The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness

TL;DR

This paper investigates the constraints on scattering amplitudes imposed by maximal spin bounds and high-energy softness, deriving bounds on low-energy parameters and exploring string-inspired models with exponential high-energy softness.

Contribution

It introduces a new approach to bounding low-energy Wilson coefficients using Regge trajectory constraints and demonstrates a stringy amplitude with exponential high-energy softness.

Findings

Maximal spin bounds improve constraints on low-energy coefficients.

High-energy softness is compatible with existing bounds and does not affect low-energy observables.

Constructed a string-inspired amplitude with exponential high-energy softness.

Abstract

We explore the space of meromorphic amplitudes with extra constraints coming from the shape of the leading Regge trajectory. This information comes in two guises: it bounds the maximal spin of exchanged particles of a given mass; it leads to sum rules obeyed by the discontinuity of the amplitude, which express the softness of scattering at high energies. We assume that the leading Regge trajectory is linear, and we derive bounds on the low-energy Wilson coefficients using the dual and primal approaches. For the graviton-graviton scattering in four dimensions, the maximal spin constraint leads to slightly more stringent bounds than those that follow from general constraints of analyticity, crossing, and unitarity. The exponential softness at high energies is manifest in our primal approach and is not used in our implementation of the dual approach. Nevertheless, we observe the agreement between the bounds obtained from both. We conclude that high-energy superpolynomial softness does not leave an obvious imprint on the low-energy observables. We exhibit a unitary three-parameter deformation of the Veneziano amplitude for the open string case. It has a novel, exponentially soft behavior at high energies and fixed angles. We generalize the previous analysis of this regime and present a stringy version of the lower bound on high-energy, fixed-angle scattering by Cerulus and Martin.