Systematic derivation of perturbative unitarity bounds for any models
Nico Benincasa
TL;DR
This work addresses the need for a universal method to derive perturbative unitarity bounds in beyond-the-Standard-Model theories with extended scalar sectors. It introduces anyPUB, a Mathematica-based package that constructs the high-energy $2\rightarrow2$ S-matrix from the quartic potential, block-diagonalises it via graph-theory methods, and extracts eigenvalues to enforce $|\mathrm{Re}(\mathcal{M}_i)| \le 8\pi$. The authors demonstrate analytic and numerical strategies across models, obtaining 21 distinct eigenvalues for the minimal left-right symmetric model (versus 64 in a previous study due to convention differences) and presenting the first complete unitarity constraints for the Pati-Salam model (10 analytic eigenvalues, 13 numerical). Overall, the approach provides a general, publicly available framework to constrain quartic couplings in a wide range of gauge groups and representations, enabling robust theoretical consistency checks for diverse BSM scenarios.
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.