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Excited Neutrino Search Potential of the FCC-Based Electron-Hadron Colliders.

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, [LAMBDA]. A typical consequence of the compositeness is the appearance of excited leptons and quarks [3,4]. Charged ([e.sup.*], [[mu].sup.*], [[tau].sup.*]) and neutral ([v.sup.*.sub.e], [v.sup.*.sub.[mu]], [v.sup.*.sub.[tau]]) 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 [mathematical expression not reproducible] [6] from LEP-L3 collaboration (pair production) assuming f = f' = 1, [mathematical expression not reproducible] [18] at 95% CL from HERA-H1 collaboration (single production) assuming f = f' = 1 and [mathematical expression not reproducible] [18], namely, the strongest limit, from LHC-aTlAS collaboration (pair production) assuming f = f' = 1.

The Future Circular Collider (FCC) is a post-Large Hadron Collider (LHC) accelerator project [19], with [square root of s] = 100 TeV, proposed at CERN and supported by European Union within the Horizon 2020 Framework Programme for Research and Innovation. Besides the pp option, FCC also includes [e.sup.+][e.sup.-] collider option (TLEP) at the same tunnel [20]. Construction of the future [e.sup.+][e.sup.-] and [[mu].sup.+][[mu].sup.-] colliders tangential to the FCC will also provide several ep and [mu]p collider options [21].

In this paper, we analyze the potential of the FCC-based ep colliders, namely, ERL60 [cross product] FCC, ILC [cross product] FCC, and PWFA-LC [cross product] FCC, 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 ep colliders. The ILC and the PWFA-LC mean International Linear Collider [23] and Plasma Wake Field Accelerator Linear Collider [24], respectively. The FCC-based ILC [cross product] FCC and PWFA-LC [R] FCC colliders have been proposed in [25]. Energy of the electron beams, center-of-mass energy, and luminosity values of the FCC-based ep 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 ep [right arrow] [v.sup.*]q [right arrow] e[W.sup.+]q, 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 (V = y, Z, [W.sup.[+ or -]] , and the SM leptons is described by SU(2) x U(1) invariant Lagrangian [4,27,28] as

[mathematical expression not reproducible], (1)

where [LAMBDA] is the new physics scale responsible for the existence of the excited leptons, [[??].sub.[mu]v] and [B.sub.[mu]v] 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), [[sigma].sup.[mu]v] = i([[gamma].sup.[mu]][[gamma].sup.v] - [[gamma].sup.v][[gamma].sup.[mu]])/2 where [[gamma].sup.[mu]] are the Dirac matrices, [??] denotes the Pauli matrices, and Y is hypercharge.

For an excited neutrinos, three decay modes are possible: radiative decay [v.sup.*] [right arrow] v[gamma], neutral weak decay [v.sup.*] [right arrow] vZ, and charged weak decay [v.sup.*] [right arrow] e[W.sup.+]. The branching ratios (BR) of the excited neutrino for the couplings f = f' = 1 and f = -f' = 1 are given in Figure 1. One may note that the electromagnetic interaction between excited neutrino and ordinary neutrino, namely, y-channel, vanishes for f = f' = 1. As clearly visible from Figure 1, the W-channel, whose branching ratio is ~60%, is dominant in the whole mass range for f = f' = 1. In the case of f = -f' = 1, the branching ratio for the individual decay channels reaches the constant value of 60% for the W-channel, 12% for the Z-channel, and 28% for the [gamma]-channel at higher neutrino masses ([mathematical expression not reproducible]). Since the charged weak decay ([v.sup.*] [right arrow] e[W.sup.+]) is dominant in both cases, we preferred this channel for investigating the excited neutrino in future linear collider experiments.

Neglecting the SM lepton mass, we find the decay width of excited leptons as

[GAMMA]([l.sup.*] [right arrow] lV) = [alpha][m.sup.*3]/4[[LAMBDA].sup.2] [f.sup.2.sub.V][(1 - [m.sup.2.sub.V]/[m.sup.*2]).sup.2](1 + [m.sup.2.sub.V]/2[m.sup.*2]), (2)

where [f.sub.V] is the new electroweak coupling parameter corresponding to the gauge boson V, where V = [W.sup.+], Z, [gamma], and [f.sub.[gamma]] = (f - f')/2, [f.sub.Z] = (f cot [[theta].sub.W] + f' tan [[theta].sub.W])/2, [f.sub.W] = f/[square root of (2)] sin [[theta].sub.W], where [[theta].sub.W] is the weak mixing angle and [m.sub.V] is the mass of the gauge boson. The total decay widths of the excited neutrino for the scale [mathematical expression not reproducible] is given in Figure 2.

3. 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 [right arrow] [v.sup.*]X with subsequent decay of the excited neutrino into an electron and a [W.sup.+] boson. Therefore, we consider the process ep [right arrow] [W.sup.+]eX and subprocesses eq([bar.q]) [right arrow] [W.sup.+] eq([bar.q]). 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 ep colliders, the signal cross sections for excited neutrino production are presented in Figure 3, assuming the coupling parameter f = f' = 1.

3.1. ERL60 [cross product] FCC Collider. The ERL60 [cross product] FCC is a FCC-based future ep collider with the center-of-mass energy of 3.46 TeV. Keeping in mind that the lower bound on the mass of the excited neutrino is 1.6 TeV ([mathematical expression not reproducible]), we have explored the mass limits for the discovery of the excited neutrinos in the range of 1.6 and 3.46 TeV at the ERL60 [cross product] FCC collider. To separate signal from backgrounds, final state particles (electron, [W.sup.+] boson and jets) with [p.sup.e,W,j.sub.T] > 20 GeV are required. The SM cross section after the application of these cuts is [[sigma].sub.B] = 3.96 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 [p.sub.T] distributions of the final state [W.sup.+] bosons (a), pseudorapidity ([eta]) distributions of the final state electron (b), and the [eta] distributions of the final state [W.sup.+] (c), for signals corresponding to excited neutrino masses of 1000 and 2000 GeV and the SM backgrounds. The [p.sub.T] distributions of the final state electrons are the same as those of the final state [W.sup.+] bosons. As can be seen from Figure 4, the kinematical cuts [p.sup.W,e.sub.T] > 200 GeV, -5 < [[eta].sup.e] < -1 and -4.5 < [[eta].sup.W] < -2 drastically reduce the background while keeping the signal almost unchanged. The invariant mass distributions of the e[W.sup.+] system after the application of all kinematical cuts is reported in Figure 5. The separation of the signal from the background improved.

A natural way of extracting the excited neutrino signal, and the same time suppressing the SM background is to impose a cut on the e[W.sup.+] invariant mass in addition to kinematical cuts. Therefore, we have selected events within the mass window [mathematical expression not reproducible].

We define statistical significance (SS) of the expected signal yield as

SS = [absolute value of ([[sigma].sub.S+B] - [[sigma].sub.B])]/[square root of ([[sigma].sub.B])][square root of ([L.sub.int])], (3)

where [[sigma].sub.S+B] denotes the cross section due to the excited neutrino production and the SM backgrounds, [[sigma].sub.B] denotes the SM cross section, and [L.sub.int] is the integrated luminosity of the collider. Assuming f = f' = 1 and [mathematical expression not reproducible], we have calculated the signal, the background cross sections, and SS in e[W.sup.+] 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 ERL60 [cross product] FCC collider can discover the excited neutrino in [v.sup.*] [right arrow] [W.sup.+]e decay mode for the coupling f = f' = 1 up to the mass of 2452 GeV taking into account the discovery criterion SS [greater than or equal to] 5 (99% CL).

3.2. ILC [cross product] FCC Collider. The ILC [cross product] FCC collider with the center-of-mass energy of 10 TeV can search for the excited neutrino in a wider mass range compared to the ERL60 [cross product] FCC collider. We have explored the mass limits for discovery of the excited neutrinos in the mass range from 1.6 to 10 TeV. In order to separate the excited neutrino signals from the background we have required [p.sup.e,W,j.sub.T] > 20 GeV, as for the ERL60 [cross product] FCC collider. Subsequently, the SM background cross section for the ILC [cross product] FCC collider is found to be [[sigma].sub.B] = 15.74 pb. The normalized [p.sub.T] distributions of the final state electrons, the [eta] distributions of the final state [W.sup.+] bosons, and the [eta] distributions of the final state electrons are presented in Figure 6. Also in this case, final state electrons and [W.sup.+] bosons have the same [p.sub.T] distribution. The kinematical cuts [p.sup.W,e.sub.T] > 200 GeV, -3.4 < [[eta].sup.W] < 0.4, and -5 < [[eta].sup.e] < 1 are optimal for increasing the potential discovery. The invariant mass distributions of the e[W.sup.+] system after the application of all kinematical cuts is reported in Figure 7.

Signal and background cross sections in e[W.sup.+] invariant mass bins [mathematical expression not reproducible] and the SS values calculated for [L.sub.int] = 10 [fb.sup.-1] and [L.sub.int] = 100 [fb.sup.-1] are summarized in Table 3.

Assuming f = f' = 1 and [mathematical expression not reproducible], taking into account the calculated SS values for SS [greater than or equal to] 5 criterion, the ILC [cross product] FCC collider can probe the excited neutrino up to the masses of 5635 and 6460 GeV for the integrated luminosities of [L.sub.int] = 10 [fb.sup.-1] and [L.sub.int] = 100 [fb.sup.-1], respectively.

3.3. PWFA-LC [cross product] FCC Collider. If the excited neutrinos had not been observed at the ERL60 [cross product] FCC and the ILC [cross product] FCC colliders, they would have been explored up to the mass of 31.6 TeV at the PWFA-LC [cross product] FCC collider that has the widest research potential. We have explored the mass limits for discovering the excited neutrinos in a broad mass spectrum from 1.6 to 31.6 TeV. The SM background cross section is found to be [[sigma].sub.B] = 58.15 pb after the application of the same initial kinematical cuts. Figure 8 shows the [p.sub.T] distributions of the final state [W.sup.+] bosons, the [eta] distributions of the final state electrons, and the [eta] distributions of the [W.sup.+] boson for the excited neutrino masses of 5000, 10000, 15000, and 20000 GeV versus the backgrounds. As already discussed, the [p.sub.T] distributions of the [W.sup.+] bosons are the same for the final state electrons. By requiring [p.sup.W,e.sub.T] > 400 GeV -5 < [[eta].sup.e] < 2.5, and -2.5 < [[eta].sup.W] < 1, the background is suppressed, whereas the signal remains almost unchanged. The invariant mass distributions of the e[W.sup.+] system obtained after application of all cuts is reported in Figure 9. We have also required the e[W.sup.+] invariant masses to be in the range [mathematical expression not reproducible].

Assuming f = f' = 1 and [mathematical expression not reproducible], the signal and the background cross sections for PWFA-LC [cross product] FCC collider, as well as the SS values, are summarized in Table 4 for two integrated luminosity values, namely, [L.sub.int] = 1 [fb.sup.-1] and [L.sub.int] = 10 [fb.sup.-1]. For the energy scale of [mathematical expression not reproducible], the PWFA-LC [cross product] FCC collider can probe the excited neutrino up to the masses of 10200 and 13960 GeV for the integrated luminosities of [L.sub.int] = 1 [fb.sup.-1] and [L.sub.int] = 10 [fb.sup.-1], respectively.

4. Conclusion

This work has shown that the FCC-based ep 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 ERL60 [cross product] FCC ([square root of s] = 3.46 TeV), the ILC [cross product] FCC ([square root of s] = 10 TeV), and the PWFA-LC [cross product] FCC ([square root of s] = 31.6 TeV). The simulations have been performed assuming the energy scale A = mr* and the coupling parameter f = f' = 1. 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 ep colliders offer the possibility of probing the excited neutrino over a very large mass range.

https://doi.org/10.1155/2017/4726050

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.

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A. Caliskan

Faculty of Engineering and Natural Sciences, Department of Physics Engineering, Gumushane University, 29100 Gumushane, Turkey

Correspondence should be addressed to A. Caliskan; acaliskan@gumushane.edu.tr

Received 20 October 2017; Accepted 9 December 2017; Published 31 December 2017

Academic Editor: Anna Cimmino

Caption: Figure 1: The branching ratios (%) depending on the mass of the excited neutrino for f = f' = 1 (a) and f = -f' = 1 (b).

Caption: Figure 2: The total decay widths of the excited neutrino for the scale [mathematical expression not reproducible] and the coupling f = f' = 1.

Caption: Figure 3: The total cross sections as a function of the excited neutrino mass at the ep colliders with various center-of-mass energies, assuming f = f' = 1 and [mathematical expression not reproducible].

Caption: Figure 4: The normalized transverse momentum distributions of the final state [W.sup.+] bosons (a), the normalized pseudorapidity distributions of the final state electrons (b), and the normalized pseudorapidity distributions of the final state [W.sup.+] bosons (c) for f = f' = 1 and [mathematical expression not reproducible] at the ERL60 [cross product] FCC collider

Caption: Figure 5: The invariant mass distributions of the excited neutrino signal and the corresponding background for [mathematical expression not reproducible] and f = f' = 1 at the ERL60 [cross product] FCC collider.

Caption: Figure 6: The normalized transverse momentum distributions of the final state electrons (a), the normalized pseudorapidity distributions of the final state [W.sup.+] bosons (b), and the normalized pseudorapidity distributions of the final state electrons (c) for f = f' = 1 and [mathematical expression not reproducible] at the ILC [cross product] FCC collider

Caption: Figure 7: The invariant mass distributions of the excited neutrino signal and the corresponding background for [mathematical expression not reproducible] and f = f' = 1 at the ILC [cross product] FCC collider.

Caption: Figure 8: The normalized transverse momentum distributions of the final state [W.sup.+] bosons (a), the normalized pseudorapidity distributions of the final state electrons (b), and the normalized pseudorapidity distributions of the final state [W.sup.+] bosons (c) for f = f' = 1 and [mathematical expression not reproducible] at the PWFA-LC [cross product] FCC collider.

Caption: Figure 9: The invariant mass distributions of the excited neutrino signal and the corresponding background for [mathematical expression not reproducible] and f = f' = 1 at the PWFA-LC [cross product] FCC collider.
Table 1: Main parameters of the FCC-based ep colliders.

Colliders                     [E.sub.e] (TeV)    CM energy (TeV)

ERL60 [cross product] FCC           0.06              3.46
ILC [cross product] FCC             0.5                10
PWFA-LC [cross product] FCC          5                31.6

Colliders                          [L.sub.int]
                              ([fb.sup.-1] per year)

ERL60 [cross product] FCC               100
ILC [cross product] FCC               10-100
PWFA-LC [cross product] FCC            1-10

Table 2: The statistical significance (SS) values and the cross
sections of the excited neutrino signal and relevant backgrounds at
ERL60 [cross product] FCC collider with [square root of s] = 3.46
TeV and [L.sub.int] = 100 [fb.sup.-1], assuming
[mathematical expression not reproducible] and f = f' = 1.

Mass (GeV)  [[sigma].sub.S+B] (pb)    [[sigma].sub.B] (pb)     SS

1600          7.21 x [10.sup.-3]       1.86 x [10.sup.-4]     162.9
1800          2.47 x [10.sup.-3]       9.60 x [10.sup.-5]     76.5
2000          7.65 x [10.sup.-4]       4.15 x [10.sup.-5]     35.5
2200          2.09 x [10.sup.-4]       1.49 x [10.sup.-5]     15.9
2300          1.03 x [10.sup.-4]       8.48 x [10.sup.-6]     10.2
2400          4.82 x [10.sup.-5]       4.64 x [10.sup.-6]      6.4
2500          2.14 x [10.sup.-5]       2.41 x [10.sup.-6]      3.8
2600          8.85 x [10.sup.-6]       1.19 x [10.sup.-6]      2.2
2700          3.32 x [10.sup.-6]       5.41 x [10.sup.-7]      1.1

Table 3: The statistical significance (SS) values and the cross
sections of the excited neutrino signal and relevant background at the
ILC [cross product] FCC collider with [square root of s] = 10 TeV
assuming the coupling f = f' = 1 and the energy scale
[mathematical expression not reproducible].

Mass (GeV)   [[sigma].sub.B] (pb)    [[sigma].sub.S+B] (pb)

2000          1.81 x [10.sup.-3]       1.47 x [10.sup.-1]
2500          1.24 x [10.sup.-3]       5.85 x [10.sup.-2]
3000          7.37 x [10.sup.-4]       2.43 x [10.sup.-2]
3500          3.94 x [10.sup.-4]       1.03 x [10.sup.-2]
4000          1.85 x [10.sup.-4]       4.28 x [10.sup.-3]
4500          8.27 x [10.sup.-5]       1.74 x [10.sup.-3]
5000          3.58 x [10.sup.-5]       6.69 x [10.sup.-4]
5500          1.47 x [10.sup.-5]       2.43 x [10.sup.-4]
6000          6.07 x [10.sup.-6]       8.15 x [10.sup.-5]
6500          2.26 x [10.sup.-6]       2.49 x [10.sup.-5]
7000          7.83 x [10.sup.-7]       6.69 x [10.sup.-6]
7500          2.37 x [10.sup.-7]       1.49 x [10.sup.-6]

Mass (GeV)     [L.sub.int] =        [L.sub.int] =
             10 [fb.sup.-1] SS    100 [fb.sup.-1] SS

2000               342.1                1081.9
2500               162.9                 515.1
3000                86.8                 274.7
3500                49.6                  157
4000                 30                  95.1
4500                18.1                 57.4
5000                10.5                 33.4
5500                5.9                  18.8
6000                 3                    9.6
6500                1.5                   4.7
7000                0.6                   2.1
7500                0.2                   0.8

Table 4: The statistical significance (SS) values and the cross
sections of the excited neutrino signal and relevant background at the
PWFA-LC[cross product] FCC collider with [square root of s] = 31.6
TeV assuming the coupling f = f' = 1 and the energy scale
[mathematical expression not reproducible].

Mass (GeV)  [[sigma].sub.B] (pb)    [[sigma].sub.S+B] (pb)

2000         1.16 x [10.sup.-3]       2.92 x [10.sup.-1]
4000         1.03 x [10.sup.-3]       9.00 x [10.sup.-2]
6000         6.30 x [10.sup.-4]       2.42 x [10.sup.-2]
8000         3.59 x [10.sup.-4]       7.47 x [10.sup.-3]
10000        1.78 x [10.sup.-4]       2.45 x [10.sup.-3]
12000        6.55 x [10.sup.-5]       8.02 x [10.sup.-4]
14000        2.27 x [10.sup.-5]       2.57 x [10.sup.-4]
16000        7.71 x [10.sup.-6]       7.66 x [10.sup.-5]
18000        2.51 x [10.sup.-6]       2.06 x [10.sup.-5]
20000        7.42 x [10.sup.-7]       4.85 x [10.sup.-6]

Mass (GeV)   [L.sub.int] =        [L.sub.int] =
            1 [fb.sup.-1] SS    10 [fb.sup.-1] SS

2000              270.5               855.6
4000              87.6                277.2
6000              29.7                 93.9
8000              11.8                 37.5
10000              5.3                  17
12000              2.8                 9.1
14000              1.5                 4.9
16000              0.7                 2.4
18000              0.3                 1.1
20000              0.1                 0.4

Table 5: The mass limits for the exclusion (2[sigma]), the observation
(3[sigma]), and the discovery (5[sigma]) of the excited neutrinos at
the different ep colliders assuming the coupling f = f' = 1 and the
energy scale [mathematical expression not reproducible].

Colliders                      [L.sub.int]     2[sigma] (GeV)
                              ([fb.sup.-1])

ERL60 [cross product] FCC          100              2618
ILC [cross product] FCC             10              6300
                                   100              7025
PWFA-LC [cross product] FCC         1              13050
                                    10             16500

Colliders                     3[sigma] (GeV)   5[sigma] (GeV)

ERL60 [cross product] FCC          2547             2452
ILC [cross product] FCC            6000             5635
                                   6790             6460
PWFA-LC [cross product] FCC       11850            10200
                                  15450            13960
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Title Annotation:Research Article; Future Circular Collider
Author:Caliskan, A.
Publication:Advances in High Energy Physics
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2018
Words:4622
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