Primal S-matrix bootstrap with dispersion relations

TL;DR

This paper introduces a novel method for constructing scattering amplitudes using dispersion relations and unitarity, enabling bounds on couplings and analysis of high-energy behaviors, including spinning states and glueballs.

Contribution

The authors develop a new framework combining dispersion relations with partial wave parameterization to bound couplings and analyze Regge behavior in scattering amplitudes.

Findings

Explicit bounds on leading couplings are computed.

The method accommodates spinning bound states and constrains glueball couplings.

Inherent satisfaction of Froissart-Martin bounds and exploration of asymptotic growth sensitivity.

Abstract

We propose a new method for constructing the consistent space of scattering amplitudes by parameterizing the imaginary parts of partial waves and utilizing dispersion relations, crossing symmetry, and full unitarity. Using this framework, we explicitly compute bounds on the leading couplings and examine the Regge behaviors of the constructed amplitudes. The method also readily accommodates spinning bound states, which we use to constrain glueball couplings. By incorporating dispersion relations, our approach inherently satisfies the Froissart-Martin/Jin-Martin bounds or softer high-energy behaviors by construction. This, in turn, allows us to formulate a new class of fractionally subtracted dispersion relations, through which we investigate the sensitivity of coupling bounds to the asymptotic growth rate.