A ${\mathbb{CP}}^2$ SMEFT

TL;DR

This paper introduces a novel extension of the Standard Model where the Higgs field resides in the complex projective plane, leading to tightly constrained deviations from Standard Model predictions and implications for new physics at TeV scales.

Contribution

It proposes a new geometric framework for the Higgs field in SMEFT, constraining deviations and connecting them to a large mass scale M.

Findings

Deviations depend on a single large mass parameter M

Current data suggest M is a few TeV or larger

The model mildly breaks custodial SO(4) symmetry

Abstract

An extension of the Standard Model is proposed, where the Higgs field is valued in the complex projective plane ${\mathbb{CP}}^2$, rather than ${\mathbb{C}}^2$. Its geometry is consistent with $U(2) \simeq (SU(2) \times U(1))/ \mathbb{Z}_2$ electroweak gauge symmetry. The leading terms in the Lagrangian, beyond those of the Standard Model, are much more tightly constrained than in general SMEFTs, and the custodial $SO(4)$ symmetry of the Higgs sector is mildly broken. The predicted tree-level deviations from Standard Model phenomenology depend on a single large mass parameter $M$. Current experimental data imply that $M$ is a few TeV or larger.