Radiative corrections to Higgs boson masses for the MSSM Higgs potential with dimension-six operators

In the framework of the effective field theory approach to heavy supersymmetry radiative corrections in the Higgs sector of the minimal supersymmetric standard model (MSSM) for the effective potential decomposition up to the dimension-six operators are calculated. Symbolic expressions for the threshold corrections induced by $F$- and $D$-soft supersymmetry breaking terms are derived, and the Higgs boson mass spectrum respecting the condition $m_h=125\mathrm{GeV}$ for the lightest $CP$-even scalar is evaluated.

Figure 1

The dimensionless parameters ${\lambda }_i$, $i=1,\dots ,7$ (light gray) calculated using the analytical results of [16] and ${\kappa }_j·M_S^2$, $j=1,\dots ,13$ (dark gray) calculated at the squark mass scale (a) $M_S=5\mathrm{TeV}$ and (b) $M_S=7\mathrm{TeV}$ for $A_t=A_b=10\mathrm{TeV}$, $\mu =14\mathrm{TeV}$, and $\tan \beta =5$.

Figure 2

The dimensionless parameters (a) ${\lambda }_i$ and (b) ${\kappa }_i·M_S^2$ as a function of $M_S$ for $A_t=A_b=10\mathrm{TeV}$, $\mu =14\mathrm{TeV}$, $\tan \beta =5$. ${\lambda }_i$ are evaluated using analytical formulas from [16], where the contribution of nonleading $D$ terms is accounted for.

Figure 3

Higgs boson masses and mixing angles combination as functions of the squark mass scale $M_S$. Thin lines correspond to the effective potential $U^{(4)}$ including terms with the maximal dimension four in the fields, and thick lines are the results for masses calculated with the effective potential $U^{(6)}$ including the dimension-six operators. The MSSM parameter sets: (a) $\tan \beta =4$, $A=10\mathrm{TeV}$, $\mu =8\mathrm{TeV}$; (b) $\tan \beta =8$, $A=25\mathrm{TeV}$, $\mu =30\mathrm{TeV}$; (c), (d) $\tan \beta =5$, $A=10\mathrm{TeV}$, and $\mu =5\mathrm{TeV}$. The discontinuity in (c) at $M_S$ of about 3 TeV corresponds to the zero denominator of Eq. (25).

Figure 4

Left panel: Contours for the Higgs boson mass $m_h^{(4)}$ calculated with the dimension-four potential terms; right panel: the relative difference in percent between $m_h^{(6)}$ and $m_h^{(4)}$ masses; the parameter set $A=10\mathrm{TeV}$, $\mu =8.3\mathrm{TeV}$, $M_S=2\mathrm{TeV}$ (a), (b) and $M_S=5\mathrm{TeV}$ (c), (d).

Figure 5

Domains of the Higgs boson mass $m_h=125\pm 3\mathrm{GeV}$ for $m_A=300\mathrm{GeV}$ and the Higgs superfield mass parameter $\mu$ equal to zero, $\tan \beta =20$, calculated with (a) the dimension-four operators and (b) the dimension-six operators.