[Paper Review] Higgs bosons in the NMSSM with exact and slightly broken PQ-symmetry

D.J. Miller, Stefano Moretti+1 more|ArXiv.org|Jan 15, 2005

Particle physics theoretical and experimental studies1 references21 citations

TL;DR

This paper investigates the Higgs sector of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) under exact or slightly broken Peccei-Quinn (PQ) symmetry, showing that vacuum stability and LEP constraints enforce a strong correlation between the pseudoscalar Higgs mass $m_A$ and $μ\tan\beta$, enabling a unique signature to distinguish the NMSSM from the MSSM even when heavy Higgs states are undetected. The lightest CP-even and CP-odd Higgs bosons are predominantly singlet states with masses governed by $\kappa/\lambda \cdot \mu$, and their suppressed couplings to the Z boson allow them to evade LEP detection despite being light.

ABSTRACT

We explore the Higgs sector of the NMSSM in the limit when the Peccei--Quinn symmetry is exact or only slightly broken. In this case the Higgs spectrum has a hierarchical structure which is caused by the stability of the physical vacuum. We find a strong correlation between the parameters of the NMSSM if $κ=0$ or $κ\lesssim λ^2$. It allows one to distinguish the NMSSM with exact or softly broken PQ-symmetry from the MSSM even when extra scalar and pseudoscalar Higgs states escape direct detection.

Motivation & Objective

• To explore the Higgs sector of the NMSSM under exact or slightly broken Peccei-Quinn (PQ) symmetry.
• To identify distinctive signatures that allow the NMSSM to be distinguished from the MSSM, even when additional Higgs states are not directly observed.
• To analyze the constraints imposed by vacuum stability and LEP experimental limits on the parameter space of the NMSSM with PQ symmetry.
• To determine the role of the $\kappa$ parameter in splitting the Higgs spectrum and stabilizing the vacuum.

Proposed method

• Analyzing the tree-level Higgs potential of the NMSSM with superpotential $W = \lambda S(H_1\epsilon H_2) + \frac{1}{3}\kappa S^3$, including $F$, $D$, and soft-breaking terms.
• Studying the limit $\kappa = 0$ (exact PQ symmetry) and $\kappa \ll \lambda^2$ (slightly broken PQ symmetry) to assess vacuum stability and mass hierarchies.
• Applying constraints from LEP bounds on the Z boson coupling to light Higgs states to determine viable parameter regions.
• Using the sum rule for Higgs couplings to the Z boson to show that light CP-even and CP-odd Higgs bosons must have suppressed couplings to avoid detection.
• Evaluating the renormalization group flow to assess whether small $\kappa$ values can arise naturally from the NMSSM dynamics.
• Deriving the mass splitting between light and heavy Higgs states, with the heavy states degenerate at $m_A \approx \mu\tan\beta$.

Experimental results

Research questions

• RQ1 How does the Higgs spectrum of the NMSSM behave under exact or slightly broken Peccei-Quinn symmetry?
• RQ2 What constraints does vacuum stability impose on the NMSSM parameter space when $\kappa = 0$ or $\kappa \ll \lambda^2$?
• RQ3 Can the NMSSM be distinguished from the MSSM if the additional Higgs states are not discovered at colliders?
• RQ4 What is the role of the $\kappa/\lambda \cdot \mu$ combination in determining the masses of the lightest Higgs bosons?
• RQ5 How do LEP bounds on the Z boson coupling affect the viability of light Higgs states in the PQ-symmetric NMSSM?

Key findings

• In the exact PQ-symmetry limit ($\kappa = 0$), the lightest CP-even and CP-odd Higgs bosons are predominantly singlet states with masses governed by the combination $\kappa/\lambda \cdot \mu$, which vanishes when $\kappa = 0$.
• Vacuum stability and LEP constraints require the heavy Higgs states—specifically the pseudoscalar $A$ and the charged Higgs—to be nearly degenerate with mass $m_A \approx \mu\tan\beta$, creating a strong correlation between $m_A$ and $\mu\tan\beta$.
• The lightest CP-even Higgs boson can have a mass below the LEP exclusion limit due to its strongly suppressed coupling to the Z boson, allowing it to evade detection despite being light.
• The coupling of the lightest CP-odd Higgs to the Z boson is always small, further reducing its detectability at colliders like the LHC.
• Even if the heavy Higgs states are not observed, the presence of two light scalars and one light pseudoscalar Higgs boson could serve as a distinctive signature of the NMSSM with slightly broken PQ symmetry.
• The strong correlation between $m_A$ and $\mu\tan\beta$ provides a unique 'smoking gun' signature to distinguish the NMSSM from the MSSM, even in the absence of direct discovery of heavy Higgs states.