Dark-photon searches via $ZH$ production at $e^{+}{e}^{-}$ colliders

We study the $ZH$ associated production followed by the Higgs $H\to \gamma \overline{\gamma }$ decay into a photon plus an invisible and massless dark photon, at future high-energy $e^{+}{e}^{-}$ facilities. Large $H\to \gamma \overline{\gamma }$ decay rates (with branching ratios up to a few percent) are allowed, thanks to possible nondecoupling properties of the Higgs boson under specific conditions, and unsuppressed dark-photon couplings in the dark sector. Such large decay rates can be obtained in the framework of recent flavor models that aim to naturally explain the observed spread in the fermion mass spectrum. We analyze the experimental prospects for observing the $e^{+}{e}^{-}\to ZH$ process followed by the semi-invisible Higgs decay into a photon plus a massless invisible system. Search strategies for both the leptonic and the hadronic final states (arising from $Z\to {\mu }^{+}{\mu }^{-}$ and $Z\to q\overline{q}$, respectively) are outlined. We find that a $5\sigma$ sensitivity to a branching fraction $B{R}_{\gamma \overline{\gamma }}\sim 3\times {10}^{-4}$ can be achieved by combining the two channels with an integrated luminosity of $10{\mathrm{ab}}^{-1}$ at a c.m. energy of 240 GeV. This is considerably better than the corresponding sensitivity in alternative channels previously studied at lepton colliders. The analysis is model independent, and its results can be straightforwardly applied to the search for any Higgs two-body decay into a photon plus an undetected light particle.

Figure 1

Feynman diagrams for $e^{+}{e}^{-}\to ZH\to ({\mu }^{+}{\mu }^{-},q\overline{q})(\gamma \overline{\gamma })$.

Figure 2

Effective coupling approximation for the vertices $H\gamma \overline{\gamma }$ and $HZ\overline{\gamma }$, where $S_i$ are the messenger fields, and in, $C_{V\overline{\gamma }}$, $V=\gamma$, $Z$.

Figure 3

Branching ratio for $H\to \gamma \overline{\gamma }$ in percent as a function of the effective coupling $C_{\gamma \overline{\gamma }}$, for all other effective couplings at their SM values. The $C_{\gamma \overline{\gamma }}$ range in the plot has been chosen so as to cover the typical BR ranges predicted by the GRFM (cf. Fig. 1 in [23]).

Figure 4

The photon energy and transverse momentum distributions for the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma \overline{\gamma }$ signal and $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\nu \overline{\nu }\gamma$ background, after applying the set of basic cuts, at $\sqrt{s}=240\mathrm{GeV}$. Results for the individual resonant $WW\gamma$ and $ZZ\gamma$ background components are also shown.

Figure 5

The ${\mu }^{+}{\mu }^{-}$ and $\gamma \overline{\gamma }$ invariant-mass distributions for the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma \overline{\gamma }$ signal and $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\nu \overline{\nu }\gamma$ background, for $\sqrt{s}=240\mathrm{GeV}$. The $M_{{\mu }^{+}{\mu }^{-}}$ distributions are obtained after imposing just the set of basic cuts described in the text, whereas the $M_{\gamma \overline{\gamma }}$ distribution is affected by an additional cut $86\mathrm{GeV}<M_{{\mu }^{+}{\mu }^{-}}<96\mathrm{GeV}$. Results for the individual resonant $WW\gamma$ and $ZZ\gamma$ background components are also shown.

Figure 6

The missing-mass and missing-energy distributions for the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma \overline{\gamma }$ signal and $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\nu \overline{\nu }\gamma$ background, for $\sqrt{s}=240\mathrm{GeV}$, after imposing the invariant-mass cuts around the $M_Z$ and $m_H$ on the ${\mu }^{+}{\mu }^{-}$ and $\gamma \overline{\gamma }$ systems, respectively.

Figure 7

Signal significance for the $e^{+}{e}^{-}\to ZH\to {\mu }^{+}{\mu }^{-}\gamma \overline{\gamma }$ channel versus $B{R}_{\gamma \overline{\gamma }}$ for $10{\mathrm{ab}}^{-1}$ at 240 GeV. The left vertical grey line corresponds to a 95% C.L. exclusion, while the right line points to the $5\sigma$ discovery reach.

Figure 8

The $jj$ and $\gamma \overline{\gamma }$ invariant-mass distributions for the $e^{+}{e}^{-}\to ZH\to q\overline{q}\gamma \overline{\gamma }$ signal and backgrounds, for $\sqrt{s}=240\mathrm{GeV}$. The $M_{jj}$ distribution is obtained after imposing the set of basic cuts described in the text, whereas the $M_{\gamma \overline{\gamma }}$ distribution is obtained with an additional $50\mathrm{GeV}<M_{jj}<90\mathrm{GeV}$ cut.

Figure 9

The missing mass and missing energy distributions for the $e^{+}{e}^{-}\to ZH\to q\overline{q}\gamma \overline{\gamma }$ signal and corresponding backgrounds, for $\sqrt{s}=240\mathrm{GeV}$. The $M_{\text{miss}}$ distribution is obtained after imposing invariant-mass cuts on the $jj$ and $\gamma \overline{\gamma }$ systems around $M_Z$ and $m_H$, respectively, as described in the text. In the $\cancel{E}$ distributions, an additional $M_{\text{miss}}<20\mathrm{GeV}$ cut is imposed.

Figure 10

Signal significance for the $e^{+}{e}^{-}\to ZH\to q\overline{q}\gamma \overline{\gamma }$ channel versus $B{R}_{\gamma \overline{\gamma }}$ for $10{\mathrm{ab}}^{-1}$ at 240 GeV. The left vertical grey line corresponds to a 95% C.L. exclusion, while the right line points to the $5\sigma$ discovery reach.

Figure 11

Signal significance in the $e^{+}{e}^{-}\to ZH\to q\overline{q}\gamma \overline{\gamma }$ channel (green dotted line), $e^{+}{e}^{-}\to ZH\to {\mu }^{+}{\mu }^{-}\gamma \overline{\gamma }$ channel (blue dashed line) and in the combined search (black solid line) versus $B{R}_{\gamma \overline{\gamma }}$ for $10{\mathrm{ab}}^{-1}$ at $\sqrt{s}=240\mathrm{GeV}$. The lower and upper horizontal lines pinpoint, respectively, the 95% C.L. exclusion bound, and the $5\sigma$-significance discovery reach.