Causality, Unitarity and Symmetry in Effective Field Theory

TL;DR

This paper derives fundamental positivity bounds on effective field theories based on causality, unitarity, and symmetry considerations, especially focusing on dimension 8 operators and their implications for Standard Model-like symmetries.

Contribution

It provides a comprehensive derivation of positivity bounds for dimension 8 operators, including new bounds for mixed spin interactions, loop effects, and supersymmetric cases, unifying these results.

Findings

Positivity bounds restrict symmetry breaking in effective interactions.

Loop corrections strengthen the positivity bounds.

Supersymmetry unifies various positivity theorems.

Abstract

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension $8$ operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in $SU(2)$ and $SU(3)$ global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension $6$ operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension $8$ and $4$ legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.