Distinguishing Quantum Matter by Gravity with Differential Scattering Cross Section at Tree Level

TL;DR

This paper proposes a quantum weak equivalence principle based on differential scattering cross sections at tree level, exploring how spin properties and relativistic effects influence the scattering behavior of quantum matter.

Contribution

It introduces a new quantum weak equivalence principle using differential scattering cross sections and analyzes spin and relativistic effects on scattering differences.

Findings

Differential scattering cross sections become independent of particle properties in the large mass limit.

Spin properties cause differences in scattering cross sections at order $\mathcal{O}(p_{\mathrm{cm}}^2)$ in non-relativistic cases.

Relativistic analysis shows differences in small-angle scattering behavior depending on target particle type and spin.

Abstract

The definition of weak equivalence principle of quantum matter is an open problem at present. In order to reflect the probability of quantum system in the quantum version of weak equivalence principle, we proposed a quantum weak equivalence principle based on differential scattering cross section at tree level, that is, the differential scattering cross section does not depend on the mass and properties of the scattered particles when the target particles take the large mass limit. This version of the quantum equivalence principle we proposed will be broken by the spin properties of quantum matter. In the non-relativistic case, the difference of differential scattering cross sections of scattered particles with different spin properties scattered by target particles is mainly reflected in the order of $ \mathcal O (p _ {\mathrm{cm}} ^2) $. In the relativistic case , we studied the asymptotic behavior of differential scattering cross sections at small angles. When the target particles are scalar particles, the difference of light particles with different spin properties is mainly reflected in the $ \mathcal O (1/\theta^2) $ order. When the target particles are Dirac particles, the difference of light particles with different spin properties is mainly reflected in the $ \mathcal O (1/\theta^4) $ order. The polarization of differential scattering cross section when scattered particles are Dirac particles is investigated. The result of the degree of polarization depends on the polarization direction of the incident particles.