#### MASS LIMITS FOR NEUTRAL HIGGS BOSONS IN SUPERSYMMETRIC MODELS

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 ${{\mathit H}_{{1}}^{0}}$ (Higgs Boson) in Supersymmetric Models

VALUE (GeV) CL% DOCUMENT ID TECN  COMMENT
$> 89.7$ 1
 2008 B
DLPH $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV
$> 92.8$ 95 2
 2006 B
LEP $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV
$>84.5$ 95 3, 4
 2004 M
OPAL $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV
$>86.0$ 95 3, 5
 2002 H
L3 $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV, tan $\beta >0.4$
$>89.8$ 95 3, 6
 2002
ALEP $\mathit E_{{\mathrm {cm}}}{}\leq{}$209 GeV, tan $\beta >0.5$
• • We do not use the following data for averages, fits, limits, etc. • •
7
 2012 AQ
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.
References:
 AALTONEN 2012AQ
PR D86 091101 Search for Neutral Higgs Bosons in Events with Multiple Bottom Quarks at the Tevatron
 ABDALLAH 2008B
EPJ C54 1 Higgs Boson Searches in $\mathit CP$-Conserving and $\mathit CP$-Violating MSSM Scenarios with the DELPHI Detector
 Also
EPJ C56 165 (errat.) Erratum to ABDALLAH 2008B: Higgs Boson Searches in $\mathit CP$-Conserving and $\mathit CP$-Violating MSSM Scenarios with the DELPHI Detector
 SCHAEL 2006B
EPJ C47 547 Search for Neutral MSSM Higgs Bosons at LEP
 ABBIENDI 2004M
EPJ C37 49 Search for Neutral Higgs Boson in $\mathit CP$-Conserving and $\mathit CP$-Violating MSSM Scenarios
 ACHARD 2002H
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
 HEISTER 2002
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