Status of the MSSM Higgs sector using global analysis and direct search bounds, and future prospects at the High Luminosity LHC

In this paper, we search for the regions of the phenomenological minimal supersymmetric standard model (pMSSM) parameter space where one can expect to have moderate Higgs mixing angle ($\alpha$) with relatively light (up to 600 GeV) additional Higgses after satisfying the current LHC data. We perform a global fit analysis using most updated data (till December 2014) from the LHC and Tevatron experiments. The constraints coming from the precision measurements of the rare b-decays $B_s\to {\mu }^{+}{\mu }^{-}$ and $b\to s\gamma$ are also considered. We find that low $M_A(\lesssim 350)$ and high $\tan \beta (\gtrsim 25)$ regions are disfavored by the combined effect of the global analysis and flavor data. However, regions with Higgs mixing angle $\alpha \sim 0.1–0.8$ are still allowed by the current data. We then study the existing direct search bounds on the heavy scalar/pseudoscalar ($\mathrm{H}/\mathrm{A}$) and charged Higgs boson (${\mathrm{H}}^{\pm }$) masses and branchings at the LHC. It has been found that regions with low to moderate values of $\tan \beta$ with light additional Higgses (mass $\le 600\mathrm{GeV}$) are unconstrained by the data, while the regions with $\tan \beta >20$ are excluded considering the direct search bounds by the LHC-8 data. The possibility to probe the region with $\tan \beta \le 20$ at the high luminosity run of LHC are also discussed, giving special attention to the $\mathrm{H}\to \mathrm{hh}$, $\mathrm{H}/\mathrm{A}\to \mathrm{t}\overline{\mathrm{t}}$ and $\mathrm{H}/\mathrm{A}\to {\tau }^{+}{\tau }^{-}$ decay modes.

Figure 1

Parameter space allowed in $M_A\text{−}\tan \beta$ plane from our global fit analysis and also satisfying the flavor physics constraints on $\mathrm{Br}(\mathrm{b}\to s\gamma )$ and $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$. Magenta (black) colored triangle (circle) shaped points represent $2\sigma$ ($1\sigma$) allowed parameter space from global fits of 125 GeV Higgs data after Run-I of LHC. In the rest of our analysis, while presenting the direct search constraints and the future limits on the heavy Higgs masses and BRs, we would consider these $2\sigma$ points which satisfies our global fit analysis and the updated flavor data.

Figure 2

Scatter plots in the (a) $M_A\text{−}\tan \beta$ plane without any flavor constraint (left panel), (b) $M_A\text{−}\tan \beta$ plane only after imposing $\mathrm{Br}(\mathrm{b}\to s\gamma )$ constraint (middle panel) and (c) $M_A\text{−}\tan \beta$ plane after imposing only $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$ constraint (right panel). In Fig. 1, we show the same correlation after the imposition of both $\mathrm{Br}(\mathrm{b}\to s\gamma )$ and $\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$ constraints.

Figure 3

Left panel (a) shows the allowed parameter space in $\tan \beta \text{−}\alpha$ plane after the global fit analysis and also satisfying the flavor physics constraints. Color conventions are the same as Fig. 1. In the right panel (b), we display the same allowed parameter space but now is presented in the $M_A\text{−}\alpha$ plane.

Figure 4

The allowed parameter space in the $(\beta -\alpha )\text{−}\tan \beta$ plane is presented with different choices of $M_A$. The entire $M_A$ region is divided in four parts, namely $200<M_A<300\mathrm{GeV}$ (red/square), $300<M_A<400\mathrm{GeV}$ (black/circle), $400<M_A<500\mathrm{GeV}$ (green/triangle), and $500<M_A<600\mathrm{GeV}$ (blue/cross). The red horizontal line at $(\beta -\alpha )=1.571$ indicates the value of $(\alpha -\beta )$ at the alignment limit. We see that regions with light $M_A$ ($\le 400\mathrm{GeV}$) satisfying the alignment limit are perfectly allowed by the current data.

Figure 5

Signal strength correlations in (a) ${\mu }_{ZZ}\text{−}{\mu }_{\gamma \gamma }$, (b) ${\mu }_{ZZ}\text{−}{\mu }_{{\tau }^{+}{\tau }^{-}}$ and (c) ${\mu }_{ZZ}\text{−}{\mu }_{b\overline{b}}$ planes. Magenta (black) colored triangle (circle) shaped points represent $2\sigma$ ($1\sigma$) allowed points of our “scanned data set.”

Figure 6

Left panel shows the distribution of the quantity $\epsilon =(\frac{1}{1+{\mathrm{\Delta }}_b})\times (1-\frac{{\mathrm{\Delta }}_b}{\tan \beta \tan \alpha })$ with the variation of ${\mathrm{\Delta }}_b$. The variation of the ratios of the partial decay widths and branching ratios of the Higgs boson to the SM values for the $b\overline{b}$ and ${\tau }^{+}{\tau }^{-}$ modes with the tree level Higgs Yukawa couplings $\frac{\sin \alpha }{\cos \beta }$ are shown in the middle and right panel, respectively. For more details, see the text.

Figure 7

(a) Left: Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(H\to \gamma \gamma )]$ plane assuming gluon-gluon fusion production process. The solid red (blue dashed) line represents the observed upper limits on $\sigma \times \mathrm{Br}(H\to \gamma \gamma )$ at 95% C.L. by the CMS collaboration [56] using LHC-8 data with ${\mathrm{\Gamma }}_H=0.1\times M_H$ (0.1 GeV). Magenta colored triangle shaped points represent $2\sigma$ allowed parameter space from global fits satisfying flavor constraints (see Fig 1). (b) Right: Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{WW})]$ plane when the H is produced via ggF. The red solid line indicates the observed upper limits on $\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{WW})$ at the 95% C.L. by the CMS collaboration [59] using LHC-8 data.

Figure 8

(a) Left: Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{hh}\to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}})]$ plane assuming gluon-gluon fusion production process for $2\sigma$ allowed parameter space (represented by magenta points). The solid red line represents the observed upper limits on $\sigma \times \mathrm{Br}(H\to \mathrm{hh}\to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}})$ at 95% C.L. by the CMS collaboration [58] using 8 TeV data. (b) Right: Scatter plot in $M_H-[\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{hh}\to \mathrm{b}\overline{\mathrm{b}}\gamma \gamma )]$ for ggF production mode. The red solid line indicates the observed upper limits on $\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{hh}\to \mathrm{b}\overline{\mathrm{b}}\gamma \gamma )$ at the 95% C.L. by the CMS collaboration [57] using LHC 8 TeV data.

Figure 9

Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(\mathrm{\Phi }\to {\tau }^{+}{\tau }^{-})]$ plane where $\mathrm{\Phi }=\mathrm{H}$, A produced via (a) gluon fusion and (b) in association with $b$-quarks. The solid red (black dashed) line represents the observed upper limits on $\sigma \times \mathrm{Br}(\mathrm{\Phi }\to {\tau }^{+}{\tau }^{-})$ at 95% C.L. by the ATLAS (CMS) collaboration using LHC-8 data [54, 55]. Combined contributions of $\sigma \times \mathrm{Br}(\mathrm{\Phi }\to {\tau }^{+}{\tau }^{-})$ of both $H$ and $A$ for the $2\sigma$ allowed parameter space with $30<\tan \beta <50$, $20<\tan \beta <30$, $10<\tan \beta <20$ and $1<\tan \beta <10$ are shown in pink (cross), green (triangle), blue (circle) and violet (square), respectively.

Figure 10

(a) Left: Scatter plot in $M_A\text{−}[\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh}\to {\ell }^{+}{\ell }^{-}\mathrm{b}\overline{\mathrm{b}})]$ plane assuming gluon-gluon fusion production process for $2\sigma$ allowed parameter space (represented by magenta points). The solid red (blue dashed) line represents the observed upper limits on $\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh}\to {\ell }^{+}{\ell }^{-}\mathrm{b}\overline{\mathrm{b}})$ at 95% C.L. by the CMS collaboration using LHC-8 data [61] with narrow width (${\mathrm{\Gamma }}_A=30\mathrm{GeV}$) assumption. (b) Middle: Scatter plot in $M_A\text{−}[\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh})\times \mathrm{Br}(\mathrm{h}\to \mathrm{b}\overline{\mathrm{b}})]$ plane for ggF production mode. The red solid line indicates the observed upper limits on $\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh})\times \mathrm{Br}(\mathrm{h}\to \mathrm{b}\overline{\mathrm{b}})$ at the 95% C.L. by the ATLAS collaboration using LHC 8 TeV data [60]. (c) Right: Scatter plot in $M_A\text{−}[\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh})\times \mathrm{Br}(\mathrm{h}\to {\tau }^{+}{\tau }^{-})]$ plane for ggF production mode. The red solid line shows the observed upper limits on $\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh})\times \mathrm{Br}(\mathrm{h}\to {\tau }^{+}{\tau }^{-})$ at the 95% C.L. by the ATLAS collaboration using LHC 8 TeV data [60].

Figure 11

(a) Left: Scatter plot in $M_{H^{\pm }}\text{−}[\sigma \times \mathrm{Br}({\mathrm{H}}^{\pm }\to {\tau }^{\pm }{\nu }_{\tau })]$ plane for ggF production. Magenta points represent $2\sigma$ allowed regions. The solid red (blue dashed) line represents the observed upper limits on $\sigma \times \mathrm{Br}({\mathrm{H}}^{\pm }\to {\tau }^{\pm }{\nu }_{\tau })$ at 95% C.L. by the ATLAS [62] (CMS) collaboration using LHC 8 TeV data. (b) Right: Scatter plot in $M_{H^{\pm }}\text{−}[\sigma \times \mathrm{Br}({\mathrm{H}}^{\pm }\to \mathrm{t}\overline{\mathrm{b}})]$ plane for ggF production. The solid red line shows the observed upper limits on $\sigma \times \mathrm{Br}({\mathrm{H}}^{\pm }\to \mathrm{t}\overline{\mathrm{b}})$ at 95% C.L. by the CMS collaboration using LHC 8 TeV data.

Figure 12

Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{ZZ}\to {\ell }^{+}{\ell }^{-}{\ell }^{+}{\ell }^{-})]$ plane assuming gluon-gluon fusion production process. Magenta colored points represents for $2\sigma$ allowed parameter space. The solid red line (blue dashed line) represents the expected upper limits on $\sigma \times \mathrm{Br}(\mathrm{H}\to \mathrm{ZZ}\to {\ell }^{+}{\ell }^{-}{\ell }^{+}{\ell }^{-})$ at 95% C.L. by the ATLAS (CMS) collaboration [94, 95] for 14 TeV LHC with $\mathcal{L}=3000{\mathrm{fb}}^{-1}$.

Figure 13

Scatter plot in $M_A\text{−}[\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zh}\to {\ell }^{+}{\ell }^{-}\mathrm{b}\overline{\mathrm{b}})]$ plane assuming gluon-gluon fusion production process. Magenta colored points represents for $2\sigma$ allowed parameter space. The solid red line (blue dashed line) represents the expected upper limits on $\sigma \times \mathrm{Br}(\mathrm{A}\to \mathrm{Zb}\to {\ell }^{+}{\ell }^{-}\mathrm{b}\overline{\mathrm{b}})$ at 95% C.L. by the ATLAS (CMS) collaboration for 14 TeV LHC with $\mathcal{L}=3000{\mathrm{fb}}^{-1}$ [94, 95].

Figure 14

Sensitivity of di-Higgs final state in $M_A\text{−}\tan \beta$ plane at HL-LHC from $b\overline{b}\gamma \gamma$ channel with $\mathcal{L}=3000{\mathrm{fb}}^{-1}$. The magenta colored points are $2\sigma$ allowed points from global analysis and the black circled points are expected to be probed at HL-LHC (see Sec. 4a3 for details).

Figure 15

Distribution of $t\overline{t}$ invariant mass for some representative SUSY benchmark points with $M_H=400\mathrm{GeV}$ (green), 500 GeV (blue), 600 GeV (red) and SM $t\overline{t}$ background (black). The distribution has been drawn before applying the cut on invariant mass ($C5$) in signal region SR-loose (see text for details) for integrated luminosity $\mathcal{L}=3000{\mathrm{fb}}^{-1}$. We consider $\mathrm{NNLO}+\mathrm{NNLL}$ cross section for SM $t\overline{t}$ production at 14 TeV LHC (966 pb) and for signal the no of events has been estimated assuming single $H$ production cross section to be 1 pb with $\mathrm{Br}(H\to t\overline{t})=100\%$.

Figure 16

Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(\mathrm{H},\mathrm{A}\to \mathrm{t}\overline{\mathrm{t}})]$ plane assuming both H and A production via ggF at 14 TeV LHC. Magenta colored points represents for $2\sigma$ allowed parameter space. Red line corresponds to $\sigma \times \mathrm{Br}(H,A\to t\overline{t})=1\mathrm{pb}$.

Figure 17

Left: Scatter plot in $M_H\text{−}[\sigma \times \mathrm{Br}(\mathrm{\Phi }\to {\tau }^{+}{\tau }^{-})]$ plane where $\mathrm{\Phi }=\mathrm{H}$, A produced in association with $b$-quarks. The entire $\tan \beta$ region is splitted into different pieces, the regions with $20<\tan \beta <50$, $10<\tan \beta <20$, $5<\tan \beta <10$ and $1<\tan \beta <5$ are shown in red (cross), pink (triangle), blue (circle) and green (square), respectively. The solid red (black) line represents the expected upper limits on $\sigma \times \mathrm{Br}(\mathrm{\Phi }\to {\tau }^{+}{\tau }^{-})$ at the HL-LHC with $\mathcal{L}=3000{\mathrm{fb}}^{-1}$. Right: Sensitivity of $H/A\to {\tau }^{+}{\tau }^{-}$ final states in $M_A\text{−}\tan \beta$ plane. The magenta (plus) points are the $2\sigma$ allowed points corresponding to our scanned data set, while the blue (square) and green (cross) points are expected to be probed at HL-LHC considering 20% and 10% systematic uncertainties, respectively.