Could a light Higgs boson illuminate the dark sector?

The impact a new neutral light particle of spin 0, $1/2$, 1, or $3/2$ could have on the tiny width of a light Higgs boson is systematically analyzed. To this end, we include all the relevant effective interactions, whether renormalizable or not, and review the possible signatures in the Higgs decay modes with missing energy. This includes the fully invisible Higgs boson decay, as well as modes with standard model gauge bosons or fermions in the final state. In many cases, simply preventing these modes from being dominant suffices to set tight model-independent constraints on the masses and couplings of the new light states.

Figure 1

The behavior of $\Gamma (h^0\to \varphi \varphi )$ (left panel) and $\Gamma (h^0\to \psi \psi )$ (right panel), normalized to the total SM Higgs boson width (set at ${\Gamma }_h^{\mathrm{SM}}=4\mathrm{MeV}$), as a function of $m_{\varphi }=\delta m_{\varphi }$ and $m_{\psi }=\delta m_{\psi }$; see Eq. (6). For the fermionic case, we plot separately the scalar ($\sim c_S^2$) and pseudoscalar ($\sim c_P^2$) contributions, even though $c_{LR}$ or $c_{RL}$ is set to 1 separately (so $\delta m_{\psi }$ does not vanish).

Figure 2

Region in the ${\lambda }^{\prime }-m_{\varphi }$ and $\Lambda -m_{\psi }$ planes (setting either $c_S$ or $c_P$ to $-1$ in the rate, and assuming ${\lambda }^{\prime }>0$) allowed by the constraint $\Gamma (h^0\to \varphi \varphi /\psi \psi )<{\Gamma }_h^{\mathrm{SM}}/5$. The red (plain) lines correspond to ${\overline{m}}_{\varphi ,\psi }=0$, in which case the physical mass is purely electroweak, $m_{\varphi ,\psi }=\delta m_{\varphi ,\psi }$; see Eq. (6). The upper bounds in Eq. (8) correspond to the maximal $m_{\varphi ,\psi }=\delta m_{\varphi ,\psi }<M_h/2$ values such that these lines lie within the allowed regions. The lower bounds in Eq. (10) are the points at which these curves intersect the boundaries of the allowed regions, since the minimal $m_{\varphi }^2={\overline{m}}_{\varphi }^2+\delta m_{\varphi }^2$ and $m_{\psi }={\overline{m}}_{\psi }+\delta m_{\psi }$ values such that $\Gamma (h^0\to \varphi \varphi /\psi \psi )\approx {\Gamma }_h^{\mathrm{SM}}/5$ are those for which ${\overline{m}}_{\varphi ,\psi }\approx 0$ if no fine-tuning between the dark and electroweak mass terms is allowed. Because of the shapes of these curves, the bounds in Eqs. (8, 10) coincide.

Figure 3

Region in the ${\epsilon }_H-m_V$ and $\Lambda -m_{\Psi }$ planes (setting either $c_S$ or $c_P$ to 1 in the rate, and assuming ${\epsilon }_H>0$) allowed by the constraint $\Gamma (h^0\to VV/\Psi \Psi )<{\Gamma }_h^{\mathrm{SM}}/5$. The red (plain) lines correspond to ${\overline{m}}_{V,\Psi }=0$, in which case the physical mass is purely electroweak, $m_{V,\Psi }=\delta m_{V,\Psi }$; see Eq. (11). Except above about $M_h/2$, these lines lie entirely outside of the allowed region (compare with Fig. 2), corresponding to the bounds in Eq. (12). Note that the mass values to the left of these curves require a fine-tuning between the dark and electroweak contributions to the physical masses.

Figure 4

(a) Comparison between the SM processes induced by $h^0\to Z{Z}^{*}[\to \nu \overline{\nu }]$ and the contact interactions producing $h^0\to ZXX$, $X=\varphi$, $\psi$, $V$, $\Psi$ or $h^0\to Z\nu X$, $X=\psi$, $\Psi$. Generically, the NP processes are suppressed by $O(v^2/{\Lambda }^2)$ since the $Z$ propagator of the SM process gets substituted by a $1/{\Lambda }^2$ factor for the effective operators. (b) Same for the SM $h^0\to W^{(*)}{W}^{*}$ processes. (c) The fermionic channels induced by the operator of Eq. (5), and enhanced by $\mathcal{O}(M_h^2/{\Lambda }^2)$ compared to the dark effective interactions of Eq. (41) when MFV holds.

Figure 5

Region in the ${\epsilon }_2^H-m_V$ plane allowed by the constraint $\Gamma (h^0\to VZ)<{\Gamma }_h^{\mathrm{SM}}/5$ (green, lower right) and by the electroweak $\rho$ parameter (grey, upper left). The red (plain) line corresponds to $m_V^2=-\delta m_V^2$; see Eq. (19). Except above about $M_h-M_Z$, it lies entirely outside of the green region, corresponding to the bound (21), and enters the grey area at around $m_V\approx 2.4\mathrm{GeV}$; see Eq. (22). The $m_V$ values to the left of this curve require a fine-tuning between ${\overline{m}}_V^2$ and $\delta m_V^2$. The right panel shows the same using a logarithmic mass scale, in order to emphasize the strengthening of the bound as $m_V\to 0$. Note that the constraint on ${\epsilon }_2^H$ from the $\rho$ parameter depends on $m_V$, but this is hidden by the plot scales.

Figure 6

Region in the $\Lambda -m_{\Psi }$ plane allowed by requiring $\Gamma (h^0\to \Psi \nu )<{\Gamma }_h^{\mathrm{SM}}/5$ (blue, middle region), as induced by the operator of Eq. (43). We have set $d_0^{\ell }=1$ and summed over $\ell =e$, $\mu$, $\tau$ and $\Psi \nu \equiv \Psi \overline{\nu }+\overline{\Psi }\nu$. The allowed area for the $h^0\to \Psi \Psi$ mode (green, upper right region), as induced by the operator of Eq. (5d) and shown in Fig. 3, is plotted here using the logarithmic mass scale. The red (plain) line denotes $m_{\Psi }=v^2/(2\Lambda )$ and lies entirely out of the allowed regions, except for masses just below or anywhere above the kinematical endpoints.

Figure 7

Comparison between the dominant rates into dark particles and the total SM Higgs boson width, as a function of the Higgs boson mass $M_h$ and setting the Wilson coefficients of the relevant operators to 1. The dark rates are plotted assuming purely electroweak dark particle masses and thus represent natural upper bounds. Indeed, if one tries to increase a given dark rate by enhancing the coupling to the Higgs boson, then the dark particle gets more massive and the curve also shifts to the right. The only way to prevent this would be to allow for a strong cancellation between the dark and electroweak contributions to the dark particle mass, i.e., to fine-tune them. So, barring this, dark scalars or fermions can never hide a heavy Higgs boson, while dark vectors and spin $3/2$ states could, but only when the breaking of the dark gauge invariance is hard.