Soft pattern of Rutherford scattering from heavy target mass expansion

Abstract

Abstract 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) hits
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 spin-${1\over 2}$ fermion. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.