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Bounds on scalar masses in two Higgs doublet models

P. M. Ferreira, D. R. T. Jones

TL;DR

This paper analyzes how stability and perturbativity bounds shape the scalar sector of the two-Higgs doublet model (2HDM) across multiple realizations, including $Z_2$ and $U(1)$ symmetries, softly broken variants, and the full CP-conserving potential, while incorporating LEP Higgs limits. It computes one-loop beta functions and imposes bounded-from-below and perturbativity constraints up to the unification scale $M_U$, using RG-improved potential reasoning to ensure viability across scales and to constrain quartic couplings. The results show that a $Z_2$-symmetric 2HDM is tightly restricted, with the lightest neutral scalar typically below about 55 GeV, whereas softly broken or full CP-conserving cases admit heavier spectra but remain sensitive to LEP constraints through the $ZZh$ coupling; CP-breaking minima tend to prefer lighter scalars and are particularly constrained. The analysis highlights the role of the couplings $ ext{lambda}_6$ and $ ext{lambda}_7$ via their beta functions and discusses RG-invariant basis-invariant conditions (ERPS), illustrating how RG running shapes the viability of different vacua in 2HDM.

Abstract

A thorough analysis of stability and perturbativity bounds is performed in several versions of the two-Higgs doublet model, for both CP-conserving and spontaneously broken CP minima. LEP results further aid in establishing very strict constraints on the mass of the lighter Higgs particle.

Bounds on scalar masses in two Higgs doublet models

TL;DR

This paper analyzes how stability and perturbativity bounds shape the scalar sector of the two-Higgs doublet model (2HDM) across multiple realizations, including and symmetries, softly broken variants, and the full CP-conserving potential, while incorporating LEP Higgs limits. It computes one-loop beta functions and imposes bounded-from-below and perturbativity constraints up to the unification scale , using RG-improved potential reasoning to ensure viability across scales and to constrain quartic couplings. The results show that a -symmetric 2HDM is tightly restricted, with the lightest neutral scalar typically below about 55 GeV, whereas softly broken or full CP-conserving cases admit heavier spectra but remain sensitive to LEP constraints through the coupling; CP-breaking minima tend to prefer lighter scalars and are particularly constrained. The analysis highlights the role of the couplings and via their beta functions and discusses RG-invariant basis-invariant conditions (ERPS), illustrating how RG running shapes the viability of different vacua in 2HDM.

Abstract

A thorough analysis of stability and perturbativity bounds is performed in several versions of the two-Higgs doublet model, for both CP-conserving and spontaneously broken CP minima. LEP results further aid in establishing very strict constraints on the mass of the lighter Higgs particle.

Paper Structure

This paper contains 12 sections, 49 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. The 2HDM potential
  3. Model with $Z_2$ symmetry
  4. The case $v_2 = 0$
  5. Model with softly broken $Z_2$ symmetry
  6. Normal minima
  7. CP breaking minima
  8. Model with a softly broken $U(1)$ symmetry
  9. The full CP conserving potential
  10. Conclusions
  11. The one loop $\beta$-functions
  12. Renormalization group invariance and the exceptional region of parameter space

Figures (6)

  • Figure 1: Results of scan of the 2HDM potential with $Z_2$ symmetry.
  • Figure 2: $\sin^2(\alpha-\beta)$ versus the mass of the lightest Higgs boson, for a potential with a $Z_2$ symmetry.
  • Figure 3: $\sin^2(\alpha-\beta)$ versus the mass of the lightest Higgs boson, for the normal minimum of a potential with a softly broken $Z_2$ symmetry.
  • Figure 4: $g_{ZZh}^2$ versus the mass of the lightest Higgs boson, for the CP breaking minimum of a potential with a softly broken $Z_2$ symmetry.
  • Figure 5: $\sin^2(\alpha-\beta)$ versus the mass of the lightest Higgs boson, for the CP breaking minimum of a potential with a softly broken $U(1)$ symmetry.
  • ...and 1 more figures