Exotic leptons at future linear colliders

Doubly charged excited leptons give rise to interesting signatures for physics beyond the standard model at the present Large Hadron Collider. These exotic states are introduced in extended isospin multiplets which couple to the ordinary leptons and quarks either with gauge or contact effective interactions or a combination of both. In this paper we study the production and the corresponding signatures of doubly charged leptons at the forthcoming linear colliders, and we focus on the electron-electron beam setting. In the framework of gauge interactions, the interference between the $t$ and $u$ channels is evaluated that has been neglected so far. A pure leptonic final state is considered ($e^{-}{e}^{-}\to e^{-}{e}^{-}{\nu }_e{\overline{\nu }}_e$) that experimentally translates into a like-sign dilepton and missing transverse energy signature. We focus on the standard model irreducible background, and we study the invariant like-sign dilepton mass distribution for both the signal and background processes. Finally, we provide the 3 and 5-sigma statistical significance exclusion curves in the model parameter space. We find that for a doubly charged lepton mass $m^{*}\approx 2\mathrm{TeV}$ the expected lower bound on the compositeness scale at Compact Linear Collider, $\mathrm{\Lambda }>25\mathrm{TeV}$, is much stronger than the current lower bound from the LHC ($\mathrm{\Lambda }>5\mathrm{TeV}$) and remains highly competitive with the bounds expected from run II of the LHC.

Figure 1

Diagrams for the process $e^{-}{e}^{-}\to E^{--}{\nu }_e$ induced by the contact interaction Lagrangian ($a$ and $b$) and gauge interaction Lagrangian ($c$ and $d$). Solid lines stand for electrons and electron neutrinos, wiggled lines for the $W$ boson, and solid double lines for the doubly charged lepton. We label with different momenta, $p_1$ and $p_2$, the incoming electrons.

Figure 2

The plot shows the total cross sections for the process $e^{-}{e}^{-}\to E^{--}{\nu }_e$. In the left panel, the total cross section against the center of mass energy is displayed for the different isospin multiplets. The solid blue line stands for $E^{--}\in I_W=1$ and the dashed red one for $E^{--}\in I_W=3/2$ with the interference contribution taken into account. At variance, the orange dot-dashed curve is the result when the interference is not considered. The right panel shows the total cross section against mass. Also here the curves for different multiplets are displayed. The compositeness parameters are set to ($m^{*}=0.5\mathrm{TeV}$, $\mathrm{\Lambda }=5\mathrm{TeV}$). The green dots stand for the CalcHEP output.

Figure 3

The plot shows the total production cross section as a function of the excited lepton mass for different values of the compositeness scale $\mathrm{\Lambda }$. The left panel refers to 1 TeV for the energy in the center of mass (highest expected energy for the ILC), whereas in the right panel we set the collision energy at 3 TeV (highest expected energy for CLIC). Contact interactions (solid lines) dominate over the gauge interactions (dashed line) for the production of the doubly charged lepton. We use $E^{--}\in I_W=1$ for the gauge interactions.

Figure 4

The kinematic variables for the signal and the SM background are shown. With $p_T^{\max (\min )}$ we label the highest (lowest) energetic electron transverse momentum distribution, and with ${\eta }^{\max (\min )}$ we label the highest (lowest) energetic electron pseudorapidity. The model parameters are $m^{*}=0.5,0.7\mathrm{TeV}$, $\mathrm{\Lambda }=5\mathrm{TeV}$. No cuts are implemented to obtain these distributions.

Figure 5

The missing transverse momentum of the undetectable neutrino and antineutrino is shown for the signal and the SM background processes. The model parameters are $m^{*}=0.5,0.7,0.8\mathrm{TeV},\mathrm{\Lambda }=5\mathrm{TeV}$.

Figure 6

The LSD invariant mass distributions for both signal and background are displayed. In the top panels, we show the case of the ILC with $\sqrt{s}=1\mathrm{TeV}$ with the base kinematic cuts (left) and with the improved kinematic cuts (right). Signal distributions are shown for $\mathrm{\Lambda }=10\mathrm{TeV}$ and different values of the doubly charged lepton mass $m^{*}=0.5,0.65,0.8\mathrm{TeV}$. The lower panels show the case of the CLIC at $\sqrt{s}=3\mathrm{TeV}$ again with the base kinematic cuts (left) and with the improved kinematic cuts (right). Signal distributions are shown for $\mathrm{\Lambda }=15\mathrm{TeV}$ and different values of the doubly charged lepton mass $m^{*}=1.5,2.0,2.5\mathrm{TeV}$.

Figure 7

Contour plots of the statistical significance ($S$) at 3 and 5-sigma values, in the parameter space ($\mathrm{\Lambda },m^{*}$) within the statistical error on $S$ (dashed lines). The regions below the curves are excluded respectively at 3-sigma level (black line) or at the 5-sigma level (red line). We show both cases of $\sqrt{s}=1\mathrm{TeV}$, upper panel, and $\sqrt{s}=3\mathrm{TeV}$, lower panel, for two different choices of the integrated luminosity $L=125{\mathrm{fb}}^{-1}$ and $L=250{\mathrm{fb}}^{-1}$.

Figure 8

Comparison of the exclusion curves at the 3-sigma level in the parameter space ($\mathrm{\Lambda },m^{*}$) from the ILC (left) and CLIC (right), for $L=250{\mathrm{fb}}^{-1}$ solid (black) line and $L=125{\mathrm{fb}}^{-1}$ dashed (red) line, with the bounds from run I and run II of the LHC. In particular we show the ATLAS bound for $\sqrt{s}=7$ TeV and $L=13{\mathrm{fb}}^{-1}$ in clear (yellow) shaded area [27], the CMS bound for $\sqrt{s}=8$ TeV and $L=19.7{\mathrm{fb}}^{-1}$ in light (blue) shaded area [44], and the prospected bounds from run II of the LHC ($\sqrt{s}=14\mathrm{TeV}$, $300{\mathrm{fb}}^{-1}$) [22], dot-dashed (orange) line. The dark (blue) shaded area is the region of the parameter space not allowed by requiring the internal consistency of the model, or that $m^{*}\le \mathrm{\Lambda }$. Thus, the points in the dark (blue) shaded region $\mathrm{\Lambda }<m^{*}$ describe models which are not viable.