Unitarity Cuts of the Worldsheet

Submission summary

 Authors (as Contributors): Lorenz Eberhardt · Sebastian Mizera
Submission information
Date accepted: 2022-10-18
Date submitted: 2022-10-13 16:32
Submitted by: Eberhardt, Lorenz
Submitted to: SciPost Physics
Ontological classification
Specialties:
• High-Energy Physics - Theory
Approach: Theoretical

Abstract

We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten's $i\varepsilon$ prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity cuts of the annulus, M\"obius strip, and torus topologies exactly in $\alpha'$. With the help of tropical analysis, we show how the intricate pattern of thresholds (normal and anomalous) opening up arises from the worldsheet computation. The result is a manifestly-convergent representation of the imaginary parts of amplitudes, which has the analytic form expected from Cutkosky rules in field theory, but bypasses the need for performing laborious sums over the intermediate states. We use this representation to study various physical aspects of string amplitudes, including their behavior in the $(s,t)$ plane, exponential suppression, decay widths of massive strings, total cross section, and low-energy expansions. We find that planar annulus amplitudes exhibit a version of low-spin dominance: at any finite energy, only a finite number of low partial-wave spins give an appreciable contribution to the imaginary part.

Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

We would like to thank the two referees for their careful reading of the paper and their remarks. We addressed all their comments, see the list of changes below.

List of changes

All of the requested changes of referee 1 were typos and we fixed them according to their suggestions. Similarly, point (1.), (2.), (3.) and (5.) of referee 2 are typos and we fixed them accordingly. Regarding point (4.) of referee 2, we agree that this can be a bit misleading and have reformulated it accordingly. The relevant sentence now reads
Tree-level amplitudes only feature meromorphic functions of the kinematics (with isolated poles corresponding to propagators going on-shell), while in the low-energy limit the answers can be usually matched with the field-theory intuition for placement of branch cuts.''