Higgs partner searches and dark matter phenomenology in a classically scale invariant Higgs boson sector

In a previous work, a classically scale invariant extension of the standard model was proposed, as a potential candidate for resolving the hierarchy problem, by minimally introducing a complex gauge singlet scalar and generating radiative electroweak symmetry breaking by means of the Coleman-Weinberg mechanism. Postulating the singlet sector to respect the $CP$ symmetry, the existence of a stable pseudoscalar dark matter candidate with a mass in the TeV range was demonstrated. Moreover, the model predicted the presence of another physical $CP$-even Higgs boson (with suppressed tree-level couplings), in addition to the 125 GeV scalar discovered by the LHC. The viable region of the parameter space was determined by various theoretical and experimental considerations. In this work, we continue to examine the phenomenological implications of the proposed minimal scenario by considering the constraints from the dark matter relic density, as determined by the Planck Collaboration, as well as the direct detection bounds from the LUX experiment. Furthermore, we investigate the implications of the collider Higgs searches for the additional Higgs boson. Our results are comprehensively demonstrated in unified exclusion plots, which analyze the viable region of the parameter space from all relevant angles, demonstrating the testability of the proposed scenario.

Figure 1

Validity of the narrow-width approximation for the $\sigma$ boson. The panels display the ratio of the boson’s total width to its mass as a function of its mass for $m_{\sigma }\le 1\mathrm{TeV}$. Three values of the mixing angle—motivated by the experimental constraints [9]—are selected for illustration in each panel. In the left panel ($M_N=300\mathrm{GeV}$), the decay channel of the $\sigma$ scalar to a pair of right-handed neutrinos is kinematically open, whereas in the right panel ($M_N=1000\mathrm{GeV}$), such a decay is not permitted. The effect of this non-SM decay mode is, thus, negligible in the entire mass range of interest.

Figure 2

Left panel: Theoretical curves of the $\mu$ parameter (29) as a function of the $\sigma$ boson mass, for three representative values of the mixing angle, along with the most stringent experimental upper limit from LEP [7] and LHC [14] Higgs searches at 95% C.L. Right panel: The experimental exclusion limits in the $\sin \omega \text{−}{m}_{\sigma }$ plane. All colored regions are excluded at 95% C.L., taking into account the electroweak precision tests (dot-dashed line), direct measurements of the LHC 125 GeV $h$ Higgs’ properties (solid line), and the LEP and LHC Higgs searches (dotted line).

Figure 3

Pair annihilation of the $\chi$ WIMP dark matter into the (dominant) pairs of scalar, fermion, and vector final states. Diagrams in the top three rows illustrate their scattering process in all possible channels with the corresponding mediators.

Figure 4

Constraint from the dark matter relic abundance in the $\sin \omega \text{−}{M}_{\chi }$ plane, for benchmark values of the right-handed neutrino mass $M_N$ (columns) and the input parameter ${\lambda }_m^{-}$ (rows). The thick (red) band represents the thermal relic density of the cold WIMP pseudoscalar as constrained by the data from the Planck Collaboration [15]. The thickness of the line corresponds to the $1\sigma$ uncertainty quoted by the collaboration. A dependence on the sign of the ${\lambda }_m^{-}$ parameter is negligible. In addition, the experimental exclusion bounds from the electroweak precision tests (dot-dashed line) and the direct measurements of the LHC 125 GeV Higgs’ properties (solid line) at 95% C.L. are displayed, which set the upper limit on the mixing angle. The solid black region, inferred from the stability condition of the one-loop potential (18), determines the formal lower bound on the WIMP mass $M_{\chi }$ for each selected value of $M_N$. The enumerated thin contours represent the values of the $x_{\mathrm{fo}}$ parameter (34), illustrating the validity of the nonrelativistic treatment ($x_{\mathrm{fo}}\gg 3$) and hence the cold dark matter nature of the pseudoscalar $\chi$. The observed relic density is comfortably accommodated within the allowed region of the model’s parameter space.

Figure 5

Elastic scattering of a dark matter WIMP $\chi$ off a nucleon $N$. The process is mediated by the exchange of the $h$ and $\sigma$ scalars.

Figure 6

Theoretically calculated curves of the WIMP-nucleon elastic scattering spin-independent cross section (39) as a function of the WIMP mass, for four representative values of the mixing angle motivated by the experimental constraints. The panels correspond to benchmark values of the right-handed neutrino mass $M_N$ (columns) and the input parameter ${\lambda }_m^{-}$ (rows). In addition, the exclusion bound from the LUX direct detection experiment [16] is displayed (dashed line), setting the current upper limit on the scattering cross section. The solid black region, inferred from the stability condition of the one-loop potential (18), determines the formal lower bound on the WIMP mass $M_{\chi }$ for each selected value of $M_N$. Furthermore, the shaded region indicates the projected exclusion bound from the future Xenon1T experiment [17].

Figure 7

Constraining the $\sin \omega \text{−}{m}_{\sigma }$ plane for various choices of the parameters ${\lambda }_m^{-}$ and $M_N$. All colored regions are excluded. The experimental constraints are, at 95% C.L., derived from the electroweak precision tests (dot-dashed line), direct measurements of the LHC 125 GeV Higgs’ properties (solid line), and the LEP and LHC Higgs searches (dotted line). The formal perturbative unitarity bound (long-dashed line) is also depicted. In all panels, the parameter space is, nonetheless, most severely restricted by the LUX direct detection data (short-dashed line) at 90% C.L., permitting only small mixings and setting a lower limit on the $\sigma$ mass. The thick (red) band, within the allowed region, corresponds to satisfying the observational value of the WIMP relic abundance within the $1\sigma$ uncertainty quoted by the Planck Collaboration.

Figure 8

Constraining the $\sin \omega \text{−}{M}_{\chi }$ plane for various choices of the parameters ${\lambda }_m^{-}$ and $M_N$. The solid black region, inferred from the stability condition of the one-loop potential (18), determines the formal lower bound on the WIMP mass $M_{\chi }$ for each selected value of $M_N$. (See the caption of Fig. 7 for the details of the plots.)

Figure 9

Constraining the $m_{\sigma }\text{−}{M}_{\chi }$ plane for various choices of the parameters ${\lambda }_m^{-}$ and $M_N$. The solid black region, inferred from the stability condition of the one-loop potential (18), determines the formal lower bound on the WIMP mass $M_{\chi }$ for each selected value of $M_N$, while the vertically shaded region is excluded by the $|\sin \omega |\le 1$ condition. (See the caption of Fig. 7 for the details of the plots.)

Figure 10

Scatter plots displaying the viable region of the model’s parameter space for three values of the right-handed Majorana neutrino masses (columns) in the $\sin \omega \text{−}{m}_{\sigma }$, $\sin \omega \text{−}{M}_{\chi }$, and $m_{\sigma }\text{−}{M}_{\chi }$ planes (rows). The scattered points pass perturbative unitarity, one-loop triviality and vacuum stability conditions (assuming a cutoff scale higher than $10^5\mathrm{GeV}$) [9], WIMP relic density within the $1\sigma$ uncertainty quoted by the Planck Collaboration, and the LUX direct detection constraints at 90% C.L. The blue circles correspond to $|{\lambda }_m^{-}|\le 1$, whereas the red triangles represent $|{\lambda }_m^{-}|>1$. All colored regions are excluded. (See the caption of Fig. 7 for the details of the plots.)

Figure 11

Feynman rules for the relevant trilinear couplings.

Figure 12

Feynman rules for the relevant quartic couplings.