We investigate the soft behavior of the tree-level Rutherford scattering process.We consider two types of Rutherford scattering processes:One in which a low-energy massless point-like projectile(say,a spin-1/2 or spin...We investigate the soft behavior of the tree-level Rutherford scattering process.We consider two types of Rutherford scattering processes:One in which a low-energy massless point-like projectile(say,a spin-1/2 or spin-0 electron)hits a static massive composite target particle carrying various spins(up to spin-2),and one where 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 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 when the target particle is a composite spin-1/2 fermion.展开更多
基金Supported in part by the National Natural Science Foundation of China(11925506,12475090).
文摘We investigate the soft behavior of the tree-level Rutherford scattering process.We consider two types of Rutherford scattering processes:One in which a low-energy massless point-like projectile(say,a spin-1/2 or spin-0 electron)hits a static massive composite target particle carrying various spins(up to spin-2),and one where 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 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 when the target particle is a composite spin-1/2 fermion.
