Soft Symmetry Breaking as a Nonstandard Source of Mass: Phenomenological Insights from the Two-Higgs-Doublet Model

Abstract

The soft-breaking parameter, $m_{12}^2$, frequently appearing in the 2HDM scalar potential is much more remarkable than being just a nonstandard parameter that helps make the BSM scalars super heavy. In fact, as we show through explicit calculations, it should be treated as the direct but concise embodiment of new non-electroweak spontaneous symmetry breaking effects at very high energy scales, wherein lies its quiddities. Consequently, it is argued that $m_{12}^2$ and the electroweak VEV serve as two distinct sources for the nonstandard scalar masses, which are completely unrelated to each other. Such distinctions allow us to define parameters that conveniently capture the fraction of the nonstandard scalar masses derived from the electroweak VEV. Finally, we demonstrate that constraints can already be placed on such fractions from the current measurements of the diphoton signal strength and from direct searches of new nonstandard scalar resonances in the diphoton channel.

Figures (5)

• Figure 1: The scattered points indicate the allowed regions in the various parameter planes that satisfy the constraints from perturbative unitarity, boundedness from below (BFB), and the electroweak $T$-parameter. The dashed black outer contours in the top two panels correspond to the constraints derived from Eq. (\ref{['e:fCfAuni']}). Similarly, the dashed black outer contours in the bottom two panels arise from Eq. (\ref{['e:uni_bfb1']}). For the bottom panels, we have chosen $\tan\beta = 1$ and $m_H = m_h$, respectively, as these yield the most relaxed constraints. Note that these constraints only depend on the scalar sector of the 2HDM and therefore are valid for all the 2HDM variants that feature a softly-broken $Z_2$ symmetry.
• Figure 2: The allowed parameter space for the CP-even (H) and CP-odd (A) neutral scalars is shown in the upper and lower panels, respectively. Red points in the left (middle) column are excluded by $\tau\tau$ searches from gluon-fusion (bottom-associated) production, while those in the right column are excluded by $t\overline{t}$ bounds from top-associated production. These bounds from the direct searches are derived assuming a type-II Yukawa structure. Gray points in all panels are disfavored by the requirement $\Gamma_{H(A)} < m_{H(A)}$, where $\Gamma_{H(A)}$ is the total decay width of H(A). The teal background points satisfy all the constraints in Fig. \ref{['fig:uniMvsf']}.
• Figure 3: In the left (right) panel, the red points are excluded by charged Higgs searches in the $\tau\nu$ ($t\overline{b}$) channelATLAS:2018gfmATLAS:2021upq. In both these cases, the charged Higgs is produced via $pp\to H^{+} t \overline{b}$ mode. In both panels, the regions indicated by gray points are disfavored by the requirement $\Gamma_C < m_C$, where $\Gamma_C$ denotes the total decay width of the charged scalar. The exclusion contour arising from the $b \to s\gamma$ constraintMisiak:2017bggAtkinson:2021eox is shown as a blue solid line. The entire range of $\tan\beta$ is excluded due to this bound for $m_{C} < 580$ GeV. The bounds from the direct searches and $b \to s\gamma$ are derived assuming a type-II Yukawa structure.
• Figure 4: In the left (right) panel, the teal scattered points satisfy the combined constraints from unitarity, BFB conditions, the $T$-parameter and direct LHC search limit. In the left panel light pink (purple) colored band represents allowed region which is consistent with current (future) $\mu_{\gamma\gamma}$ measurements at 95% C.L. In the right panel, the red scattered points are disallowed from direct search limits arising from $p p \to H/A \to \gamma \gamma$ process. We note that these constraints are specific to the type-II Yukawa structure of the 2HDM.
• Figure 5: Points satisfying the combined constraints from unitarity, BFB conditions, and $\Gamma_{H,A,C} < m_{H,A,C}$, while remaining consistent with the current measurement of $\mu_{\gamma\gamma}$. Points highlighted in purple are disallowed from the anticipated future measurement of $\mu_{\gamma\gamma}$ with improved precision. These constraints are chosen such that the resulting bounds remain applicable to all variants of the 2HDM with a softly-broken $Z_2$ symmetry. The red solid line at $f_A=0$ corresponds to the case of a 2HDM potential with a softly-broken U(1) symmetry. Additionally, we note that $f_X = 1$ ($X \equiv C, H, A$) implies $\Lambda^2 = 0$ according to Eq. (\ref{['e:nonstandrad_frac']}), corresponding to the limiting case in which the 2HDM scalar potential possesses an exact $Z_2$ symmetry