Gravitational Compton Scattering

Graviton is the mediating particles of gravitational interaction. As it is difficult to detect it in the observation, we don’t know whether it really exists now. The research of gravitational Compton scattering, which the interaction between graviton and scalar, spinor and vector particles, may provide a beneficial reference for detecting the existence of the graviton indirectly. So, the explore of gravitational Compton scattering has great significance.Graviton is the particle of spin-2, which coupled with not only the material, but also itself. This makes the calculation of gravitational scattering process much more Complicated. However, the string theory studies in recent years have shown that gravity has the factorization property, namely the scattering amplitude of gravity can be decomposed into the products of the scattering amplitude of two gauge field. This is the famous KLT relationship. It was found in string theory firstly, but valid in quantum field theory also. In particular, the gravitational Compton scattering amplitude can be decomposed into the products of the QED scattering amplitude, which can simplify the calculation greatly. On the other hand, polarization vector can be written as spinor product according to the formula of helicity, which can simplify the amplitude calculation further.After getting the scattering amplitude, people often calculate its sum of squares to obtain the scattering cross section. However, the cross section calculate by this way is unpolarized and miss the polarization information. In order to extract the polarization information of the scattering process, it is necessary to analyze the differential cross section of polarization.In this article, we use the method of helicity and KLT relations, calculate the gravitational Compton scattering amplitude and cross section, and compare the difference of polarized and unpolarized cross section. We found that when the scattering angle is less than 90 degrees, the synthetic polarization plays a leading role; in contrast, when the scattering angle is greater than 90 degrees, the reversed polarization occupies the main position.