Hunting for scalar lepton partners at future electron colliders

New physics close to the electroweak scale is well motivated by a number of theoretical arguments. However, colliders, most notably the Large Hadron Collider, have failed to deliver evidence for physics beyond the Standard Model. One possibility for how new electroweak-scale particles could have evaded detection so far is if they carry only electroweak charge, i.e., are color neutral. Future $e^{+}{e}^{-}$ colliders are prime tools to study such new physics. Here, we investigate the sensitivity of $e^{+}{e}^{-}$ colliders to scalar partners of the charged leptons, known as sleptons in supersymmetric extensions of the Standard Model. In order to allow such scalar lepton partners to decay, we consider models with an additional neutral fermion, which in supersymmetric models corresponds to a neutralino. We demonstrate that future $e^{+}{e}^{-}$ colliders would be able to probe most of the kinematically accessible parameter space, i.e., where the mass of the scalar lepton partner is less than half of the collider’s center-of-mass energy, with only a few days of data. Besides constraining more general models, this would allow to probe some well motivated dark matter scenarios in the Minimal Supersymmetric Standard Model, in particular the incredible bulk and stau coannihilation scenarios.

Figure 1

Illustration of slepton pair production via $Z$-boson and photon exchange at a lepton collider and subsequent decays of the sleptons $\tilde{\ell }$ into a charged SM lepton $\ell$ of the same flavor as the slepton and a neutralino $\chi$. Note that for selectrons ($\tilde{\ell }=\tilde{e}$) there are additional ($e^{+}{e}^{-}\to {\tilde{e}}^{+}{\tilde{e}}^{-}$) production diagrams where a neutralino $\chi$ is exchanged in the $t$ channel. We only consider the production of smuons and staus in this work. As discussed in the text, although we use SUSY-inspired language to refer to the states $\tilde{\ell }$ and $\chi$, our analysis is not confined to SUSY models.

Figure 2

Distribution of leading lepton momenta $p({\ell }_1)$ in the (${\mu }^{+}{\mu }^{-}+\cancel{E}$) final state after kinematic cuts described in the text and denoted in the figures. The left panel is for a center-of-mass energy of $\sqrt{s}=250\mathrm{GeV}$ and the right panel for $\sqrt{s}=500\mathrm{GeV}$. Both panels are for unpolarized beams $P=(0.0,0.0)$. In each panel, the stacked histogram shows the different background components as indicated in the legend. Note that the ($e^{+}{e}^{-}\to 2\mu 2\nu$) background category (green) excludes events which stem from on-shell $W^{+}{W}^{-}$ pair production, such events are shown separately (purple). The ($\gamma \gamma \to 2\mu (2n)\nu$) background category includes both ($\gamma \gamma \to 2\mu 2\nu$) and ($\gamma \gamma \to 2\mu 4\nu$) events. The solid lines show ($e^{+}{e}^{-}\to \gamma /Z\to {\tilde{\mu }}^{+}{\tilde{\mu }}^{-}\to {\mu }^{+}{\mu }^{-}\chi \chi$) signal distributions for the various benchmark values of the smuon mass $m_{\tilde{\mu }}$ and neutralino mass $m_{\chi }$ indicated in the legend.

Figure 3

Scaling of the slepton production cross section with the left-right mixing angle $\sin \alpha$ for different beam polarizations as indicated in the legend. $\sin \alpha =0$ corresponds to left-handed sleptons, ${\tilde{\ell }}_1={\tilde{\ell }}_L$, and $\sin \alpha =1$ to right-handed sleptons, ${\tilde{\ell }}_1={\tilde{\ell }}_R$.

Figure 4

Same as the right panel of Fig. 2 but for mostly left-handed $P=(-0.8,-0.3)$ and mostly right-handed $P=(0.8,0.3)$ polarization configurations of the electron/positron beams. We remind the reader that we express polarizations via $P=[P_R(e^{-}),P_R(e^{+})]$, see Eq. (5) for the definition of $P_R$. The colors for the respective background components and lines of the benchmark signal distributions are the same as in the right panel of Fig. 2. Note that the relative normalization of the signal distributions compared to that of the background is largely insensitive to the left-right mixing of the sleptons when the electron/positron beams are unpolarized. The relative normalization of the signal to background varies the most for the production of right-handed sleptons in polarized beam configurations, as shown here and discussed in the text.

Figure 5

Distribution of leading lepton momenta $p({\ell }_1)$ in the ($e^{\pm }{\mu }^{\mp }+\cancel{E}$) final state after kinematic cuts described in the text and denoted in the figures. The left panel is for a center-of-mass energy of $\sqrt{s}=250\mathrm{GeV}$ and the right panel for $\sqrt{s}=500\mathrm{GeV}$, and both panels are for unpolarized beams $P=(0.0,0.0)$. In each panel, the stacked histogram shows the different background components as indicated in the legend. Note that the ($e^{+}{e}^{-}\to e\mu 2\nu$) background category (green) excludes events which stem from on-shell $W^{+}{W}^{-}$ pair production, such events are shown separately (purple). The ($\gamma \gamma \to e\mu (2n)\nu$) background category includes both ($\gamma \gamma \to e\mu 2\nu$) and ($\gamma \gamma \to e\mu 4\nu$) events. The solid lines show ($e^{+}{e}^{-}\to \gamma /Z\to {\tilde{\tau }}^{+}{\tilde{\tau }}^{-}\to e^{\pm }{\mu }^{\mp }\chi \chi {\nu }_e{\nu }_{\mu }{\nu }_{\tau }{\overline{\nu }}_{\tau }$) signal distributions for the various benchmark values of the stau mass $m_{\tilde{\tau }}$ and neutralino mass $m_{\chi }$ indicated in the legend.

Figure 6

The left [right] panel shows our projections for the smallest smuon [stau] signal cross section ${\sigma }^{\min }$ which could be probed at an $\sqrt{s}=500\mathrm{GeV}$ $e^{+}{e}^{-}$ collider with $L=1{\mathrm{ab}}^{-1}$ of data and mostly right-handed beams $P=(0.8,0.3)$ in the (${\mu }^{+}{\mu }^{-}+\cancel{E}$) [($e^{\pm }{\mu }^{\mp }+\cancel{E}$)] final state. For reference, the solid black (dashed red) line indicates where ${\sigma }^{\min }$ coincides with the cross section in the model presented in Sec. 2 for left-handed (right-handed) smuons/staus. The region to the lower left of the respective contours, i.e., almost all of the parameter space where $m_{\tilde{\ell }}<\sqrt{s}/2$, is within the projected sensitivity. Note that in both panels, the solid black and dashed red lines overlap for $m_{\chi }\to m_{\tilde{\ell }}$. For the smuon case (left panel), the dashed red line for right-handed smuons coincides with $m_{\tilde{\mu }}\to 250\mathrm{GeV}$ for $m_{\chi }\lesssim 240\mathrm{GeV}$ and is not visible on the plot. We would like to remind the reader that the signal cross section in our model matches that in SUSY models if the respective slepton and neutralino are the next-to-lightest and lightest supersymmetric states, respectively. Note that the range of the color scale indicating the value of ${\sigma }^{\min }$ differs between the panels. The “island” in the right panel at $m_{\tilde{\tau }}\approx 115\mathrm{GeV}$, $m_{\chi }\approx 65\mathrm{GeV}$ is an artifact of the statistical fluctuations in the Monte Carlo simulations of the signal (and to a lesser extent, the backgrounds).

Figure 7

Smallest integrated luminosity $L^{\min }$ which would allow to probe the pair production of right-handed smuons at an $e^{+}{e}^{-}$ collider with $\sqrt{s}=500\mathrm{GeV}$. The left panel is for mostly left-handed polarization of the electron and positron beams, $P=(-0.8,-0.3)$, while the right panel is for mostly right-handed beam polarization $P=(0.8,0.3)$. Here, we assumed that the smuon can only decay into a muon and a neutralino, $\mathrm{BR}({\tilde{\mu }}^{\pm }\to {\mu }^{\pm }\chi )=1$, cf. the discussion in Sec. 2. Note that the value of the smuon pair production cross section is fixed by the gauge couplings of the smuons, hence, the production cross section in our model discussed in Sec. 2 is the same as the cross section in SUSY models if the smuon and the neutralino are the next-to-lightest and lightest supersymmetric particles, respectively. The dashed (solid) black line indicates $L^{\min }=10{\mathrm{fb}}^{-1}$ ($L^{\min }=1{\mathrm{ab}}^{-1})$.

Figure 8

Same as Fig. 7 but for right-handed staus in the ($e^{\pm }{\mu }^{\mp }+\cancel{E}$) final state. The islands at $m_{\tilde{\tau }}\approx 115\mathrm{GeV}$, $m_{\chi }\approx 65\mathrm{GeV}$ are an artifact of the statistical fluctuations in the Monte Carlo simulations of the signal (and to a lesser extent, the backgrounds).

Figure 9

Projected sensitivity to stau pair production in the (${\mu }^{+}{\mu }^{-}+\cancel{E}$) final state at an $\sqrt{s}=500\mathrm{GeV}$ $e^{+}{e}^{-}$ collider assuming longitudinal polarization of the electron/positron beams $P=(0.8,0.3)$. (Left panel) Smallest cross section ${\sigma }^{\min }$ which could be probed with $L=1{\mathrm{ab}}^{-1}$ of data. (Right panel) Smallest integrated luminosity $L^{\min }$ required to probe right-handed staus if the signal cross section is given by those in our model described in Sec. 2. The islands at $m_{\tilde{\tau }}\approx 150\mathrm{GeV}$, $m_{\chi }\approx 120\mathrm{GeV}$ are an artifact of the statistical fluctuations in the Monte Carlo simulations of the signal (and to a lesser extent, the backgrounds).

Figure 10

Same as Fig. 6 but for $\sqrt{s}=250\mathrm{GeV}$ and $L=0.5{\mathrm{ab}}^{-1}$.

Figure 11

Distribution of the missing energy $\cancel{E}$ (left panel) and its polar angle $\cos \theta (\cancel{E})$ (right panel) in the $({\mu }^{+}{\mu }^{-}+\cancel{E})$ final state before any kinematic cuts. The stacked histogram shows the different background components as listed in the legend. The solid lines show $(e^{+}{e}^{-}\to \gamma /Z\to {\tilde{\mu }}^{+}{\tilde{\mu }}^{-}\to {\mu }^{+}{\mu }^{-}\chi \chi )$ signal distributions for various benchmark values of the smuon mass $m_{\tilde{\mu }}$ and neutralino mass $m_{\chi }$ indicated in the legend.

Figure 12

Distributions of the polar angle of the leading charged lepton $\cos \theta ({\ell }_1)$ (left panel) and the invariant mass of the charged leptons $m_{\ell \ell }$ (right panel) in the $({\mu }^{+}{\mu }^{-}+\cancel{E})$ final state after the first set of kinematic cuts described in the text. We use the same colors for the respective background components and signal benchmarks as in Fig. 11.

Figure 13

Distribution of leading lepton momentum $p({\ell }_1)$ for stau searches in the (${\mu }^{+}{\mu }^{-}+\cancel{E}$) final state after kinematic cuts.

Figure 14

Distribution of the missing energy $\cancel{E}$ (left panel) and the opening angle between the charged leptons in the plane transverse to the beam, $\mathrm{\Delta }\varphi ({\ell }^{+},{\ell }^{-})$ (right panel) in the $(e^{\pm }{\mu }^{\mp }+\cancel{E})$ final state before any kinematic cuts. The stacked histogram shows the different background components as listed in the legend. The solid lines show $(e^{+}{e}^{-}\to \gamma /Z\to {\tilde{\tau }}^{+}{\tilde{\tau }}^{-}\to e^{\pm }{\mu }^{\mp }\chi \chi )$ signal distributions for various benchmark values of the stau mass $m_{\tilde{\tau }}$ and neutralino mass $m_{\chi }$ indicated in the legend.