[Paper Review] Higgs masses and couplings in the NMSSM

Ulrich Ellwanger, C. Hugonie|ArXiv.org|Jun 19, 2000

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper derives upper bounds on the masses of the lightest and second-lightest CP-even Higgs bosons in the NMSSM, including dominant two-loop corrections. It shows that a Higgs boson with coupling R > 1/2 (strong coupling) can have a mass up to 190 GeV if the lighter Higgs (R < 1/2) is excluded below 133.5 GeV, enabling full coverage of the NMSSM parameter space via combined LEP and Tevatron searches.

ABSTRACT

We give the upper bounds on the masses of the lightest and second lightest CP even Higgs bosons in the NMSSM, the MSSM extended by a gauge singlet. The dominant two loop corrections are included. Since the coupling R of the lightest Higgs scalar to gauge bosons can be small, we study in detail the relation between masses and couplings of both lightest scalars. We present upper bounds on the mass of a 'strongly' coupled Higgs (R&gt;1/2) as a function of lower experimental limits on the mass of a 'weakly' coupled Higgs (R&lt;1/2). With the help of these results, the whole parameter space of the model can be covered.

Motivation & Objective

• To determine the upper bounds on the masses of the lightest and second-lightest CP-even Higgs bosons in the NMSSM, including dominant two-loop quantum corrections.
• To analyze the interplay between Higgs couplings (R) and masses, especially when the lightest Higgs has a suppressed coupling (R < 1/2).
• To provide a framework for covering the entire NMSSM parameter space using experimental lower limits on weakly coupled Higgs bosons and upper limits on strongly coupled ones.
• To guide experimental searches at LEP and Tevatron by deriving constraints on the second-lightest Higgs mass as a function of its coupling strength.

Proposed method

• The effective potential is computed up to two-loop order, including leading logarithmic corrections from top quark and stop loops.
• Dominant two-loop corrections are evaluated using the effective potential expansion, focusing on terms proportional to hₜ⁴ and hₜ⁶, with resummation of leading logarithms.
• Wave function renormalization and Higgs-top Yukawa coupling corrections are included to properly relate physical masses and couplings.
• The Higgs mass bounds are derived by combining tree-level relations with radiative corrections, assuming M_susy ≤ 1 TeV.
• The analysis uses the relation R₁ = 1 − R₂ to map constraints from weakly coupled Higgs (R₁ < 1/2) to strongly coupled Higgs (R₂ > 1/2).
• Numerical results are presented in a mass-coupling plot (fig. 3), showing upper limits on m₂ as a function of R₂ for fixed m₁.

Experimental results

Research questions

• RQ1 What is the maximum possible mass of the second-lightest CP-even Higgs boson in the NMSSM when its coupling to vector bosons is strong (R₂ > 1/2), given constraints on the lightest Higgs?
• RQ2 How do two-loop corrections affect the upper bound on the lightest Higgs mass in the NMSSM compared to the MSSM?
• RQ3 What is the required experimental lower limit on the mass of a weakly coupled Higgs (R₁ < 1/2) to exclude the entire NMSSM parameter space?
• RQ4 Can the full parameter space of the NMSSM be probed using only LEP and Tevatron data, assuming a Higgs with R ≈ 1/2 and m ≈ 133.5 GeV is excluded?
• RQ5 What is the maximum mass of the second-lightest Higgs when the lightest Higgs is nearly invisible (R₁ → 0)?

Key findings

• The upper bound on the mass of the second-lightest CP-even Higgs boson (m₂) reaches up to 190 GeV when its coupling R₂ is near 0.5, provided the lightest Higgs (m₁) is excluded below 133.5 GeV.
• For R₂ → 1 (i.e., R₁ → 0), the upper bound on m₂ reduces to the standard upper limit on the lightest Higgs, approximately 133.5 GeV.
• The upper limit on m₂ is saturated only in the limit m₁ → 0, which requires strong experimental constraints on the lightest Higgs with R₁ < 1/2.
• A Higgs boson with coupling R₁ ≈ 1/2 and mass m₁ ≈ 133.5 GeV must be excluded to test the full NMSSM parameter space.
• The present LEP II lower limit on m₁ for R₁ < 1/2 leads to an upper bound of about 160 GeV on m₂ for R₂ ≈ 0.5.
• To fully probe the NMSSM, it is necessary to exclude a Higgs boson with 1/3 < R < 1 and mass below 135 GeV, assuming a 30 fb⁻¹ luminosity at the Tevatron.