Rare $Z$ boson decays to a hidden sector

We demonstrate that rare decays of the Standard Model $Z$ boson can be used to discover and characterize the nature of new hidden-sector particles. We propose new searches for these particles in soft, high-multiplicity leptonic final states at the Large Hadron Collider. The proposed searches are sensitive to low-mass particles produced in $Z$ decays, and we argue that these striking signatures can shed light on the hidden-sector couplings and mechanism for mass generation.

Figure 1

Feynman diagram illustrating dark Higgs ($h_{\mathrm{D}}$) and dark photon ($A^{\prime }$) production in rare $Z$ boson decays. The dark photons in $h_{\mathrm{D}}$ decay can be on or off shell.

Figure 2

Projected 95% c.l. sensitivity of an LHC search with $\mathcal{L}=40{\mathrm{fb}}^{-1}$ at $\sqrt{s}=13\mathrm{TeV}$ for $Z\to h_{\mathrm{D}}{A}^{\prime }\to 4\ell +X$ where $4\ell$ are required to reconstruct $m_{h_{\mathrm{D}}}$. The sensitivity is expressed in terms of the accessible branching fraction of $Z\to h_{\mathrm{D}}{A}^{\prime }$ decays.

Figure 3

Projected 95% c.l. sensitivity of an LHC search with $\mathcal{L}=40{\mathrm{fb}}^{-1}$ at $\sqrt{s}=13\mathrm{TeV}$ for $Z\to h_{\mathrm{D}}{A}^{\prime }\to 4\ell +X$ where $4\ell$ are required to reconstruct $m_{h_{\mathrm{D}}}$. Each curve is labeled by the value of $m_{h_{\mathrm{D}}}$ in GeV. The dotted line gives the sensitivity of the Drell-Yan search from Ref. [32]. We also show existing constraints from electroweak precision observables [32], BABAR [40], and LHCb [47]. The three sets of lines from bottom (dark) to top (light) correspond to ${\alpha }_{\mathrm{D}}=1$, 0.1, and 0.01.

Figure 4

Sensitivity projections for the $Z\to h_{\mathrm{D}}{A}^{\prime }\to 4\ell +X$ search for integrated luminosity of $300{\mathrm{fb}}^{-1}$ (upper dark lines) and $3000{\mathrm{fb}}^{-1}$ (lower faint lines) at $\sqrt{s}=13\mathrm{TeV}$ and ${\alpha }_{\mathrm{D}}=0.1$. The dotted green line shows the projected LHCb sensitivity with $15{\mathrm{fb}}^{-1}$ from Ref. [29], while the dashed lines show the projections for the proposed Drell-Yan search from Ref. [32]. Notation and existing bounds are the same as in Fig. 3.

Figure 5

Projected sensitivity to the scenario where $m_{h_{\mathrm{D}}}<m_{A^{\prime }}$, which gives rise to displaced decays of the dark Higgs. Projections are shown for $\sqrt{s}=13\mathrm{TeV}$ and $\mathcal{L}=40{\mathrm{fb}}^{-1}$. In the top panel, we compute the sensitivity for 10 signal events after cuts to $ϵ$ in the $(m_{A^{\prime }},ϵ)$ plane for different values of $m_{h_{\mathrm{D}}}$ (labeled in GeV); for each $m_{A^{\prime }}$ point we have selected the $h_{\mathrm{D}}$ lifetime that gives the optimal reach in $ϵ$. In the bottom panel we compute the expected sensitivity in the $(m_{A^{\prime }},c{\tau }_{h_{\mathrm{D}}})$ plane for $m_{h_{\mathrm{D}}}=15\mathrm{GeV}$. The projected reach of the displaced search exceeds the existing constraints from electroweak precision observables (LHCb prompt search, showing the envelope of the exclusion contour) within the solid (dotted) black contours.