Factorization in Graviton Scattering and the "Natural" Value of the g-factor

TL;DR

This work addresses the question of a universal, spin-independent natural gyromagnetic ratio $g_S$ for particles with arbitrary spin. It combines historical critiques of Belinfante's $g_S=1/S$ with the case for $g_S=2$ drawn from the GDH sum rule, high-energy Compton scattering, and a new graviton-scattering factorization framework. The key contribution is the graviton-factorization result, which expresses the elastic graviton amplitude as a product of spin-0 and spin-$S$ Compton amplitudes times a kinematic factor, and shows that avoiding unphysical $1/m^2$ terms → consistent with unitarity, necessarily requires $g_S=2$. The findings reinforce the universality of $g_S=2$, aligning with SM predictions for the charged leptons and the $W$-boson, and linking gravitational amplitude structure to fundamental electromagnetic properties through factorization.

Abstract

The factorization property of graviton scattering amplitudes is reviewed and show to be valid only if the "natural" value of the gyromagnetic ratio $g_S=2$ is employed -- independent of spin.

Figures (2)

• Figure 1: Diagrams relevant to Compton scattering.
• Figure 2: Diagrams relevant for gravitational Compton scattering.