Consequences of Minimal Entanglement in Bosonic Field Theories

TL;DR

This paper explores how minimal entanglement in bosonic field theory scattering processes relates to emergent symmetries, revealing that the connection varies with different scattering channels and models.

Contribution

It generalizes minimal entanglement constraints from qubits to qudits and analyzes their implications in scalar field models and the two Higgs doublet model.

Findings

Minimal entanglement constrains couplings to be quartic with instabilities.

In the two Higgs doublet model, minimal entanglement does not permit enhanced symmetries.

The entanglement-symmetry connection depends on the specific scattering channel.

Abstract

In this paper, we study a recently discovered connection between scattering that minimally entangles and emergent symmetries. In a perturbative expansion, we have generalized the constraints of minimal entanglement scattering, beyond qubits, to general qudits of dimension $d.$ Interestingly, projecting on any qubit subspaces, the constraints factorize, so that it is consistent to analyze minimal entanglement by looking at all such subspaces. We start by looking at toy models with two scalar fields, finding that minimal entanglement only allows quartic couplings which have instabilities at large field values and no symmetries. For the two Higgs doublet model, by considering $H^+ H^-\to H^+ H^-$ scattering, we show that minimal entanglement in this channel does not allow an interacting parameter point with enhanced symmetries. These results show that the connection between minimal entanglement and symmetries depends strongly on the scattering channels analyzed and we speculate on the potential resolutions.