Testing triplet fermions at the electron-positron and electron-proton colliders using fat jet signatures

The addition of $SU(2{)}_L$ triplet fermions of zero hypercharge with the Standard Model (SM) helps to explain the origin of the neutrino mass by the so-called seesaw mechanism. Such a scenario is commonly known as the type-III seesaw model. After the electroweak symmetry breaking, the mixings between the light and heavy mass eigenstates of the neutral leptons are developed and play important roles in the study of the charged and neutral multiplets of the triplet fermions at the colliders. In this article, we study such interactions to produce these multiplets of the triplet fermion at the electron-positron and electron-proton colliders at different center-of-mass energies. We focus on the heavy triplets, for example, having mass in the TeV scale so that their decay products including the SM, the gauge bosons, or the Higgs boson can be sufficiently boosted, leading to a fat jet. Hence, we probe the mixing between light-heavy mass eigenstates of the neutrinos and compare the results with the bounds obtained by the electroweak precision study.

Figure 1

Branching ratio (Br) of ${\mathrm{\Sigma }}^0$ (left) and ${\mathrm{\Sigma }}^{\pm }$ (right) into the SM particles as a function of $M_{\mathrm{\Sigma }}$ for $V_e=0.019$, $V_{\mu }=0$, and $V_{\tau }=0$.

Figure 2

Branching ratio (Br) of ${\mathrm{\Sigma }}^0$ (left) and ${\mathrm{\Sigma }}^{\pm }$ (right) into the SM particles as a function of $M_{\mathrm{\Sigma }}$ for $V_e=V_{\mu }=0.0001$ and $V_{\tau }=0$.

Figure 3

The production modes of the ${\mathrm{\Sigma }}^0$ and ${\mathrm{\Sigma }}^{\pm }$ at the $e^{-}{e}^{+}$ collider.

Figure 4

Cross section for the triplet fermion production at the $e^{-}{e}^{+}$ collider. The production cross sections for the varying center-of-mass energy $(\sqrt{s})$ are shown in the upper panel, fixing the mass of the triplet at $M_{\mathrm{\Sigma }}=500\mathrm{GeV}$ (upper, left) and at $M_{\mathrm{\Sigma }}=1\mathrm{TeV}$ (upper, right). The production cross sections of the triplet fermion as a function of mass are shown in the lower panel for two different values of $\sqrt{s}$ at 1 TeV (lower, left) and 3 TeV (lower, right). To calculate the associate production of the ${\mathrm{\Sigma }}^{\pm },{\mathrm{\Sigma }}^0$ with the SM leptons, we consider $V_e=0.019$ [26, 73]; however, the pair production of ${\mathrm{\Sigma }}^{+}{\mathrm{\Sigma }}^{-}$ is direct.

Figure 5

The production modes of the ${\mathrm{\Sigma }}^0$ and ${\mathrm{\Sigma }}^{-}$ at the $e^{-}p$ collider, which is suppressed by $|V_{\ell }{|}^2$.

Figure 6

Cross section for the processes, ${\mathrm{\Sigma }}^{0}j$ and ${\mathrm{\Sigma }}^{-}j$, in the $e^{-}p$ collider as a function of $M_{\mathrm{\Sigma }}$ with fixed $\sqrt{s}$ at 1.3 (top, left), 1.8 (top, right), and 3.46 TeV (bottom). We have considered $V_e=0.019$ [26, 73] to calculate the production cross sections.

Figure 7

Fat jet ($J$) production from the ${\mathrm{\Sigma }}^{+}$ and ${\mathrm{\Sigma }}^0$ at the $e^{+}{e}^{-}$ collider from the $s$-channel (left) and $t$-channel (right) processes.

Figure 8

Normalized missing momentum distributions of the signal and background events for $M_{\mathrm{\Sigma }}=900\mathrm{GeV}$ at the $\sqrt{s}=1\mathrm{TeV}$ (left panel) and $M_{\mathrm{\Sigma }}=1$, 2 TeV at the $\sqrt{s}=3\mathrm{TeV}$ (right panel) at $e^{-}{e}^{+}$ colliders.

Figure 9

Same as in Fig. 8, but now for $\cos {\theta }_e$ distribution.

Figure 10

Same as in Fig. 8, but now for fat jet $p_T$ distribution.

Figure 11

Same as in Fig. 8, but now for leading lepton $p_T$ distribution.

Figure 12

Same as in Fig. 8, but now for invariant mass distribution of fat jet.

Figure 13

Fat $b$-jet $(J_b)$ production from the ${\mathrm{\Sigma }}^{+}$ and ${\mathrm{\Sigma }}^0$ at the $e^{-}{e}^{+}$ collider from the $s$-channel (left) and $t$-channel (right) processes.

Figure 14

Normalized distributions of missing momentum, fat-$b$ $p_T$ and fat-$b$ invariant mass of the signal and background events for $M_{\mathrm{\Sigma }}=1$, 2 TeV at the $\sqrt{s}=3\mathrm{TeV}$ at $e^{-}{e}^{+}$ colliders.

Figure 15

Fat jet ($J$) production from the ${\mathrm{\Sigma }}^{+}$ at the $e^{-}{e}^{+}$ collider from the $s$-channel (left) and $t$-channel (right) processes.

Figure 16

Normalized $p_T^{e_1}$ (upper left), $p_T^{e_2}$ (upper right), $m_J$ (lower left), and $p_T^J$ (lower right) distributions before applying any selection cuts for the $e^{-}{e}^{+}\to e^{-}{\mathrm{\Sigma }}^{+}\to e^{-}{e}^{+}Z\to e^{-}{e}^{+}J$ process. The red and black distributions correspond to signal for $M_{\mathrm{\Sigma }}=1\mathrm{TeV}$ and $M_{\mathrm{\Sigma }}=2.2\mathrm{TeV}$, while the green distribution is for the dominant $Z/\gamma jj$ background.

Figure 17

Fat jet ($J$) production from the ${\mathrm{\Sigma }}^{\pm }$ at the $e^{+}{e}^{-}$ collider from the $s$-channel process.

Figure 18

Signal significance for the final states $2J+p_T^{\mathrm{miss}}$ (left panel) and $2J_b+e^{-}{e}^{+}$ (right panel) from the pair production of ${\mathrm{\Sigma }}^{\pm }$ with luminosity 1, 3, and $5{\mathrm{ab}}^{-1}$, respectively, at the $\sqrt{s}=3\mathrm{TeV}$ $e^{-}{e}^{+}$ collider.

Figure 19

Fat jet ($J$) production from the ${\mathrm{\Sigma }}^{-}$ and ${\mathrm{\Sigma }}^0$ at the $e^{-}p$ collider from the $t$-channel process.

Figure 20

Normalized fat jet $p_T$, leading lepton $p_T$, fat jet invariant mass, and lepton distributions for the final state $e^{\pm }+J+j_1$. The black and red lines correspond to signal for $M_{\mathrm{\Sigma }}=1$ and 1.5 TeV, respectively.

Figure 21

Sensitivity reach of the mixing angle with the luminosities $\mathcal{L}=1$, 3, and $5{\mathrm{ab}}^{-1}$ at $3\sigma$ and $5\sigma$ significance from the final state $e^{\pm }+J+p_T^{\mathrm{miss}}$ at $\sqrt{s}=1\mathrm{TeV}$ (top, left) and $\sqrt{s}=3\mathrm{TeV}$ (top, right), respectively, at the $e^{-}{e}^{+}$ collider. The same for the final states $J_b+p_T^{\mathrm{miss}}$ (bottom, left) and $e^{+}+e^{-}+J$ (bottom, right), respectively, at the $\sqrt{s}=3\mathrm{TeV}$ $e^{-}{e}^{+}$ collider with same luminosities like the top panel. The limit from the EWPD for the electron flavor has been represented by the black dot-dashed line from Ref. [73].

Figure 22

Sensitivity reach of the mixing angle with the luminosities $\mathcal{L}=1$, 3, and $5{\mathrm{ab}}^{-1}$ at $3\sigma$ and $5\sigma$ significance, from the final state $e^{\pm }+J+j_1$ at $\sqrt{s}=3.46\mathrm{TeV}$ of the $e^{-}p$ collider.