Systematic derivation of perturbative unitarity bounds for any models

TL;DR

This paper introduces a universal algorithm, anyPUB, for deriving perturbative unitarity bounds in high-energy scattering processes across diverse models, validated against existing results and applied to complex theories like Pati-Salam.

Contribution

The paper presents a systematic, model-independent algorithm for deriving unitarity bounds, applicable to any gauge group or field representation, including novel results for Pati-Salam models.

Findings

Validated the method on various models against literature

Derived the first perturbative unitarity bounds for Pati-Salam model

Provided a simple, analytical approach for high-energy scattering matrices

Abstract

In this letter, we provide a simple algorithm, anyPUB, to systematically derive the $2 \rightarrow 2$ scattering matrix in the high-energy limit for any kind of models, irrespective of their gauge group or their field representation. After computing the eigenvalues analytically and/or numerically from this matrix, we impose perturbative unitarity bounds on them. We tested our method on various models and validated the results against the literature. Finally, as a concrete application of our approach, we discuss the case of the minimal left-right symmetric model and derive, for the first time, the perturbative unitarity constraints in the Pati-Salam model.