Effective potential methods and the Higgs mass spectrum in the MSSM

TL;DR

The paper extends analytic two-loop leading-log Higgs mass calculations in the MSSM to arbitrary squark spectra, including left-right mixing. It combines a high-scale MSSM effective potential with a low-scale RG-improved two-Higgs-doublet model, implementing explicit threshold matching at stop/sbottom decoupling scales and defining pole masses with self-energy corrections. The authors derive general mass-matrix expressions and threshold contributions for non-degenerate squark masses and show that their results reproduce known degenerate-case results while enabling precise predictions across broad SUSY parameter spaces, including scenarios with light stops. This framework enhances the reliability of MSSM Higgs sector predictions and their phenomenological implications for collider physics and SUSY searches.

Abstract

We generalize the analytical expressions for the two-loop leading-log neutral Higgs boson masses and mixing angles to the case of general left- and right-handed soft supersymmetry breaking stop and sbottom masses and left--right mixing mass parameters ($m_Q, m_U, m_D, A_t, A_b$). This generalization is essential for the computation of Higgs masses and couplings in the presence of light stops. At high scales we use the minimal supersymmetric standard model effective potential, while at low scales we consider the two-Higgs doublet model (renormalization group improved) effective potential, with general matching conditions at the thresholds where the squarks decouple. We define physical (pole) masses for the top-quark, by including QCD self-energies, and for the neutral Higgs bosons, by including the leading one-loop electroweak self-energies where the top/stop and bottom/sbottom sectors propagate. For $m_Q=m_U=m_D$ and moderate left--right mixing mass parameters, for which the mass expansion in terms of renormalizable Higgs quartic couplings is reliable, we find excellent agreement with previously obtained results.

Figures (9)

• Figure 1: Plot of the Higgs mass $m_h$ from Eq. (\ref{['decmasa']}) (solid lines), the RG improved one-loop MSSM effective potential (dashed lines) and the MSSM effective potential considered at $Q^2=m_t^2$ (dotted lines), as described in section 2, for $M_t=175$ GeV, $m_A = M_{S}$, and $A_t = \mu =0$. The lower set corresponds to $\tan\beta=1.6$, and the upper set to $\tan\beta = 15$.
• Figure 2: Plot of the Higgs mass $m_h$ as a function of $A_t$, from Eq. (\ref{['decmasa']}), using the exact threshold function (\ref{['umbral']}) (solid line) and the approximation (\ref{['expumbral']}) (dashed line), for $M_t=175$ GeV, $\mu=0$ and $m_A=M_S=1$ TeV. The upper set corresponds to $\tan\beta=15$ and the lower set to $\tan\beta=1.6$.
• Figure 3: Plot of the Higgs mass $m_h$ as a function of $m_Q$ (solid line), for $M_t=175$ GeV, $\tan\beta = 1.6$, $\mu=A_b=0$, $m_U = m_D = 1$ TeV, and values of the CP-odd Higgs mass $m_A$ and the stop mixing mass parameter $A_t$ equal to $m_Q$. The dashed and dotted lines denote the same as in Fig. 1.
• Figure 4: The same as in Fig. 3, but for $m_U = m_D = 100$ GeV.
• Figure 5: Plot of the pole Higgs mass $M_h$ as a function of $m_Q$, for $M_t=175$ GeV, $\tan\beta=1.6$, $\mu=A_b=0$, $m_U = m_D = 1000$ GeV and $m_A = 300$ GeV. The different lines denote different values of the $A_t$ parameter. Starting from below at $m_Q = 1$ TeV, $A_t = 0$, 0.6, 1.0, 1.5, 1.8, 2.0 and 2.4 TeV, respectively.