Bespoke Dual Resonance

TL;DR

This paper introduces a new class of customizable dual resonance amplitudes with a tunable mass spectrum, maintaining desirable high-energy behavior and locality, extending string theory concepts to broader particle scattering models.

Contribution

It provides explicit closed-form expressions for bespoke dual resonant amplitudes with arbitrary mass spectra, expanding the scope of string-inspired scattering models.

Findings

Amplitudes are well-behaved in the ultraviolet.

Residues are polynomial in momentum transfer, ensuring locality.

Deviations from string theory still satisfy partial wave unitarity.

Abstract

Dual resonance is one of the great miracles of string theory. At a fundamental level, it implies that the particles exchanged in different channels are subtly equivalent. Furthermore, it is inextricably linked to the property of exceptionally tame high-energy behavior. In this paper, we present explicit, closed-form expressions for a new class of dual resonant amplitudes describing an infinite tower of spins for an arbitrary mass spectrum. In particular, the input of our construction is a user-defined, fully customizable choice of masses. The resulting "bespoke" amplitudes are well behaved in the ultraviolet and analytic except at simple poles whose residues are polynomial in the momentum transfer, in accordance with locality. The absence of branch cuts can be seen using Newton's identities, but can also be made manifest by expressing the amplitudes as a simple dlog integral of the Veneziano amplitude that remaps the linear Regge trajectories of the string to a tunable spectrum. We identify open regions of parameter space that firmly deviate from string theory but nevertheless comport with partial wave unitarity. Last but not least, we generalize our construction to the scattering of any number of particles in terms of a dlog transform of the Koba-Nielsen worldsheet integral formula.