[Paper Review] R-Parity Violation and Supersymmetric Higgs Masses

A. V. Gladyshev, R. S. Parpalak|arXiv (Cornell University)|Jun 29, 2010

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper investigates R-parity violating supersymmetric models with neutrino Yukawa couplings, showing that the R-parity violating term $\lambda_i\bar{\nu}_i H_u H_d$ contributes an F-term to the Higgs potential, raising the tree-level mass of the lightest neutral Higgs boson. This upward shift in the upper bound on the lightest Higgs mass relaxes constraints from LEP, slightly reopening parameter space excluded in the minimal supersymmetric standard model (MSSM) for small $\tan\beta$. The effect resembles the NMSSM but arises from neutrino-sector R-parity violation.

ABSTRACT

We consider the supersymmetric extension of the Standard Model with neutrino Yukawa interactions and R-parity violation. We found that R-parity breaking term λνH_u H_d leads to an additional F-type contribution to the Higgs scalar potential, and thus to the masses of supersymmetric Higgs bosons. The most interesting consequence is the modification of the tree-level expression for the lightest neutral supersymmetric Higgs boson mass. It appears that due to this contribution the bound on the lightest Higgs mass may be shifted upwards, thus slightly opening the part of the model parameter space excluded by non-observation of the light Higgs boson at LEP in the framework of the Minimal Supersymmetric Standard Model.

Motivation & Objective

• To investigate the impact of R-parity violating neutrino Yukawa interactions on the Higgs sector in supersymmetric models.
• To determine whether the $\lambda_i\bar{\nu}_i H_u H_d$ term alters the tree-level Higgs mass spectrum in the MSSM.
• To assess whether such modifications relax the upper bound on the lightest Higgs boson mass, potentially reopening parameter space excluded by LEP.
• To compare the resulting Higgs mass structure with that of the NMSSM and the standard MSSM.

Proposed method

• The study extends the MSSM by including R-parity violating neutrino Yukawa couplings in the superpotential, specifically $\lambda_i\bar{\nu}_i H_u H_d$.
• The F-term contribution from this R-parity violating term is derived and added to the scalar Higgs potential, modifying the tree-level potential structure.
• The scalar potential is minimized, and the second derivatives are computed to extract the physical Higgs mass matrices.
• The resulting mass eigenstates are calculated using the modified potential, with explicit expressions derived for $m_{h^0}^2$, $m_{A^0}^2$, and $m_{H^\pm}^2$ including the $\varepsilon$-dependent correction.
• The parameter $\varepsilon = \lambda_i v_u / (\sqrt{2} M_Z)$ is introduced to quantify the strength of the R-parity violating contribution.
• The results are compared to the standard MSSM and NMSSM mass bounds, particularly focusing on the behavior for small and large $\tan\beta$.

Experimental results

Research questions

• RQ1 How does the R-parity violating term $\lambda_i\bar{\nu}_i H_u H_d$ affect the tree-level Higgs mass in the MSSM?
• RQ2 Does this contribution raise the upper bound on the lightest neutral Higgs boson mass, and if so, under what conditions?
• RQ3 To what extent does this modification relax the LEP exclusion bounds on the MSSM parameter space, especially for small $\tan\beta$?
• RQ4 How does the resulting Higgs mass spectrum compare quantitatively to that of the NMSSM?

Key findings

• The R-parity violating term $\lambda_i\bar{\nu}_i H_u H_d$ contributes an F-term to the Higgs potential, modifying the scalar potential and thus the Higgs masses.
• The tree-level mass of the lightest neutral Higgs boson is raised according to $m_{h^0}^2 = M_Z^2 (\cos^2 2\beta + 2\varepsilon^2 \sin^2 2\beta)$, where $\varepsilon$ quantifies the strength of the R-parity violation.
• For small $\tan\beta$, the upward shift in the Higgs mass bound is significant, potentially reopening parameter space excluded by the LEP bound of 114 GeV.
• For $\tan\beta > 10$, the correction becomes negligible, and the Higgs mass bound and excluded parameter space revert to those of the standard MSSM.
• The charged Higgs boson mass receives a negative correction proportional to $\varepsilon^2$, given by $m_{H^\pm}^2 = m_{A^0}^2 + M_W^2 - 2\varepsilon^2 M_Z^2$, which may affect phenomenology.
• The model's Higgs mass structure qualitatively resembles the NMSSM, with a similar $\sin^2 2\beta$-enhanced correction, though arising from different dynamics.