#### Abstract

The production potential of the excited neutrinos at the FCC-based electron-hadron colliders, namely, the with TeV, the with TeV, and the with TeV, has been analyzed. The branching ratios of the excited neutrinos have been calculated for the different decay channels and shown that the dominant channel is . We have calculated the production cross sections with the process of and the decay widths of the excited neutrinos with the process of . The signals and corresponding backgrounds are studied in detail to obtain accessible mass limits. It is shown that the discovery limits obtained on the mass of the excited neutrino are GeV for , GeV for ( GeV for ), and GeV for ( GeV for ), for the center-of-mass energies of , , and TeV, respectively.

#### 1. Introduction

The Standard Model (SM) of particle physics has so far been in agreement with the results of numerous experiments. The discovery of the Higgs boson [1] has also increased the reliability of the SM. However, there are some problems which have not been entirely solved by the SM, such as quark-lepton symmetry, family replication, number of families, fermion’s masses and mixing pattern, and hierarchy problems. Several theories beyond the SM (BSM), including extra dimensions, supersymmetry (SUSY), and compositeness, have been proposed to solve these problems. The best way to explain the inflation of fundamental particles in the SM is to assume that they have more fundamental matter constituents. Therefore, a natural explanation for the replication of the SM fermionic families is lepton and quark compositeness, in which both matter and antimatter elementary particles have a substructure called preon [2]. The composite models have been characterized by an energy scale, namely, compositeness scale, . A typical consequence of the compositeness is the appearance of excited leptons and quarks [3, 4]. Charged and neutral excited leptons are predicted by the composite models. The SM fermions are considered as ground states of a rich and heavier spectrum of the excited states. An excited spin-1/2 lepton is considered to be both the lowest radial and orbital excitation. Excited states with spin-3/2 are also expected to exist [5].

No evidence for excited lepton production has been found so far in searches based on data samples collected by the LEP [6], HERA [7], Tevatron [8], CMS [9], and ATLAS [10] experiments. For the excited electron [11, 12], muon [13], and neutrino [14–17], there are some phenomenological studies at the future high-energy colliders.

Current experimental lower bounds on the masses of the excited neutrinos are GeV [6] from LEP-L3 collaboration (pair production) assuming , GeV [18] at 95% CL from HERA-H1 collaboration (single production) assuming and TeV [18], namely, the strongest limit, from LHC-ATLAS collaboration (pair production) assuming .

The Future Circular Collider (FCC) is a post-Large Hadron Collider (LHC) accelerator project [19], with TeV, proposed at CERN and supported by European Union within the Horizon Framework Programme for Research and Innovation. Besides the option, FCC also includes collider option (TLEP) at the same tunnel [20]. Construction of the future and colliders tangential to the FCC will also provide several and collider options [21].

In this paper, we analyze the potential of the FCC-based colliders, namely, , , and , for the excited neutrino searches. The ERL60 denotes energy recovery linac proposed for the LHeC main option [22] and can also be used for the FCC-based colliders. The ILC and the PWFA-LC mean International Linear Collider [23] and Plasma Wake Field Accelerator Linear Collider [24], respectively. The FCC-based and colliders have been proposed in [25]. Energy of the electron beams, center-of-mass energy, and luminosity values of the FCC-based colliders are presented in Table 1 [25, 26].

We introduce the effective Lagrangian, the decay widths, and the branching ratios of the excited neutrinos in Section 2. In Section 3, we analyze the signal and backgrounds for the process , and finally we summarize our results in Section 4.

#### 2. Production of the Excited Neutrinos

The interaction between a spin-1/2 excited lepton, a gauge boson , and the SM leptons is described by invariant Lagrangian [4, 27, 28] aswhere is the new physics scale responsible for the existence of the excited leptons, and are the field strength tensors, and are the gauge couplings, and are the scaling factors for the gauge couplings of and , where are the Dirac matrices, denotes the Pauli matrices, and is hypercharge.

For an excited neutrinos, three decay modes are possible: radiative decay , neutral weak decay , and charged weak decay . The branching ratios (BR) of the excited neutrino for the couplings and are given in Figure 1. One may note that the electromagnetic interaction between excited neutrino and ordinary neutrino, namely, -channel, vanishes for . As clearly visible from Figure 1, the -channel, whose branching ratio is ~60%, is dominant in the whole mass range for . In the case of , the branching ratio for the individual decay channels reaches the constant value of 60% for the -channel, 12% for the -channel, and 28% for the -channel at higher neutrino masses ( GeV). Since the charged weak decay () is dominant in both cases, we preferred this channel for investigating the excited neutrino in future linear collider experiments.

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Neglecting the SM lepton mass, we find the decay width of excited leptons aswhere is the new electroweak coupling parameter corresponding to the gauge boson , where , , , and , , , where is the weak mixing angle and is the mass of the gauge boson. The total decay widths of the excited neutrino for the scale is given in Figure 2.

#### 3. Signal and Background Analysis

We analyze the potentials of the future collider machines to search for the excited neutrinos via the single production reaction with subsequent decay of the excited neutrino into an electron and a boson. Therefore, we consider the process and subprocesses . The signal and background analysis were done at the parton level by using the high-energy simulation program CALCHEP in the version 3.6.25 [29]. We used the CTEQ6L [30] parton distribution functions in our calculations.

For a comparison of different FCC-based colliders, the signal cross sections for excited neutrino production are presented in Figure 3, assuming the coupling parameter .

##### 3.1. Collider

The is a FCC-based future collider with the center-of-mass energy of TeV. Keeping in mind that the lower bound on the mass of the excited neutrino is TeV ( TeV), we have explored the mass limits for the discovery of the excited neutrinos in the range of and TeV at the collider. To separate signal from backgrounds, final state particles (electron, boson and jets) with GeV are required. The SM cross section after the application of these cuts is pb. In order to define the kinematical cuts best suited for discovery, we have plotted the normalized transverse momentum and the normalized pseudorapidity distributions of the final state particles. Figure 4 shows the normalized distributions of the final state bosons (a), pseudorapidity () distributions of the final state electron (b), and the distributions of the final state (c), for signals corresponding to excited neutrino masses of and GeV and the SM backgrounds. The distributions of the final state electrons are the same as those of the final state bosons. As can be seen from Figure 4, the kinematical cuts GeV, and drastically reduce the background while keeping the signal almost unchanged. The invariant mass distributions of the system after the application of all kinematical cuts is reported in Figure 5. The separation of the signal from the background improved.

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A natural way of extracting the excited neutrino signal, and the same time suppressing the SM background is to impose a cut on the invariant mass in addition to kinematical cuts. Therefore, we have selected events within the mass window .

We define statistical significance (SS) of the expected signal yield aswhere denotes the cross section due to the excited neutrino production and the SM backgrounds, denotes the SM cross section, and is the integrated luminosity of the collider. Assuming and , we have calculated the signal, the background cross sections, and SS in invariant mass bins since the signal is concentrated in a small region proportional to the invariant mass resolution. The results are summarized in Table 2. The collider can discover the excited neutrino in decay mode for the coupling up to the mass of GeV taking into account the discovery criterion (% CL).

##### 3.2. Collider

The collider with the center-of-mass energy of TeV can search for the excited neutrino in a wider mass range compared to the collider. We have explored the mass limits for discovery of the excited neutrinos in the mass range from to TeV. In order to separate the excited neutrino signals from the background we have required GeV, as for the collider. Subsequently, the SM background cross section for the collider is found to be pb. The normalized distributions of the final state electrons, the distributions of the final state bosons, and the distributions of the final state electrons are presented in Figure 6. Also in this case, final state electrons and bosons have the same distribution. The kinematical cuts GeV, , and are optimal for increasing the potential discovery. The invariant mass distributions of the system after the application of all kinematical cuts is reported in Figure 7.

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Signal and background cross sections in invariant mass bins and the SS values calculated for and are summarized in Table 3.

Assuming and , taking into account the calculated SS values for criterion, the collider can probe the excited neutrino up to the masses of and GeV for the integrated luminosities of and , respectively.

##### 3.3. Collider

If the excited neutrinos had not been observed at the and the colliders, they would have been explored up to the mass of TeV at the collider that has the widest research potential. We have explored the mass limits for discovering the excited neutrinos in a broad mass spectrum from to TeV. The SM background cross section is found to be pb after the application of the same initial kinematical cuts. Figure 8 shows the distributions of the final state bosons, the distributions of the final state electrons, and the distributions of the boson for the excited neutrino masses of , , , and GeV versus the backgrounds. As already discussed, the distributions of the bosons are the same for the final state electrons. By requiring GeV , and , the background is suppressed, whereas the signal remains almost unchanged. The invariant mass distributions of the system obtained after application of all cuts is reported in Figure 9. We have also required the invariant masses to be in the range .

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Assuming and , the signal and the background cross sections for collider, as well as the SS values, are summarized in Table 4 for two integrated luminosity values, namely, and . For the energy scale of , the collider can probe the excited neutrino up to the masses of and GeV for the integrated luminosities of and , respectively.

#### 4. Conclusion

This work has shown that the FCC-based colliders have a great potential for the excited neutrino searches. We give a realistic estimate for the excited neutrino signal and the corresponding background at three different colliders, namely, the ( TeV), the ( TeV), and the ( TeV). The simulations have been performed assuming the energy scale and the coupling parameter . The mass limits for exclusion, observation, and discovery of the excited neutrinos at the three colliders are given in Table 5, for the different integrated luminosity values. As a result, these three FCC-based colliders offer the possibility of probing the excited neutrino over a very large mass range.

#### Conflicts of Interest

The author declares that he has no conflicts of interest.

#### Acknowledgments

The author is grateful to A. Ozansoy and S. O. Kara for useful discussions and model file supports. This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant no. 114F337.