Dark matter searches in the mono-$Z$ channel at high energy $e^{+}{e}^{-}$ colliders

We explore the mono-$Z$ signature for dark matter searches at future high energy $e^{+}{e}^{-}$ colliders. In the context of effective field theory, we consider two kinds of contact operators describing dark matter interactions with electroweak gauge bosons and with electron/positron, respectively. For five benchmark models, we propose kinematic cuts to distinguish signals from backgrounds for both charged leptonic and hadronic decay modes of the $Z$ boson. We also present the experimental sensitivity to cutoff scales of effective operators and compare it with that of the Fermi-LAT indirect search and demonstrate the gains in significance for the several configurations of polarized beams.

Figure 1

DM production processes $e^{+}{e}^{-}\to \chi \overline{\chi }Z$ due to the DM couplings to $ZZ/Z\gamma$ (a) and $e^{\pm }$ (b) are illustrated.

Figure 2

Distributions of backgrounds and signals in the charged leptonic channel for $\sqrt{s}=500\mathrm{GeV}$ are demonstrated. The dot-dashed vertical lines denote the locations of our selection cuts. (a), (b), (c), and (d) show the normalized distributions of $p_{\mathrm{T}}$ before cut 2, differential cross sections with respect to $m_{\ell \ell }$ before cut 3, differential cross sections with respect to $m_{\mathrm{rec}}$ before cut 4 and normalized distributions of ${\theta }_{\ell \ell }$ before cut 5, respectively. Note that the distributions in (a) and (d) are normalized, while those in (b) and (c) are not.

Figure 3

Distributions of backgrounds and signals in the hadronic channel for $\sqrt{s}=500\mathrm{GeV}$ are demonstrated. (a), (b), (c), and (d) show the normalized distributions of $p_{\mathrm{T}}$ before cut 2, differential cross sections with respect to $m_{jj}$ before cut 3, normalized distributions of $m_{\mathrm{rec}}$ before cut 4, and normalized distributions of ${\theta }_{jj}$ before cut 5, respectively. The dot-dashed vertical lines denote the location of our selection cuts. Note that the distributions in (a), (c), and (d) are normalized, while those in (b) are not.

Figure 4

$3\sigma$ reaches in the $m_{\chi }$-$\mathrm{\Lambda }$ plane at $e^{+}{e}^{-}$ colliders are provided with $\sqrt{s}=250\mathrm{GeV}$, 500 GeV, and 1 TeV. (a), (b), (c), (d), and (e) correspond to the DM interaction operators ${\mathcal{O}}_{\text{F1}}$ ($\mathrm{\Lambda }={\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_2$), ${\mathcal{O}}_{\text{F2}}$ ($\mathrm{\Lambda }={\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_2$), ${\mathcal{O}}_{\mathrm{FH}}$, ${\mathcal{O}}_{\mathrm{FP}}$, and ${\mathcal{O}}_{\mathrm{FA}}$, respectively. The dot-dashed (solid) lines denote the charged leptonic (hadronic) channel. Here the integrated luminosities are assumed to be $1000{\mathrm{fb}}^{-1}$.

Figure 5

$3\sigma$ reaches in the $m_{\chi }$-$<{\sigma }_{\mathrm{ann}}v>$ plane at $e^{+}{e}^{-}$ colliders are shown with the integrated luminosity of $1000{\mathrm{fb}}^{-1}$. The dot-dashed (solid) lines denote the charged leptonic (hadronic) channel. The dotted lines indicate the Fermi-LAT 95% C.L. upper limits on DM annihilation cross sections into $ZZ$ (a) and into $e^{+}{e}^{-}$ (b) [52]. A factor of 2 is introduced to convert the Fermi-LAT limit from self-conjugated DM particles to non-self-conjugated DM particles.

Figure 6

$3\sigma$ reaches in the $m_{\chi }$-$\mathrm{\Lambda }$ plane for different ${\mathrm{\Lambda }}_1$-${\mathrm{\Lambda }}_2$ relations in the hadronic channel at $\sqrt{s}=500\mathrm{GeV}$ are shown with an integrated luminosity $1000{\mathrm{fb}}^{-1}$.

Figure 7

$3\sigma$ reaches in the $m_{\chi }$-$\mathrm{\Lambda }$ plane, with unpolarized beams and with optimal polarized beams in the charged leptonic (dot-dashed lines) and hadronic (solid lines) channels for $\sqrt{s}=500\mathrm{GeV}$, are shown with the integrated luminosity $1000{\mathrm{fb}}^{-1}$. (a), (b), (c), (d), and (e) correspond to the DM interaction operators ${\mathcal{O}}_{\text{F1}}$ ($\mathrm{\Lambda }={\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_2$), ${\mathcal{O}}_{\text{F2}}$ ($\mathrm{\Lambda }={\mathrm{\Lambda }}_1={\mathrm{\Lambda }}_2$), ${\mathcal{O}}_{\mathrm{FH}}$, ${\mathcal{O}}_{\mathrm{FP}}$, and ${\mathcal{O}}_{\mathrm{FA}}$, respectively.