The minimal supersymmetric model has two complex doublets of Higgs bosons. The resulting physical states are two scalars [${{\mathit H}_{{1}}^{0}}$ and ${{\mathit H}_{{2}}^{0}}$, where we define ${\mathit m}_{{{\mathit H}_{{1}}^{0}}}$ $<$ ${\mathit m}_{{{\mathit H}_{{2}}^{0}}}$], a pseudoscalar (${{\mathit A}^{0}}$), and a charged Higgs pair (${{\mathit H}^{\pm}}$). ${{\mathit H}_{{1}}^{0}}$ and ${{\mathit H}_{{2}}^{0}}$ are also called ${{\mathit h}}$ and ${{\mathit H}}$ in the literature. There are two free parameters in the Higgs sector which can be chosen to be ${\mathit m}_{{{\mathit A}^{0}}}$ and tan $\beta $ = $\mathit v_{2}/\mathit v_{1}$, the ratio of vacuum expectation values of the two Higgs doublets. Tree-level Higgs masses are constrained by the model to be ${\mathit m}_{{{\mathit H}_{{1}}^{0}}}{}\leq{}{\mathit m}_{{{\mathit Z}}}$, ${\mathit m}_{{{\mathit H}_{{2}}^{0}}}{}\geq{}{\mathit m}_{{{\mathit Z}}}$, ${\mathit m}_{{{\mathit A}^{0}}}{}\geq{}{\mathit m}_{{{\mathit H}_{{1}}^{0}}}$, and ${\mathit m}_{{{\mathit H}^{\pm}}}{}\geq{}{\mathit m}_{{{\mathit W}}}$. However, as described in the review on ``Status of Higgs Boson Physics'' in this Volume these relations are violated by radiative corrections.
The observed signal at about 125 GeV, see section ``${{\mathit H}^{0}}$'', can be interpreted as one of the neutral Higgs bosons of supersymmetric models. Unless otherwise noted, we identify the lighter scalar ${{\mathit H}_{{1}}^{0}}$ with the Higgs discovered at 125 GeV at the LHC (AAD 2012AI, CHATRCHYAN 2012N).
Unless otherwise noted, the experiments in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions search for the processes ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit H}_{{1}}^{0}}{{\mathit Z}^{0}}$ in the channels used for the Standard Model Higgs searches and ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit H}_{{1}}^{0}}{{\mathit A}^{0}}$ in the final states ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ and ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ . Unless otherwise stated, the following results assume no invisible ${{\mathit H}_{{1}}^{0}}$ or ${{\mathit A}^{0}}$ decays. Unless otherwise noted, the results are given in the m${}^{max}_{h}$ scenario, CARENA 2013 .
In ${{\mathit p}}{{\overline{\mathit p}}}$ and ${{\mathit p}}{{\mathit p}}$ collisions the experiments search for a variety of processes, as explicitly specified for each entry. Limits on the ${{\mathit A}^{0}}$ mass arise from these direct searches, as well as from the relations valid in the minimal supersymmetric model between ${\mathit m}_{{{\mathit A}^{0}}}$ and ${\mathit m}_{{{\mathit H}_{{1}}^{0}}}$. As discussed in the review on ``Status of Higgs Boson Physics'' in this Volume, these relations depend, via potentially large radiative corrections, on the mass of the ${{\mathit t}}~$quark and on the supersymmetric parameters, in particular those of the stop sector. These indirect limits are weaker for larger ${{\mathit t}}$ and ${{\widetilde{\mathit t}}}$ masses. To include the radiative corrections to the Higgs masses, unless otherwise stated, the listed papers use theoretical predictions incorporating two-loop corrections, and the results are given for the m${}^{mod+}_{h}$ benchmark scenario, see CARENA 2013 .

Mass Limits for ${{\boldsymbol H}_{{1}}^{0}}$ (Higgs Boson) in Supersymmetric Models INSPIRE search

$> 89.7$ 1
DLPH $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV
$> 92.8$ 95 2
LEP $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV
$>84.5$ 95 3, 4
OPAL $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV
$>86.0$ 95 3, 5
L3 $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV, tan $\beta >0.4$
$>89.8$ 95 3, 6
ALEP $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV, tan $\beta >0.5$
• • • We do not use the following data for averages, fits, limits, etc. • • •
TEVA ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit H}_{{1,2}}^{0}}$ $/$ ${{\mathit A}^{0}}{+}$ ${{\mathit b}}{+}$ ${{\mathit X}}$ , ${{\mathit H}_{{1,2}}^{0}}$ $/$ ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$
1  ABDALLAH 2008B give limits in eight $\mathit CP$-conserving benchmark scenarios and some $\mathit CP$-violating scenarios. See paper for excluded regions for each scenario. Supersedes ABDALLAH 2004 .
2  SCHAEL 2006B make a combined analysis of the LEP data. The quoted limit is for the $\mathit m{}^{{\mathrm {max}}}_{h}$ scenario with ${\mathit m}_{{{\mathit t}}}$ = 174.3 GeV. In the $\mathit CP$-violating CPX scenario no lower bound on ${\mathit m}_{{{\mathit H}_{{1}}^{0}}}$ can be set at 95$\%$ CL. See paper for excluded regions in various scenarios. See Figs. $2 - 6$ and Tabs. $14 - 21$ for limits on ${\mathit \sigma (}$ ${{\mathit Z}}{{\mathit H}^{0}}{)}\cdot{}$ B( ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ ) and ${\mathit \sigma (}$ ${{\mathit H}_{{1}}^{0}}{{\mathit H}_{{2}}^{0}}{)}\cdot{}$ B(${{\mathit H}_{{1}}^{0}},{{\mathit H}_{{2}}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ ).
3  Search for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit H}_{{1}}^{0}}{{\mathit A}^{0}}$ in the final states ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit b}}{{\overline{\mathit b}}}$ and ${{\mathit b}}{{\overline{\mathit b}}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ , and ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit H}_{{1}}^{0}}{{\mathit Z}}$ . Universal scalar mass of 1$~$TeV, SU(2) gaugino mass of 200 GeV, and $\mu $= $-200$ GeV are assumed, and two-loop radiative corrections incorporated. The limits hold for ${\mathit m}_{{{\mathit t}}}$=175 GeV, and for the $\mathit m{}^{{\mathrm {max}}}_{h}$ scenario.
4  ABBIENDI 2004M exclude 0.7 $<$ tan ${{\mathit \beta}}$ $<$ 1.9, assuming ${\mathit m}_{{{\mathit t}}}$ = 174.3 GeV. Limits for other MSSM benchmark scenarios, as well as for $\mathit CP$ violating cases, are also given.
5  ACHARD 2002H also search for the final state ${{\mathit H}_{{1}}^{0}}$ ${{\mathit Z}}$ $\rightarrow$ 2 ${{\mathit A}^{0}}{{\mathit q}}{{\overline{\mathit q}}}$ , ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$ . In addition, the MSSM parameter set in the ``large-$\mu $'' and ``no-mixing'' scenarios are examined.
6  HEISTER 2002 excludes the range $0.7<$tan $\beta <2.3$. A wider range is excluded with different stop mixing assumptions. Updates BARATE 2001C.
7  AALTONEN 2012AQ combine AALTONEN 2012X and ABAZOV 2011K. See their Table I and Fig. 1 for the limit on cross section times branching ratio and Fig. 2 for the excluded region in the MSSM parameter space.
PR D86 091101 Search for Neutral Higgs Bosons in Events with Multiple Bottom Quarks at the Tevatron
EPJ C54 1 Higgs Boson Searches in $\mathit CP$-Conserving and $\mathit CP$-Violating MSSM Scenarios with the DELPHI Detector
EPJ C47 547 Search for Neutral MSSM Higgs Bosons at LEP
EPJ C37 49 Search for Neutral Higgs Boson in $\mathit CP$-Conserving and $\mathit CP$-Violating MSSM Scenarios
PL B545 30 Search for Neutral Higgs Bosons of the Minimal Supersymmetric Standard Model in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Interactions at $\sqrt {s }$ = 209-GeV
PL B526 191 Final Results of the Searches for Neutral Higgs Bosons in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at$\sqrt {s }$ up to 209 GeV