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Search for Excited Spin-3/2 Neutrinos at LHeC.

1. Introduction

The Standard Model (SM) of the particle physics agrees with experimental results from the operating colliders. The first run of the Large Hadron Collider (LHC) brought the expected Higgs boson discovery, so a crucial part of the SM has been completed. But there is still no satisfying explanation of the three-family structure of leptons and quarks and their mass hierarchy. An attractive explanation is lepton and quark compositeness [1-3]. In composite models, known leptons and quarks have a substructure characterized by an energy scale called the compositeness scale, A. A natural consequence of compositeness is the occurrence of excited states [4-7]. Phenomenologically, an excited lepton can be regarded as a heavy lepton sharing the same leptonic quantum number with the corresponding SM lepton. If leptons present composite structures, they can be considered as spin-1/2 bound states containing three spin-1/2 or spin-1/2 and spin-0 subparticles. Bound states of spin-3/2 leptons are also possible with three spin-1/2 [1-3] or spin-1/2 and spin-1 subparticles in the framework of composite models [8]. The motivations for spin-3/2 particles come from two different scenarios; spin-3/2 leptons appear in composite models [9-13] and a spin-3/2 gravitino is the superpartner of graviton in supergravity [14]. Theories beyond the Standard Model that contain exotic particles are discussed in [15-19].

Both excited spin-1/2 and spin-3/2 neutrinos can be produced at future high energy lepton, hadron, and leptonhadron colliders. Elaborate studies on excited spin-1/2 neutrinos can be found in [20-30]. Also, one can find excited spin-1/2 neutrino production by ultra-high energy neutrinos in [31] and the impact of excited spin-1/2 neutrinos on v[bar.v] [right arrow] [gamma][gamma] process in [32].

The mass limit for excited spin-1/2 neutrinos obtained from their pair production ([e.sup.+][e.sup.-] [right arrow] [v.sup.*][v.sup.*] process) by L3 Collaboration at [square root of s] = 189 - 209 GeV, assuming f = -f', where f and f' are the new couplings determined by the composite dynamics, is [m.sup.*] > 102.6 GeV [33]. Assuming f = f' and f/[LAMBDA] = 1/[m.sup.*], for single production of excited spin-1/2 neutrino in ep collisions taking into account all the decay channels, the H1 Collaboration sets the exclusion limit for the mass range of excited neutrino [m.sup.*] > 213 GeV at 95% C.L. [34]. Recently, a search was performed by the ATLAS Collaboration taking into account pair production of excited spin-1/2 neutrinos either through contact or gauge-mediated interactions and their decay proceeds via the same mechanism. Considering events with at least three charged leptons with [LAMBDA] = [m.sup.*], with f = f' = 1 and with an integrated luminosity of

20.3 [fb.sup.-1] of pp collisions at [square root of s] = 8 TeV, a lower mass limit of 1.6 TeV is obtained for every excited spin-1/2 neutrino flavour [35].

Excited spin-3/2 neutrinos are not as well studied in the litterateur as the spin-1/2. An investigation of the production and decay processes of the single heavy spin-3/2 neutrino was performed in [36, 37]. A study of the potential of future high energy [e.sup.+][e.sup.-] linear colliders to probe excited spin-3/2 neutrino signals in different decay modes by considering three phenomenological currents taking into account the corresponding background was done in [8].

Studies are ongoing for the development of a new ep collider, the Large Hadron Electron Collider (LHeC), with an electron beam of 60 GeV, to possibly 140 GeV, and a proton beam of the LHC [38-41] or in the future the Future Circular Collider lepton-hadron collider (FCC-eh) [42,43]. The LHeC is the highest energy lepton-hadron collider under design and is considered as a linac-ring collider. Linac-ring type colliders were proposed in [44] and the physics potentials and advantages of these type lepton-hadron colliders are discussed in [45,46]. Latest results for excited neutrino searches coming from the first ep collider HERA have showed that ep colliders are so competitive to pp and [e.sup.+][e.sup.-] colliders and very important for the investigation of beyond SM physics [34, 38-41]. With the design luminosity of [10.sup.33] [cm.sup.-2] [s.sup.-1] the LHeC is intended to exceed the HERA luminosity by a factor of ~100. So it would be a major opportunity to push forward the investigations done in the LHC.

This work is a continuation of the previous works on excited neutrinos [8, 25]. In this work, in Section 2 we introduce the phenomenological currents for excited neutrinos and give their decay widths. In Section 3, we consider single production of excited spin-1/2 and spin-3/2 neutrinos at ep colliders. We take into account the signal in [v.sup.*] [right arrow] eW decay mode of excited neutrinos as well as corresponding backgrounds at LHeC with [square root of s] = 1.3 TeV and [square root of s] = 1.98 TeV. We plot the invariant mass distributions for single production of excited neutrinos with spin-1/2 and spin-3/2. Last, we plot the contour plots for the excited neutrino couplings to obtain the exclusion limits. Investigation on excited fermions with spin-1/2 takes an important part in the physics program of LHeC [38, 39]. Although the latest limit for excited spin-1/2 neutrinos set by the ATLAS experiment is high, it is important to examine the excited neutrinos with different spins at high energy lepton-hadron colliders. This work is the only dedicated work which gives the comparative results for both excited spin-1/2 and spin-3/2 neutrinos to comprehend the potential of next ep collider.

2. Physical Preliminaries

An excited spin-1/2 neutrino is the lowest radial and orbital excitation according to the classification by SU(2) x U(1) quantum numbers. Interactions between excited spin-1/2 neutrino and ordinary leptons are of the magnetic transition type [47-49]. The effective current for the interaction between an excited spin-1/2 neutrino, a gauge boson (V = [gamma], Z, [W.sup.[+ or -]]), and the SM lepton is given by

[mathematical expression not reproducible], (1)

where [lambda] is the new physics scale; [g.sub.e] is electromagnetic coupling constant with [g.sub.e] = [square root of A[pi][alpha]]; k, p, and q are the four momentum of the SM lepton, excited spin-1/2 neutrino, and the gauge boson, respectively. fv is the new electroweak coupling parameter corresponding to the gauge boson V and [[sigma].sup.[micro]v] = i([[gamma].sup.[mu]][[gamma].sup.v] - [[gamma].sup.v][y.sup.[mu]])/2 with [[gamma].sup.[mu]] being the Dirac matrices. An excited neutrino has three possible decay modes, each one of which is related to a vector boson [gamma], W, and Z. These decay modes are radiative decay [v.sup.*] [left arrow] v[gamma], neutral weak decay [v.sup.*] [right arrow] vZ, and charged weak decay [v.sup.*] [right arrow] eW. Neglecting SM lepton mass we find the decay width of the excited spin-1/2 neutrino as

[mathematical expression not reproducible] (2)

where [f.sub.[gamma]] = (f - f')/2, [f.sub.Z] = (f cot [[theta].sub.w] + f tan [[theta].sub.w])/2, and [f.sub.W] = f / [square root of 2] sin [[theta].sub.W]; [[theta].sub.w] is the weak mixing angle and [m.sub.V] is the mass of the gauge boson. The couplings f and f' are the scaling factors for the gauge couplings of SU(2) and U(1). Unless f = f', the electromagnetic interaction of excited neutrino and SM neutrino exists. Branching ratios of excited spin-1/2 neutrino for two choices f = -f' = 1 and f = f' = 1 are presented in Table 1. One may note that for the choice f = -f = 1 the branching ratio for the eW channel is =60%. Hence, to choose the [v.sup.*] [right arrow] eW mode for the analysis is more feasible.

The two phenomenological currents for the interactions between an excited spin-3/2 neutrino, a gauge boson (V = [gamma], Z, [W.sup.[+ or -]]), and the SM lepton are given by

[mathematical expression not reproducible], (3)

where [u.sup.[mu]](p, 3/2) represents the Rarita-Schwinger vectorspinor [50].

Decay widths of excited spin-3/2 neutrinos for the [v.sup.*] [right arrow] v[gamma] decay mode for the two currents are given by

[mathematical expression not reproducible]. (4)

and for the neutral and charged weak decay modes ([v.sup.*] [right arrow] vZ and [v.sup.*] [right arrow] eW), they are given as

[mathematical expression not reproducible], (5)

where [kappa] = [([m.sub.V]/[m.sup.*]).sup.2], V = Z, W, and l = e, v. Branching ratios and total decay width of excited spin-3/2 neutrinos with [J.sub.1] and [J.sub.2] are given in Tables 2 and 3, respectively. Also, total decay width of excited neutrinos as a function of their mass ([m.sup.*]) is shown in Figure 1.

3. Single Production at ep Collider

The excited spin-1/2 and spin-3/2 neutrinos can be produced singly at future ep colliders via i-channel W exchange. In our calculations we use the program CALCHEP [51-53]. The Feynman diagrams for the subprocesses [e.sup.-]q [right arrow] [v.sup.*]q' and [e.sup.-][bar.q'] [right arrow] [v.sup.*][bar.q] are shown in Figure 2.

Neglecting SM quark masses, the explicit formulas for the differential cross-section of the subprocesses [e.sup.-]q [right arrow] [v.sup.*]q' and [e.sup.-][bar.q'] [right arrow] [v.sup.*] [bar.q] for the two phenomenological spin-3/2 currents [J.sub.1] and [J.sub.2] are

[mathematical expression not reproducible], (6)

where [V.sub.qq'] is the CKM matrix element, t is the Mandelstam variable, and s is the square of center-of-mass energy of the collider. Also, differential cross-section expression for the excited spin-1/2 neutrino is

[mathematical expression not reproducible]. (7)

Total cross-section as a function of excited neutrino mass is shown in Figure 3 for the center-of-mass energies [square root of s] = 1.3 TeV and [square root of s] = 1.98 TeV.

In our analysis we chose the [v.sup.*] [right arrow] eW mode because of the high branching ratio of the charged current decay channel. [v.sup.*] [right arrow] v[gamma] and [v.sup.*] [right arrow] vZ decay modes will have larger uncertainty because of the missing transverse momentum ([[??].sub.T]) due to the neutrino in the final state. We consider the ep [right arrow] [v.sup.*]X [right arrow] [e.sup.-][W.sup.+]X process and put some kinematical cuts for the final state detectable particles. We deal with the subprocesse [e.sup.-]q([bar.q']) [right arrow] [W.sup.+][e.sup.-]q]([bar.q]) and impose the acceptance cuts

[p.sup.e,q.sub.T] > 20 GeV,

[absolute value of ([[eta].sup.e,q])] < 2.5. (8)

Feynman diagrams for the [e.sup.-]q [right arrow] [e.sup.-][W.sup.+]q' SM process are presented in Figure 4. The main background process that gives the same final state as excited neutrino signal is multijet neutral current deep inelastic scattering (NC DIS) events. After applying these cuts we obtained the SM background cross-section for the process ep [right arrow] [v.sup.*]X [right arrow] [e.sup.- ][W.sup.+]X as [[sigma].sub.B] = 0.334 pb for [square root of s] = 1.3 TeV and [[sigma].sub.B] = 0.928 pb for [square root of s] = 1.98 TeV. In order to discriminate the excited neutrino signal we plot the invariant mass distributions for the system for the masses [m.sup.*] = 400, 500,600 GeV at [square root of s] = 1.3 TeV and for the masses [m.sup.*] = 700, 800, 900 GeV at [square root of s] = 1.98 TeV in Figures 5 and 6, respectively.

We plot the rate of [[sigma].sub.B+S]/[[sigma].sub.B] as a function of excited neutrino mass in Figure 7 to examine the contribution of excited neutrinos to the process [e.sup.-]q([bar.q']) [right arrow] [W.sup.+][e.sup.-]q'([bar.q]) and also to investigate the separation of different excited neutrino models. Here [[sigma].sub.B+S] corresponds the cross-section calculated for the presence of excited neutrino (signal) and Standard Model (background) both, and [[sigma].sub.B] is the SM (background) cross-section. In these figures, the separation of spin-1/2, spin-3/2 with [J.sub.1] and spin-3/2 with [J.sub.2] excited neutrinos can be easily seen.

In order to get accessible limits for the excited neutrinos at high energy collider, we plot the contours for excited neutrinos with spin-1/2 and spin-3/2. We choose the W boson decay as W [right arrow] 2j. Here we consider the statistical significance:

SS = [[sigma].sub.s]/[square root of [[sigma].sub.B]][square root of [L.sub.int]]. (9)

Here [L.sub.int] is the integrated luminosity of the ep collider and we choose [L.sub.int] = 100 [fb.sup.-1] as the LHeC design luminosity. Our results for the SS are shown in Tables 4 and 5.

For the criteria SS [greater than or equal to] 3 (95% C.L.) we plot the [c.sub.iV] - [c.sub.iA] (i = 1,2) contour plot for excited spin-3/2 neutrinos for both phenomenological currents and the f - f' contour plot for the excited spin-1/2 neutrinos. In Figures 8 and 9, we choose the excited neutrino mass [m.sup.*] = 400 GeV for the analysis at [square root of s] = 1.3 TeV and [m.sup.*] = 800 GeV for the analysis at [square root of s] = 1.98 TeV. We see from these figures the allowed regions for the [c.sub.iV] - [c.sub.iA] (i = 1,2) and f - f' couplings for the masses [m.sup.*] = 400 GeV at = 1-3 TeV and [m.sup.*] = 800 GeV at [square root of s] = 1.98 TeV. The values which we chose in our calculations for the coupling parameters ([c.sub.iV] = [c.sub.iA] = 0.5 for the excited spin-3/2 neutrinos and f = -f' = 1 for the excited spin-1/2 neutrinos) are compatible with the contour plots.

4. Conclusion

We searched for the excited spin-3/2 neutrino signal at lepton-hadron collider LHeC for two different centers of mass energies. We used two different phenomenological currents for the spin-3/2 excited neutrinos, and we used the same value of [c.sub.iV], [c.sub.iA] (i = 1,2) couplings. Since there is no theoretical prediction for the single production of excited neutrinos and the effective currents have unknown couplings, we did not consider the interference between the currents. A more detailed calculation shows an important parameter space in which the interference terms could be important.

We also deal with the spin-1/2 excited neutrinos for comparison. Our analysis shows that the spin-1/2 and spin-3/2 excited neutrino signals discrimination is apparent at next ep colliders. Here we only take into account the effective currents describing the gauge interactions of excited and standard particles. It is possible to include the contact interactions which may enlarge the mass and coupling limits.

It is possible to search for single production of excited spin-3/2 neutrinos at the LHC but it has smaller cross-section than LHeC. Therefore, the potential of LHeC is better than LHC to determine the limits on couplings of excited spin-3/2 neutrinos.

Excited neutrinos with different spins would manifest themselves in three families. Here, we only investigated the excited electron neutrino. It is also possible to make the same analysis for excited muon neutrinos. Single production of excited muon neutrinos is possible at muon-hadron colliders. Physics of [micro]p colliders was studied in [54]. One can find the main parameters of FCC-based [micro]p collider in [43, 55].

http://dx.doi.org/10.1155/2016/1739027

Competing Interests

The authors declare that they have no competing interests.

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A. Ozansoy, (1) V. An, (1) and V. Cetinkaya (2)

(1) Department of Physics, Ankara University, Tandogan, 06100 Ankara, Turkey

(2) Department of Physics, Dumlupinar University, Merkez, 43100 Kutahya, Turkey

Correspondence should be addressed to A. Ozansoy; aozansoy@science.ankara.edu.tr

Received 1 June 2016; Revised 21 September 2016; Accepted 19 October 2016

Academic Editor: Andrea Coccaro

Caption: FIGURE 1: Total decay width of excited neutrinos according to their mass. Here, it is taken as [LAMBDA] = [m.sup.*] and f = -f' = 1 for excited spin-1/2 neutrinos and [c.sub.iV] = [c.sub.iA] = 0.5 (i = 1,2) for excited spin- 3/2 neutrinos for the two phenomenological currents.

Caption: FIGURE 2: Feynman diagrams.

Caption: FIGURE 3: Cross-sections for the excited neutrino production with A = [m.sup.*] and f = -f' for spin-1/2 ones and [c.sub.iV] = [c.sub.iA] = 0.5 (i = 1,2) for spin-3/2 ones at ep collider at [square root of s] = 1.3 TeV and [square root of s] = 1.98 TeV

Caption: FIGURE 4: Feynman diagrams for the SM background process [e.sup.-]q [right arrow] [e.sup.-][W.sup.+]q'.

Caption: FIGURE 5: Invariant mass distributions of eW system for the single production of excited spin-1/2 for f = -f' = 1 and excited spin-3/2 neutrinos with [J.sub.1] and [J.sub.2] for [c.sub.iV] = [c.sub.iA] = 0.5 (i = 1,2) at [square root of s] = 1.3 TeV.

Caption: FIGURE 6: Invariant mass distributions of eW system for the single production of excited spin-1/2 for f = -f' = 1 and excited spin-3/2 neutrinos with [J.sub.1] and [J.sub.2] for [c.sub.iV] = [c.sub.iA] = 0.5 (i = 1,2) at [square root of s] = 1.98 TeV.

Caption: FIGURE 7: [[sigma].sub.B+S]/[[sigma].sub.B] - [m.sup.*] plots for [square root of s] = 1.3 TeV (a) and [square root of s] = 1.98 TeV (b). (f = - f' = 1 for the spin-1/2 and [c.sub.iV] = [c.sub.iA] = 0.5 (i = 1,2) for the spin-3/2.)

Caption: FIGURE 8: Contour plots for excited spin-3/2 neutrinos for the [J.sub.1] and [J.sub.2].

Caption: FIGURE 9: Contour plots for excited spin-1/2 neutrinos.
TABLE 1: Branching ratios and total decay width of excited spin-1-2
neutrinos for f = -f' = 1 (f = f' = 1). Here it is taken as [LAMDA] =
[m.sup.*].

[m.sup.*] (GeV)    [GAMMA] (GeV)   % BR ([v.sup.*] [right arrow]
                                             v[gamma])

300                    1.91                   30.5 (0)
500                    3.36                   28.9 (0)
750                    5.12                   28.4 (0)
1000                   6.87                   28.2 (0)
1500                   10.35                  28.1 (0)
2000                   13.82                  28.1 (0)
2500                   17.28                  28.1 (0)
3000                   20.75                  28.1 (0)

[m.sup.*] (GeV)     % BR ([v.sup.*]     % BR ([v.sup.*]
                   [right arrow] vZ)   [right arrow] eW)

300                   10.7 (38.3)         58.9 (61.7)
500                   11.1 (38.9)         60.0 (61.1)
750                   11.3 (39.0)         60.3 (61.0)
1000                  11.3 (39.1)         60.4 (60.9)
1500                  11.4 (39.1)         60.5 (60.9)
2000                  11.4 (39.1)         60.5 (60.9)
2500                  11.4 (39.1)         60.5 (60.9)
3000                  11.4 (39.1)         60.5 (60.9)

TABLE 2: Branching ratios and total decay width of excited spin-3/2
neutrinos with [J.sub.l]. Here it is taken as [c.sub.iV] = [c.sub.iA]
= 0.5 and [LAMBDA] = [m.sup.*].

[M.sup.*] (GeV)   [GAMMA] (GeV)       % BR ([v.sup.*]
                                  [right arrow] v[gamma])

300                   1.21                 24.0
500                   3.89                 12.5
750                   11.11                 6.5
1000                  24.61                 3.9
1500                  78.89                 1.8
2000                 183.50                 1.1
2500                 355.20                 0.7
3000                 611.00                 0.5

[M.sup.*] (GeV)    % BR ([v.sup.*]     % BR ([v.sup.*]
                  [right arrow] vZ)   [right arrow] eW)

300                     34.4                41.6
500                     39.0                48.5
750                     41.2                52.3
1000                    42.1                54.0
1500                    42.8                55.3
2000                    43.1                55.9
2500                    43.2                56.1
3000                    43.3                56.2

TABLE 3: Branching ratios and total decay width of excited spin-3/2
neutrinos with [J.sub.2]. Here it is taken as [c.sub.2V] =
[c.sub.iA] = 0.5 and [LMABDA] = [m.sup.*].

[m.sup.*] (GeV)    [GAMMA] (GeV)       % BR ([v.sup.*]
                                    [right arrow] v[gamma])

300                     0.55                  8.8
500                     2.71                  3.0
750                     9.31                  1.3
1000                   22.21                  0.7
1500                   75.26                  0.3
2000                   178.7                  0.2
2500                   349.2                  0.1
3000                   603.6                  0.1

[m.sup.*] (GeV)     % BR ([v.sup.*]     % BR ([v.sup.*]
                   [right arrow] vZ)   [right arrow] eW)

300                      38.4                 52.8
500                      41.8                 55.3
750                      42.7                 56.0
1000                     43.0                 56.2
1500                     43.3                 56.4
2000                     43.4                 56.5
2500                     43.4                 56.5
3000                     43.4                 56.5

TABLE 4: Statistical significance SS for ep collider with
[square root of s] = 1.3 TeV
for excited spin-1/2 neutrinos and excited spin-3/2 neutrinos with
[J.sub.1] and [J.sub.2].

[m.sup.*] (GeV)   SS(J(1/2))   SS([J.sub.1](3/2))   SS([J.sub.2](3/2))

400                 110.2             75.4                135.6
500                  25.5             30.7                 30.0
600                  5.5              11.9                 7.9
700                  1.0              4.2                  2.2

TABLE 5: Statistical significance SS for ep collider with [square root
of s] = 1.98 TeV for excited spin-1/2 neutrinos and excited spin-3/2
neutrinos with [J.sub.1] and [J.sub.2].

[m.sup.*] (GeV)   SS(J(1/2))   SS([J.sub.1](3/2))   SS([J.sub.2](3/2))

600                  56.3             51.0                235.9
700                  22.4             28.0                 76.5
800                  8.8              15.1                 28.9
900                  3.3              8.04                 12.0
1000                 1.2              4.2                  5.3
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Title Annotation:Research Article
Author:Ozansoy, A.; An, V.; Cetinkaya, V.
Publication:Advances in High Energy Physics
Date:Jan 1, 2017
Words:5166
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