Excited neutrino search potential of the FCC-based electron-hadron colliders

The production potential of the excited neutrinos at the FCC-based electron-hadron colliders, namely the ERL60$\otimes$FCC with $\sqrt{s}=3.46$ TeV, the ILC$\otimes$FCC with $\sqrt{s}=10$ TeV, and the PWFA-LC$\otimes$FCC with $\sqrt{s}=31.6$ 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 $\nu^{\star}\rightarrow eW^{+}$. We have calculated the production cross sections with the process of $ep\rightarrow\nu^{\star}q\rightarrow eW^{+}q$ and the decay widths of the excited neutrinos with the process of $\nu^{\star}\rightarrow eW^{+}$. 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 $2452$ GeV for $L_{int}=100$ $fb^{-1}$, $5635$ GeV for $L_{int}=10$ $fb^{-1}$ ($6460$ GeV for $L_{int}=100$ $fb^{-1}$), and $10200$ GeV for $L_{int}=1$ $fb^{-1}$ ($13960$ GeV for $L_{int}=10$ $fb^{-1}$), for the center-of-mass energies of $3.46$, $10$, and $31.6$ TeV, respectively.


I. INTRODUCTION
The Standard Model (SM) of the 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, hierarchy problems etc. A number of theories beyond the SM (BSM), including extra dimensions, supersymmetry (SUSY), compositeness and so on, have been proposed for solving these problems. One of the most important of these theories is compositeness in which quarks and leptons have a substructure called preon [2].
The composite models have been characterized by an energy scale, namely compositeness scale, Λ. A typical consequence of the compositeness is the appearance of excited leptons and quarks [3,4]. Charged (e ⋆ , µ ⋆ ,τ ⋆ ) and neutral (ν ⋆ e , ν ⋆ µ , ν ⋆ τ ) 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 the lowest radial and orbital excitation. Excited states with spin-3/2 are also expected to exist [5].
The Future Circular Collider (FCC) is a post-LHC accelerator project [19], with √ s = 100 TeV, proposed at CERN and supported by European Union within Horizon 2020 Framework Programme for Research and Innovation. Besides the pp option, it includes e + e − collider option (TLEP) at the same tunnel [20]. Construction of the future e + e − and µ + µ − colliders tangential to the FCC will also provide several ep and µp collider options [21].
In this paper we analyze the potential of the FCC-based ep colliders, namely  [22], and can also be used for the FCC-based ep colliders. The ILC and the PWFA-LC mean International Linear Collider [23], and Plasma Wake Field Accelerator Linear Collider [24], respectively.
Center-of-mass energy and luminosity values of the FCC-based ep colliders are given in Table   I [25,26].
We introduce the effective Lagrangian, the decay widths, and the branching ratios of the excited neutrinos in Section II. In Section III, we analyze the signal and backgrounds for the process ep → ν ⋆ q → eW + q , and finally we summarize our results in Section IV.

II. PRODUCTION OF THE EXCITED NEUTRINOS
The interaction between a spin-1/2 excited lepton, a gauge boson (V = γ, Z, W ± ) and the ordinary leptons is described by SU(2) × U(1) invariant Lagrangian [4,27,28] as where Λ is the new physics scale that responsible for the existence of the excited leptons; W µν and B µν are the field strength tensors, g and g ′ are the gauge couplings, f and f ′ are the scaling factors for the gauge couplings of SU(2) and U(1); σ µν = i(γ µ γ ν −γ ν γ µ )/2 where γ µ are the Dirac matrices, − → τ denotes the Pauli matrices, and Y is hypercharge.
The excited neutrinos have three decay modes, namely radiative decay ν ⋆ → νγ, neutral weak decay ν ⋆ → νZ , and charged weak decay ν ⋆ → eW + . The branching ratios (BR) of the excited neutrino for the coupling of f = f ′ = 1 and f = −f ′ = 1 are given in Fig. 1. One may note that the electromagnetic interaction between the excited neutrino and ordinary neutrino, namely γ -channel, vanishes for the coupling of f = f ′ = 1. It is clearly seen that the W-channel whose branching ratio is ∼ 60% become dominant. For the coupling of f = −f ′ = 1, the branching ratio for the individual decay channels reaches to the constant values 60% for the W-channel, 12% for the Z-channel, and 28% for the γ -channel at higher mass values. Since the charged weak decay (ν ⋆ → eW + ) is dominant for both cases, we preferred this channel for the investigation of the excited neutrino in this paper.
Neglecting the SM lepton mass, we find the decay width of excited leptons as where f V is the new electroweak coupling parameter corresponding to the gauge boson V

III. SIGNAL AND BACKGROUND ANALYSIS
We analyze the potentials of the future ep collider machines to search for the excited neutrinos via the single production reaction ep → ν ⋆ X with subsequent decay of the excited neutrino into an electron and W + boson. So, we deal with the process ep → W + eX and subprocesses eq(q) → W + eq(q). The signal and background analysis were done at the parton level by using the high energy simulation program of CALCHEP (ver. 3.6.25) [29]. In our calculations we have used the parton distribution functions library of CTEQ6L [30].
For a comparison of different FCC-based ep colliders, the signal cross sections for excited neutrino production are presented in Fig. 3, assuming the coupling parameter of f = f ′ = 1. (pb/GeV)  almost unaffected. As for the kinematical cut of η distributions (see Fig. 5 (right)) of final state W + bosons, it was determined as −4.5 < η W < −2. The Fig. 5 (left) shows the invariant mass distributions of the eW + system after application of the all kinematical cuts for discovery. It is clearly seen that the background is suppressed.
A natural way of extracting the excited neutrino signal, and the same time suppressing the SM background is to impose a cut on the eW + invariant mass in addition to kinematical cuts for discovery. Therefore, we have specified the cuts of mass window as m ν ⋆ − 2Γ ν ⋆ < m eW < m ν ⋆ + 2Γ ν ⋆ .
By using the all kinematical cuts, we have calculated the statistical significance (SS) values of the expected signal yield using the following formula, where L int is the integrated luminosity of the collider. In the Table 2     The kinematical discovery cut of this distributions was determined as −5 < η e < 1. Table 3 presents the signal and background cross sections in eW + invariant mass bins satisfying the condition of m ν ⋆ − 2Γ ν ⋆ < m eW < m ν ⋆ + 2Γ ν ⋆ .
When we look at the calculated SS values for SS ≥ 5 criteria in Table III, for the energy scale of Λ = m ν ⋆ , the ILC⊗FCC collider can probe the excited neutrino (assuming      background, whereas the signal remains almost unchanged. The normalized pseudorapidity distributions of the W + bosons, and the invariant mass distributions of the eW + system obtained after application of the all discovery cuts are given in Fig. 9. According to this Figure, the discovery cut of the normalized pseudorapidity distributions of the final state W + bosons was determined as −2.5 < η W < 1. In addition to these cuts, we have also applied the cuts to the eW + invariant masses using the m ν ⋆ − 2Γ ν ⋆ < m eW < m ν ⋆ + 2Γ ν ⋆ .
The signal and the background cross sections for PWFA-LC⊗FCC collider with the coupling of f = f ′ = 1 and the energy scale of Λ = m ν ⋆ are presented in Table 4  , respectively, as can be understood from the Table 4.   Table V, for the different integrated luminosity values. As a result, these three FCC-based ep colliders offer the possibility to probe the excited neutrino over a very large mass range.