projectiles.

Partial breakdown of universality occurs at order $v^2/M^2$, with spin-dependent terms.

Abstract

We investigate the soft behavior of the tree-level Rutherford scattering processes mediated via $t$-channel one-graviton exchange. We consider two types of Rutherford scattering processes, {\it e.g.}, a low-energy massless structureless projectile (up to spin-$1$) hits a static massive composite particle carrying various spins (up to spin-$2$), and a slowly-moving light projectile hits a heavy static composite target. The unpolarized cross sections in the first type are found to exhibit universal forms at the first two orders in $1/M$ expansion, yet differ at the next-to-next-to-leading order, though some terms at this order still remain universal or depend on the target spin in a definite manner. The unpolarized cross sections in the second type are universal at the lowest order in projectile velocity expansion and through all orders in $1/M$, independent of the spins of both projectile and target. The universality partially breaks down at relative order-$v^2/M^2$, albeit some terms at this order still depend on the target spin in a specific manner.