On the origin of approximate custodial symmetry in the Two-Higgs Doublet Model

TL;DR

This paper investigates how the multiple point principle (MPP) in the two-Higgs doublet model (2HDM) can naturally lead to approximate custodial symmetries, suppressing CP violation and flavor-changing neutral currents, and explores the implications for Higgs boson masses and couplings.

Contribution

It demonstrates that MPP can induce approximate custodial symmetries in 2HDM, constraining Higgs properties and providing bounds on Higgs masses based on the MPP scale.

Findings

High MPP scale leads to a lightest Higgs mass below 125 GeV.

Low MPP scale allows for a heavier Higgs, up to 220 GeV.

Higgs couplings can be significantly enhanced at low MPP scales.

Abstract

We argue that the consistent implementation of the multiple point principle (MPP) in the general non-supersymmetric two Higgs doublet model (2HDM) can lead to a set of approximate global custodial symmetries that ensure CP conservation in the Higgs sector and the absence of flavour changing neutral currents (FCNC) in the considered model. In particular the existence of a large set of degenerate vacua at some high energy scale $\Lambda$ caused by the MPP can result in approximate U(1) and Z(2) symmetries that suppress FCNC and CP--violating interactions in the 2HDM. We explore the renormalisation group (RG) flow of the Yukawa and Higgs couplings within the MPP inspired 2HDM with approximate custodial symmetries and show that the solutions of the RG equations are focused near quasi--fixed points at low energies if the MPP scale scale $\Lambda$ is relatively high. We study the Higgs spectrum and couplings near the quasi--fixed point at moderate values of $\tan\beta$ and compute a theoretical upper bound on the lightest Higgs boson mass. If $\Lambda\gtrsim 10^{10} {GeV}$ the lightest CP--even Higgs boson is always lighter than $125 {GeV}$. When the MPP scale is low, the mass of the lightest Higgs particle can reach $180-220 {GeV}$ while its coupling to the top quark can be significantly larger than in the SM, resulting in the enhanced production of Higgs bosons at the LHC.