Accommodating hints of new heavy scalars in the framework of the flavor-aligned two-Higgs-doublet model

Searches for new neutral Higgs bosons of an extended Higgs sector at the LHC can be interpreted in the framework of the two-Higgs doublet model. By employing generic flavor-aligned Higgs–fermion Yukawa couplings, we propose an analysis that uses experimental data to determine whether flavor alignment is a consequence of a symmetry that is either exact or at most softly broken. We illustrate our proposal in two different scenarios based on a few 3 sigma (local) excesses observed by the ATLAS and CMS Collaborations in their searches for heavy scalars. In scenario 1, an excess of events is interpreted as $A\to ZH\to {\ell }^{+}{\ell }^{-}b\overline{b}$ (where $\ell =e$ or $\mu$), with the $CP$-odd and $CP$-even neutral scalar masses given by $m_A=610\mathrm{GeV}$ and $m_H=290\mathrm{GeV}$, respectively. In scenario 2, an excess of events in the production of $t\overline{t}$ and ${\tau }^{+}{\tau }^{-}$ final states is interpreted as decays of a $CP$-odd scalar of mass $m_A=400\mathrm{GeV}$. Scenario 1 is consistent with type-I Yukawa interactions, which can arise in a 2HDM subject to a softly-broken ${\mathbb{Z}}_2$ discrete symmetry. Scenario 2 is inconsistent with a symmetry-based flavor alignment, but can be consistent with more general flavor-aligned Higgs–fermion Yukawa couplings.

Figure 1

Signal rates for the production of $A$ and $H$ in scenario 1. The A2HDM parameter generation complies with all theoretical and experimental constraints elucidated in Sec. 4. Events inside the rectangular box with red boundaries are consistent with the conditions specified in Eqs. (57)–(60), which correspond to a small excess of events reported in Ref. [20] and interpreted as $gg\to A\to ZH\to b\overline{b}{\ell }^{+}{\ell }^{-}$ (with no significant excess in the corresponding $b$-associated production of $A$), and with the nonobservation of $gg\to H\to hh$ derived from the 95% C.L. upper limits obtained in Refs. [55, 56].

Figure 2

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Sec. 4 and the constraints of Eqs. (57)–(60). Panel (a) shows the branching ratios for the decay of $A$ into its dominant final state channels, and panel (b) shows the total $A$ width divided by its mass, as functions of $|a^U|$. Applying the 95% C.L. upper limit for $\sigma (gg\to A\to t\overline{t})$ reported in Ref. [23] eliminates points to the right of the dashed line shown in panel (b) from further consideration. The two distinct branches of a given color of points correspond to the cases where the decay $A\to W^{\pm }{H}^{\mp }$ is either kinematically allowed or disallowed.

Figure 3

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Sec. 4 and the constraints of Eqs. (57)–(60). Panels (a) and (b) exhibit the branching ratios of the four main $H$ decay channels as functions of $|a^U|$ (allowing $a^D$ to vary) and $|a^D|$ (allowing $a^U$ to vary), respectively.

Figure 4

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Section 4 and the constraints of Eqs. (57)–(60). Panel (a) show the allowed values of the flavor-alignment parameter $a^D$ as a function of $|\cos (\beta -\alpha )|$ and panel (b) shows the charged Higgs mass as a function of $a^D$.

Figure 5

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Sec. 4 and the constraints of Eqs. (57)–(60). Panel (a) shows the cross sections for gluon fusion production and $b$-associated production of $H$ multiplied by $\mathrm{BR}(H\to {\tau }^{+}{\tau }^{-})$, and panel (b) shows $\sigma (gg\to H)\times \mathrm{BR}(H\to ZZ)$ as a function of $|\cos (\beta -\alpha )|$. The vertical and horizontal red lines shown in panel (a) correspond to the $1\sigma$ exclusion limit (for $m_H=300\mathrm{GeV}$) exhibited in Eqs. (64) and (65), respectively [22]. The blue points in panel (b) correspond to the points in panel (a) that lie below the red horizontal line and to the left of the red vertical line, and the horizontal green line shown in panel (b), which corresponds to Eq. (66), reflects the 95% C.L. upper bound reported in Ref. [57].

Figure 6

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Sec. 4 and the constraints of Eqs. (57)–(60). The values of the flavor-alignment parameters $a^E$ and $a^U$ are then plotted as blue points in panel (a). The red points of panel (a) correspond to those that survive the additional constraints of Eqs. (64)–(66). The values of the cross sections for gluon fusion production and $b$-associated production of $A$ multiplied by $\mathrm{BR}(H\to {\tau }^{+}{\tau }^{-})$, subject to the same constraints as the red points of panel (a), are plotted as red points in panel (b).

Figure 7

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Sec. 4 and the constraints of Eqs. (57)–(60) and Eqs. (64)–(66). In panel (a) the values of the cross section for gluon fusion production of $H$ multiplied by $\mathrm{BR}(H\to hh)$ are plotted as a function of $|a^U|$. In panel (b), the values of the cross section for $b$-associated production of $H$ multiplied by $\mathrm{BR}(H\to hh)$ are plotted as a function of $|a^D|$.

Figure 8

Results of a scan over A2HDM parameter points in scenario 1 that satisfy the theoretical and experimental constraints elucidated in Sec. 4 and the constraints of Eqs. (57)–(60) and Eqs. (64)–(66). We plot the values of $T_I$ vs. $T_X$ for all surviving scan points. Points that lie along the horizontal (yellow) axis would be consistent with a type-X 2HDM. Points that lie along the vertical (blue) axis would be consistent with a type-I 2HDM.

Figure 9

The ratio of the $A$ width to its mass (with $m_A=400\mathrm{GeV}$) as a function of the flavor-alignment parameter $a^U$ in scenario 2 obtained in a scan over A2HDM parameters, subject to the theoretical and experimental constraints elucidated in Sec. 4. The dashed cyan (solid black) line shows the observed (expected) 95% C.L. upper limit on the gluon fusion cross section for $A\to t\overline{t}$ reported by the CMS Collaboration in Ref. [23], translated into an upper limit for $a^U$ as a function of ${\mathrm{\Gamma }}_A/m_A$. The points of the scan that lie between the dashed cyan and solid black curve are colored red, which constitute the proposed signal of scenario 2.

Figure 10

Results of a scan over A2HDM parameter points in scenario 2 that satisfy the theoretical and experimental constraints elucidated in Sec. 4. The blue points exhibit the values of the cross sections for gluon fusion production and $b$-associated production of $A$ multiplied by $\mathrm{BR}(H\to {\tau }^{+}{\tau }^{-})$. These points are colored red if the corresponding values of $a^U$ and $\mathrm{\Gamma }/m_A$ lie in the red region of Fig. 9. The $+$ indicates the best fit point for the ATLAS excess of Ref. [21] interpreted as $A$ production with $m_A=400\mathrm{GeV}$; the solid yellow and black curves correspond to the corresponding $1\sigma$ and $2\sigma$ contours. Red points within the $1\sigma$ contour are colored green. Finally, all points outside the boundary of the dashed black ellipse are excluded at the 95% C.L. by the ditau search of the CMS Collaboration [24].

Figure 11

Results of a scan over A2HDM parameter points in scenario 2 that satisfy the theoretical and experimental constraints elucidated in Sec. 4. The points shown are the subset of the green points of Fig. 10 that are contained within the dashed ellipse shown there. We exhibit (a) the predicted values of $\sigma (gg\to b\overline{b}A)\times \mathrm{BR}(A\to b\overline{b})$ as a function of $|a^D|$, and (b) the predicted values of $\sigma (gg\to b\overline{b}H)\times \mathrm{BR}(H\to b\overline{b})$ as a function of $m_H$. Points that lie above the solid line are excluded by the 95% C.L. upper limit obtained by the CMS Collaboration in Ref. [67]. The dashed black line is the expected exclusion at run 3 of the LHC.

Figure 12

Results of a scan over A2HDM parameter points in scenario 2 that lie within the region of interest, corresponding to the area of parameter space occupied by the subset of green points that lie inside the dashed black ellipse in Fig. 10 and below the dashed line in Fig. 11. Panel (a) exhibits the values of the flavor-alignment parameters $a^E$ and $a^D$ and panel (b) exhibits the masses of the heavier $CP$-even scalar $H$ and the charged Higgs boson $H^{\pm }$, for each scan point that satisfies all the specified constraints.

Figure 13

Results of a scan over A2HDM parameter points in scenario 2 that lie within the region of interest, corresponding to the area of parameter space occupied by the subset of green points that lie inside the black dashed ellipse in Fig. 10 and below the solid black lines in Fig. 11. Panel (a) exhibits the values of $T_I$ vs. $T_X$. Points that lie along the horizontal (yellow) axis would be consistent with a type-X 2HDM. Points that lie along the vertical (blue) axis would be consistent with a type-I 2HDM. Panel (b) exhibits the values of $T_{II}$ vs. $T_Y$. Points that lie along the horizontal (yellow) axis would be consistent with a type-Y 2HDM. Points that lie along the vertical (blue) axis would be consistent with a type-II 2HDM.

Figure 14

The solid black line corresponds to the 95% C.L. exclusion limit reported by the ATLAS Collaboration in Ref. [68]. The solid black lines shown in both plots above are based on $139{\mathrm{fb}}^{-1}$ of data. Assuming an additional $300{\mathrm{fb}}^{-1}$ of data during run 3 of the LHC, a naïve rescaling of the ATLAS exclusion bounds yields the dashed black lines shown in both plots.

Figure 15

Regions of the A2HDM parameter space that satisfy $|\delta \mathrm{BR}(b\to s\gamma )|\le 4\times {10}^{-5}$.

Figure 16

Regions of the A2HDM parameter space that satisfy $|\delta \mathrm{BR}(b\to s\gamma )|\le 4\times {10}^{-5}$ for fixed values of $a^U=0.1$, 0.2, 0.5, 1.0, 1.5, and 2.0. Combining the six panels above yields the plot shown in Fig. 15.

Figure 17

Regions of the A2HDM parameter space (indicated by the various colors) in the $m_{H^{\pm }}$ vs. $1/a^U$ plane that satisfy $|\delta \mathrm{BR}(b\to s\gamma )|\le 4\times {10}^{-5}$. The uncolored regions are excluded. The value of $a^D$ is fixed by $a^D=(a^U{)}^p\mathrm{sgn}p$. As $p$ varies, we include all parameter points in which $|a^D|<100$. The sequence of panels correspond to $p=1,0.6,0.1,-0.1,-0.6$, and $-1$. The case of $p=1$ [$p=-1$] corresponds to the type I [type II] 2HDM. In these two cases, in a convention where $\tan \beta$ is positive, one may identify $\tan \beta =1/a^U$.

Figure 18

LO vs. NLO constraints due to $b\to s\gamma$ in the $a^U$ vs. $a^D$ plane, with charged Higgs masses separated by color. All points shown above satisfy $|\delta \mathrm{BR}(b\to s\gamma )|\le 4\times {10}^{-5}$.

Figure 19

Impact of the $\mathrm{\Delta }{M}_{B_s}$ bound on the A2HDM parameter space. In panel (a) all points shown are from a general scan on $a^U$, $a^D$ and $m_{H^{\pm }}$ which pass the $\mathrm{\Delta }{M}_{B_s}$ bound. In panel (b) we exhibit the ratio of the $A$ width to its mass (with $m_A=400\mathrm{GeV}$) as a function of the flavor-alignment parameter $|a^U|$ in scenario 2. The blue points are the result of a scan over A2HDM parameters, subject to the theoretical and experimental constraints elucidated in Sec. 4 prior to imposing the $\mathrm{\Delta }{M}_{B_s}$ bound. The dashed cyan (solid black) line correspond to the observed (expected) 95% C.L. upper limit on the cross section for $gg\to A\to t\overline{t}$ reported by the CMS Collaboration in Ref. [23], translated into an upper limit for $|a^U|$ as a function of ${\mathrm{\Gamma }}_A/m_A$. As for the remaining scan points that lie between the dashed cyan and solid black curve, the green points are eliminated after imposing the $\mathrm{\Delta }{M}_{B_s}$ constraint. The surviving red scan points constitute the proposed signal of scenario 2.