New Sum Rules from Low Energy Compton Scattering on Arbitrary Spin Target

TL;DR

This paper derives new sum rules for low energy Compton scattering on arbitrary spin targets, generalizing known sum rules, and explores their implications for theories like supergravity, string theory, and QCD.

Contribution

It introduces two generalized sum rules for arbitrary spin targets, relating low energy couplings and constraints on gyromagnetic ratios at tree level.

Findings

Sum rules relate low energy couplings and intermediate states.

Gyromagnetic ratio can differ from 2 without unitarity violation.

Implications for supergravity, string theory, and large-N_c QCD.

Abstract

We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and the same mass as the target. The second sum rule applies if the theory at hand possesses intermediate narrow resonances with masses different from the mass of the scatterer. These sum rules are generalizations of the Gerasimov-Drell-Hearn-Weinberg sum rule. Along with the requirement of tree level unitarity, they relate different low energy couplings in the theory. Using these sum rules, we show that in certain cases the gyromagnetic ratio can differ from the "natural" value g=2, even at tree level, without spoiling perturbative unitarity. These sum rules can be used as constraints applicable to all supergravity and higher-spin theories that contain particles charged under some U(1) gauge field. In particular, applied to four dimensional N=8 supergravity in a spontaneously broken phase, these sum rules suggest that for the theory to have a good ultraviolet behavior, additional massive states need to be present, such as those coming from the embedding of the N=8 supergravity in type II superstring theory. We also discuss the possible implications of the sum rules for QCD in the large-N_c limit.