Single production of excited neutrinos at future $e^{+}e^{-}$, $ep$ and $pp$ colliders

We study the potential of the linear collider (LC) with $\sqrt{s}=0.5$ TeV, linac-ring type ep collider (LC$\otimes$LHC) with $\sqrt{s}=3.74$ TeV and the large hadron collider (LHC) with $\sqrt{s}=14$ TeV to search for excited neutrinos through transition magnetic type couplings with gauge bosons. The excited neutrino signal and corresponding backgrounds are studied in detail to obtain accessible mass limits and couplings for these three types of colliders.

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introduction
============

The proliferation of fermionic generations and their complex pattern of masses and mixing angles are expected to be addressed by composite models @Terazawa. A typical consequence of compositeness is the appearance of excited leptons ($l^\star$) and quarks ($q^\star$) @Renard [@Baur; @Hagiwara85]. Charged ($e^{\star},\mu^{\star}$ and $\tau^{\star}$) and neutral ($\nu_{e}^{\star},\nu_{\mu}^{\star}$ and $\nu_{\tau}^{\star}$) excited leptons are predicted by composite models where leptons and quarks have a substructure. Phenomenologically, an excited lepton is defined to be a heavy lepton which shares leptonic quantum number with one of the ordinary leptons.

Current limits on the masses of excited neutrinos are @Hagiwara02: $m_{\star}>99.4$ GeV from LEP (pair production) assuming $f=f'$ @Acciarri, $m_{\star}>171$ GeV from LEP (single production) assuming $f=-f'=\Lambda/m_{\star}$ @Acciarri and $m_{\star}>114$ GeV from HERA (single production) assuming $f=-f^{'}=\Lambda/m_{\star}$ @Adloff.

The production of excited leptons was studied at LEP and HERA energies @Hagiwara85 [@Boudjema] and at hadron colliders @Eboli by taking into account signal and background. The LEP and HERA bounds on excited lepton masses are low enough when compared to the expected scale $\Lambda$ for the compositeness. This motivates us to reanalyze the excited lepton production at the future colliders.

In this paper, we consider the least studied (compared to charged excited lepton production) excited neutrino production in more detail. We take into account signal as well as the backgrounds (with the interference between them) at the similar experimental conditions and compare the potential of each type of colliders to search for the single production of excited neutrinos.

Three types of colliders related to the energy frontiers in particle physics research seem to be promising in the next decade. Namely, they are Large Hadron Collider (LHC) with the center of mass energy $\sqrt{s}=14$ TeV and luminosity $L=10^{34}$cm$^{-2}$s$^{-1}$, linear $e^{+}e^{-}$ collider (LC) with $\sqrt{s}=0.5$ TeV and $L=10^{34}$cm$^{-2}$s$^{-1}$, and linac-ring type ep collider (LC$\otimes$LHC) with $\sqrt{s}=3.74$ TeV and $L=10^{31}$cm$^{-2}$s$^{-1}$ (see @Sultansoy and references therein). Even though the last one has a lower luminosity it can provide better conditions for investigations of a lot of phenomena comparing to LC due to the essentially higher center of mass energy and LHC due to more clear environment. For this reason, different phenomena (compositeness, SUSY, etc.) should be analyzed taking into account all three types of colliders. This work is a continuation of previous work devoted to the study of excited electrons @Cakir03 [@Cakir04].

Excited leptons can be classified by SU(2)$\times$U(1) quantum numbers as sequential type, mirror type and homodoublet type @Hagiwara02. In the present study, we will assume that the excited fermions have spin and isospin 1/2; higher spin and isospin assignments have been discussed in @Kuhn. We assume that excited lepton acquire their masses prior to SU(2)$\times$ U(1) symmetry breaking. Therefore, we consider their left- and right-components in weak isodoublets. The success of QED prediction for $g-2$ and small masses of leptons suggest chirality conservation, i.e., an excited lepton should not couple to both left- and right-handed components of the corresponding lepton. Transition magnetic type couplings between ordinary and excited leptons are described by the effective Lagrangian @Boudjema $$L=\frac{1}{2\Lambda}\bar{l_{R}}^{\star}\sigma^{\mu\nu}
\left[fg\frac{\overrightarrow{\tau}}{2}\cdot\overrightarrow{W}_{\mu\nu}
+f^{'}g^{'}\frac{Y}{2}B_{\mu\nu}\right]l_{L}+h.c.$$ where $\Lambda$ is the scale for the new physics that excited leptons can appear; $W_{\mu\nu}$ and $B_{\mu\nu}$ are the field strength tensors; $\overrightarrow{\tau}$ denotes the Pauli matrices, $Y=-1/2$ is the hypercharge; $g$ and $g^{'}$ are the SM gauge couplings of SU(2) and U(1), respectively; the constants $f$ and $f^{'}$ are the scaling factors for the corresponding gauge couplings.

The effective lagrangian gives rise to the following excited neutrino-lepton-gauge boson vertices: $$\begin{aligned}
V_{\alpha}^{\nu^{*}\nu\gamma}
&=&\frac{g_{e}(f-f^{^{\prime}})I_{3}}
{2\Lambda}q^{\beta}\sigma_{\alpha\beta}
(1-\gamma_{5})\nonumber\\
V_{\alpha}^{\nu^{*}\nu Z} & =&\frac{g_{e}(f\cot\theta_{W}
+f^{^{\prime}}\tan\theta_{W})I_{3}}{2\Lambda}q^{\beta}\sigma_{\alpha\beta}(1-\gamma_{5})\nonumber\\
V_{\alpha}^{\nu^{*}eW} & =&\frac{g_{e}f}{2\sqrt{2}
\Lambda\sin\theta_{W}}q^{\beta}\sigma_{\alpha\beta}(1-\gamma_{5})\end{aligned}$$

For an excited neutrino, three decay modes are possible: radiative decays $\nu^{\star}\rightarrow \nu\gamma$, neutral currents decays $\nu^{\star}\rightarrow \nu Z$ and charged current decays $\nu^{\star}\rightarrow e W$. Neglecting ordinary lepton masses the decay widths are obtained as $$\Gamma(\nu^{\star}\rightarrow (e,\nu)V)=\frac{\alpha m_{\star}^{3}}{4\Lambda^{2}}
f_{V}^{2}\left(1-\frac{m_{V}^{2}}{m_{\star}^{2}}\right)^{2}\left(1+\frac{m_{V}^{2}}{2m_{\star}^{2}}\right)$$ where $f_V\equiv (f_{\gamma}=(f-f^{'})/2$, $f_{W}=f/(\sqrt{2}\sin\theta_{W})$ and $f_{Z}=(f\cot\theta_{W}+f^{'}\tan\theta_{W})/2$); $m_V$ is the mass of the gauge boson; $\alpha$ is the electromagnetic coupling constant defined by $g_e=\sqrt{4\pi\alpha}$. The total decay width of the excited neutrino is $\Gamma=1.0$ (6.9) GeV for $m_\star=200$ (1000) GeV at $f=f^{'}=1$ and $\Lambda=m_\star$. The branching ratios (BR) of excited neutrino into ordinary leptons and gauge bosons $\gamma,Z,W$ are given in Fig. \[fig1\]. For large values of the excited neutrino mass, the branching ratio for the individual decay channels reaches to the constant values: 61% for the $W$-channel, 39% for the $Z$-channel while the photon channel vanishes at $f=f^{'}=1$ . At $f=-f^{'}=1$ the radiative decay is allowed for excited neutrino whereas it is forbidden for excited electron. In this case, branchings will be 61% for $W$-channel, 11% for $Z$-channel and 28% for photon channel at higher excited neutrino masses ($m_*>500$ GeV). Therefore, the dominating signature of $\nu^\star\to W^+e^-$ is preferable for the investigation of excited neutrino in future experiments.

![The branching ratios BR (%) depending on the mass of excited neutrino for $f=f'=1$ (thick curves) and $f=-f'=1$ (thin curves). \[fig1\]](fig1.eps)

Single production of excited neutrinos
======================================

We analyze the potentials of the LC, LC$\otimes$LHC and LHC machines to search for excited neutrinos (or antineutrinos) via the single production reactions $$e^{+}e^{-}\rightarrow \nu^{\star}\bar{\nu}$$ $$e^{-}p\rightarrow \nu^{\star}q(\bar{q})X$$ $$pp\rightarrow \nu^{\star}e^+X \qquad\textrm{and\qquad}
pp\rightarrow \nu^{\star}\bar\nu X$$

For a comparison of different colliders, the signal cross sections for the processes given above are presented in Fig. \[fig2\] assuming the scale $\Lambda=m_{*}$ and the coupling parameters $f=f^{'}=1$.

The possible final states for the signal at three different collisions are given in Table \[table1\]. As can be seen from Table \[table1\] the radiative decays $\nu^{\star}\rightarrow
\nu\gamma$ and neutral currents decays $\nu^{\star}\rightarrow \nu
Z$ will result in larger uncertainty due to the missing transverse momentum, whereas charged current decays $\nu^{\star}\rightarrow e
W$ leads to a better reconstruction for the signal. In this study, we consider the subsequent decay of excited neutrino (or antineutrino) into a W-boson and an electron (or positron). Therefore, we deal with the process $e^{+}e^{-}\rightarrow
W^+e^{-}\bar\nu$, and subprocesses $e^{-}q(\bar{q'})\rightarrow
W^+e^{-}q(\bar{q})$, $q\bar{q}\rightarrow W^+e^{-}\bar\nu$ and $q\bar{q'}\rightarrow W^+e^{-}e^+$. The signal and background were simulated at the parton level by using the program CompHEP 4.2 @Pukhov (the interference terms between signal and background processes are taken into account in the program). In our calculations, we used the parton distribution functions library CTEQ6L @Lai with the factorization scale $Q^{2}=\hat{s}$.

![The total cross sections for the single production of excited neutrino with $\Lambda=m_*$ and $f=f^{'}=1$ at $e^{-}e^{+}$ collider with $\sqrt{s}=0.5$ TeV, $ep$ collider with $\sqrt{s}=3.74$ TeV and $pp$ collider with $\sqrt{s}=14$ TeV. \[fig2\]](fig2.eps)

$e^{+}e^{-}$ Collider
---------------------

High energy electron-positron collisions provide an excellent environment for the search for excited leptons. We examine the single production of excited neutrinos ($\nu^{\star}$) at future $e^{-}e^{+}$ colliders with $\sqrt{s}=500$ GeV, through the process $e^{-}e^{+}\rightarrow \nu^{\star}\bar\nu\rightarrow
W^+e^{-}\bar\nu$. The Feynman diagram for the process $e^{-}e^{+}\rightarrow \nu^{\star}\bar\nu$ is shown in Fig. \[fig3\].

![Excited neutrino production at $e^{-}e^{+}$ colliders through the (a,b) $s-$channel and (c) $t-$ channel exchange diagrams.\[fig3\]](fig3.eps)

$$\begin{aligned}
\frac{d\sigma}{dt} =\frac{g_{e}^{4}}{64\pi s^{2}\Lambda^{2}}
[&-&\frac{2f_{W}^{2}(m_{*}^{2}-s)(m_{*}^{2}-s-t)t}{\sin^{2}\theta_{W}(m_{W}^{2}-t)^{2}}-
\frac{\sqrt{2}(-1+2c_{V})f_{W}f_{Z}st(-m_{*}^{2}+s+t)}
{\cos\theta_{W}(m_{Z}^{2}-s)\sin^{2}\theta_{W}(m_{W}^{2}-t)}\nonumber\\
& -&\frac{4\sqrt{2}f_{\gamma}f_{W}t(-m_{*}^{2}+s+t)}
{\sin\theta_{W}(m_{W}^{2}-t)}
-\frac{4f_{\gamma}^{2}\left[m_{*}^{4}+2t(s+t)-m_{*}^{2}(s+2t)\right]}{s}\nonumber\\
&
+&\frac{f_{Z}^{2}s\left[-(1-2c_{V})^{2}m_{*}^{4}-2(1+4c_{V}^{2})t(s+t)+(1-2c_{V})^{2}m_{*}^{2}(s+2t)\right]}
{4\cos^{2}\theta_{W}(m_{Z}^{2}-s)^{2}\sin^{2}\theta_{W}}\nonumber\\
&-&\frac{2f_{\gamma}f_{Z}\left[(-1+2c_{V})m_{*}^{4}+4c_{V}t(s+t)
-(-1+2c_{V})m_{*}^{2}(s+2t)\right]}
{\cos\theta_{W}(m_{Z}^{2}-s)\sin\theta_{W}} ]\end{aligned}$$

We applied the following acceptance cuts to form the signal and reduce the backgrounds $$p_{T}^{e^\pm,j}>20\textrm{ GeV}$$ $$|\eta_{e^{\pm,j}}|<2.5$$ where $p_{T}$ is the transverse momentum of the visible particle or the missing transverse momentum when a neutrino is produced. $\eta$ stands for the pseudo-rapidity of the visible particles. After applying these cuts, the SM background cross section is found to be $\sigma_B=0.89$ pb. For the W-boson decay we choose the case $W\to$2 jets. In the case of leptonic decays of W-boson the final state of the process consists of two neutrinos giving a large uncertainty in the excited neutrino mass reconstruction. The $\nu^\star\to W^+e^-$ decay of excited neutrino can be easily identified since the invariant mass of the $ejj$ system shows a peak around the excited neutrino mass. Fig. \[fig4\] shows the invariant mass $m_{ejj}$ distribution in the reaction $e^{+}e^{-}\rightarrow W^+e^{-}\bar\nu$ for the SM background and with the inclusion of an excited neutrino with masses $m_{\star}=200$ GeV, $m_{\star}=300$ GeV, $m_{\star}=400$ GeV and parameter $f=f^{'}=1$.

![Invariant mass $m_{ejj}$ distribution of signal (the scale $\Lambda=m_{*}$ and the coupling parameters $f=f^{'}=1$) and the corresponding background at $e^{-}e^{+}$ collider.\[fig4\]](fig4.eps)

A natural way of extracting the excited neutrino signal, and at the same time suppressing the SM backgrounds is to impose a cut on the $ejj$ invariant mass. Therefore, we introduced the cut $$|m_{ejj}-m_{\star}|<25\textrm{ GeV}$$ for considered range of excited neutrino masses. In Table \[table2\], we have presented the signal (for $f=f^{'}=1$) and background cross sections in $ejj$ invariant mass bins since the signal is concentrated in a small region proportional to the invariant mass resolution. In order to examine the potential of the collider to search for the excited neutrinos, we defined the statistical significance $SS$ of the signal $$SS=\frac{\left|\sigma_{S+B}-\sigma_{B}\right|}{\sqrt{\sigma_{B}}}\sqrt{L_{int}}$$ where $L_{int}$ is the integrated luminosity of the collider. The values of $SS$ evaluated at each excited neutrino mass points are shown in the last column of Table \[table2\]. As seen from the Table \[table2\], the calculated $SS$ values are higher than 5 up to the center of mass energy of the LC. Single production of excited neutrinos is feasible up to the center of mass energy of $e^{+}e^{-}$ collider even with fairly small magnetic transition couplings to the leptons. For various coupling parameters $f(=f^{'})$, we give the $SS$ values in Fig. \[fig5\]. Concerning the criteria above (SS&gt;5), even for smaller coupling as $f=f^{\prime}=0.1$ excited neutrinos with masses up to 450 GeV can be probed at the LC. We could compare the results for the cases $f=f^{'}=1$ and $f=-f^{'}=1$ to see the effects of photon coupling $f_\gamma$ in excited neutrino production mechanism. We find decreases about (15-5)% in the cross sections for the values of excited neutrino mass intervals $m_\star=200-400$ GeV. Because of the high energy of electron/positron beams, initial state radiation (ISR) can affect the production cross sections. We find 10% decrease in the signal+background cross section up to the kinematical energy range of the collision.

<span>|c|c|c|c|</span> $m_{\star}$(GeV)& $\sigma_{S+B}$(pb)& $\sigma_{B}$(pb)& $SS$200& $7.51\times10^{0}$& $6.66\times10^{-2}$& 9120.8250& $5.04\times10^{0}$& $6.53\times10^{-2}$& 6156.2300& $3.34\times10^{0}$& $7.01\times10^{-2}$& 3905.5350& $2.15\times10^{0}$& $8.81\times10^{-2}$& 2196.7400& $1.45\times10^{0}$& $1.25\times10^{-1}$& 1185.1450& $9.53\times10^{-1}$& $1.75\times10^{-1}$& 588.1475& $6.11\times10^{-1}$& $1.68\times10^{-1}$& 341.8

![Statistical significance depending on the excited neutrino mass and coupling parameters ($f=f^{'}$) at the LC for the scale $\Lambda=m_{*}$.\[fig5\]](fig5.eps)

$ep$ Collider
-------------

The magnetic transition couplings of excited neutrino to the electron allows single production of $\nu^{\star}$ through $t$-channel $W$ boson exchange. The Feynman diagrams for the subprocess $e^{-}q\rightarrow \nu^{\star}q'$ and $e^{-}\overline{q'}\rightarrow \nu^{\star}\overline{q}$ are shown in Fig. \[fig6\].

![Single production of excited neutrinos at $ep$ colliders through the subprocesses (a) $e^{-}q\rightarrow \nu^{*}q'$ and (b) $e^{-}\overline{q'}\rightarrow \nu^{*}\overline{q}$.\[fig6\]](fig6.eps)

$$\begin{aligned}
\frac{d\hat{\sigma}}{d\hat{t}}=\frac{f_{W}^{2}\,g_{e}^{4}\,\hat{t}\,
\left(\hat{s}+\hat{t}\right)\,|U_{ij}|^{2}}{32\,\pi\,
\hat{s}{\Lambda}^{2}\,\sin^{2}\theta_{W}\,
{\left(m_{W}^{2}-\hat{t}\right)}^{2}}\end{aligned}$$

After the acceptance cuts the total SM background cross section is obtained as $\sigma_{B}=1.11$ pb. Fig. \[fig7\] shows the invariant mass $m_{ejj}$ distribution in the reaction $e^{-}q\rightarrow W^{+}e^-\bar\nu$ for the SM background and the signal (for $f=f^{'}=1$) with the inclusion of an excited neutrino with masses $m_{*}=400$ GeV, $m_{*}=800$ GeV and $m_{*}=1200$ GeV.

![Invariant mass $m_{ejj}$ distribution of signal ($\Lambda=m_{*}$ and $f=f^{'}=1$) and background at $e^{-}p$ colliders.\[fig7\]](fig7.eps)

In Table \[table3\], we present the signal and background cross sections in $ejj$ invariant mass bins satisfying the condition $|m_{ejj}-m_{*}|<25\textrm{ GeV}$ for the mass range $m_{*}=200-1200$ GeV and $|m_{ejj}-m_{*}|<50\textrm{ GeV}$ for $m_{*}=1200-1500$ GeV. For various coupling parameters $f(=f^{'})$, we show the mass dependence of the $SS$ in Fig. \[fig8\]. As can be seen from Table \[table3\] LC$\otimes$LHC can discover excited neutrino in $\nu^{*}\rightarrow W^+e^-$ decay mode for $f=f^{'}=1$ up to the mass of 1300 GeV. If we take $f=-f^{'}=1$ and $\lambda=m_\star$, we find almost the same signal cross sections for higher masses as $m_\star >500$ GeV. However, a decrease in the cross section about 10% is obtained at $m_\star=200$ GeV. The effects from ISR is found to be 5% decrease in the signal+background cross section. One can conclude that the results obtained for the LC$\times$LHC turns out to be at least an order of magnitude more stringent than the present best limits coming from the HERA experiments.

<span>|c|c|c|c|</span> $m_{*}$(GeV)& $\sigma_{S+B}$(pb)& $\sigma_{B}$(pb)& $SS$200& $2.96\times10^{1}$& $1.04\times10^{-1}$& 914.6400& $4.31\times10^{0}$& $4.46\times10^{-2}$& 201.9600& $1.12\times10^{0}$& $2.09\times10^{-2}$& 76.03800& $3.62\times10^{-1}$& $9.71\times10^{-3}$& 35.71000& $1.32\times10^{-1}$& $5.30\times10^{-3}$& 17.41200& $5.41\times10^{-2}$& $5.93\times10^{-3}$& 6.251500& $1.35\times10^{-2}$& $2.50\times10^{-3}$& 2.20

![Statistical significance depending on the excited neutrino mass for different coupling parameters ($f=f^{'}$) for the process $e^{-}p\rightarrow W^+e^{-}q(\bar{q})X$ at the LC$\otimes$LHC.\[fig8\]](fig8.eps)

$pp$ Collider
-------------

At the LHC, the single production of excited neutrinos takes place through the subprocesses $q\bar{q}\rightarrow
Z^*/\gamma^*\rightarrow \nu^{*}\bar\nu\rightarrow W^+e^{-}\bar\nu$ and $q\bar{q}^{'}\rightarrow W^{+}\rightarrow \nu^{*}e\rightarrow
W^+e^-e^+$ via the Drell-Yan mechanism. The diagrams related to these subprocesses are shown in Fig. \[fig9\]. After the acceptance cuts the total SM background cross sections are obtained as $\sigma_{B}=2.73$ pb for the process $pp\rightarrow
W^{+}e^{-}\bar\nu X$ and $\sigma_{B}=0.19$ pb for $pp\rightarrow
W^+e^-e^{+}X$.

![Excited neutrino production via the (a,b) photon and $Z-$boson exchange, and (c) $W^{+}$ boson exchange diagrams at hadron colliders.\[fig9\]](fig9a.eps "fig:")\

![Excited neutrino production via the (a,b) photon and $Z-$boson exchange, and (c) $W^{+}$ boson exchange diagrams at hadron colliders.\[fig9\]](fig9b.eps "fig:")\

(c)

$$\begin{aligned}
\frac{d\widehat{\sigma}}{d\widehat{t}}(q\overline{q}
\rightarrow\nu^{*}\overline{\nu})&=&\frac{g_{e}^{4}}{1024\pi\widehat{s}^{2}\Lambda^{2}}[
-\frac{64f_{\gamma}^{2}Q_{q}^{2}[m_{*}^{2}
+2\widehat{t}(\widehat{s}+\widehat{t})-m_{*}^{2}(\widehat{s}+2\widehat{t})]}{\widehat{s}} \\
&+&\frac{64f_{\gamma}f_{Z}Q_{q}[c_{A}m_{*}^{2}(m_{*}^{2}-\widehat{s}-2\widehat{t})+c_{V}[m_{*}^{4}
+2\widehat{t}(\widehat{s}+\widehat{t})-m_{*}^{2}(\widehat{s}+2\widehat{t})]]}{\cos\theta_{W}\sin\theta_{W}
(m_{Z}^{2}-\widehat{s})} \nonumber \\
&+&\frac{f_{Z}^{2}s[2c_{A}c_{V}m_{*}^{2}(-m_{*}^{2}+\widehat{s}+2\widehat{t})-(c_{A}^{2}+c_{V}^{2})
(m_{*}^{4}+2\widehat{t}(\widehat{s}+\widehat{t})-m_{*}^{2}(\widehat{s}+2\widehat{t}))]}{\cos^{2}\theta_{W}
\sin^{2}\theta_{W}(m_{Z}^{2}-\widehat{s})^{2}}]\nonumber\end{aligned}$$

$$\begin{aligned}
\frac{d\widehat{\sigma}}{d\widehat{t}}(q\overline{q^{\prime}}\rightarrow\nu^{*}l^{+})=\frac{f_{W}^{2}g_{e}^{4}(m_{*}^{2}-\widehat{s}-\widehat{t})(-m_{*}^{2}+\widehat{t})|U_{ij}|^{2}}{64\pi\widehat{s}\Lambda^{2}\sin^{2}\theta_{W}(m_{W}^{2}-\widehat{s})^{2}}\end{aligned}$$

Fig. \[fig10\] shows the invariant mass $m_{ejj}$ distributions in the reactions $pp\rightarrow W^+e^{-}e^+ X$ for the SM background and the signal (for $f=f^{'}=1$) with masses of $m_{*}=400$ GeV, $m_{*}=800$ GeV and $m_{*}=1200$ GeV. In Table \[table4\], we present the signal and background cross sections in $ejj$ invariant mass bins satisfying the condition $|m_{ejj}-m_{*}|<25\textrm{ GeV}$ for excited neutrino mass $m_{*}=200-1200$ GeV and $|m_{ejj}-m_{*}|<50\textrm{ GeV}$ for $m_{*}=1200-2000$ GeV. Statistical significance SS are shown in Fig. \[fig11\] for $pp\rightarrow W^+e^{-}e^{+} X$ process with different couplings $f(=f')$. For the parameters $f=-f^{'}=1$, we find a maximum decrease about 5% in the signal cross sections for the considered range of excited neutrino masses. Relatively weak limits on the masses and couplings are obtained for the process $pp\rightarrow W^+e^{-}\bar\nu X$. One can conclude that the LHC will be able to extend considerably the range of excited neutrino masses up to about 1.85 TeV.

![Invariant mass $m_{ejj}$ distribution of signal and background for the processes $pp\rightarrow W^+e^{-}e^{+} X$ at $pp$ collider (LHC).\[fig10\]](fig10.eps)

<span>|c|c|c|c|c|c|c|</span> process$\rightarrow$& & $m_{*}$(GeV)& $\sigma_{S+B}$(pb)& $\sigma_{B}$(pb)& $SS$& $\sigma_{S+B}$(pb)& $\sigma_{B}$(pb)& $SS$200& $7.70\times10^{-1}$& $4.98\times10^{-2}$& 1074.0& $7.34\times10^{-1}$& $4.65\times10^{-1}$& 124.7400& $7.10\times10^{-2}$& $7.16\times10^{-3}$& 256.9& $5.90\times10^{-2}$& $4.67\times10^{-2}$& 17.9600& $1.53\times10^{-2}$& $1.61\times10^{-3}$& 116.3& $1.20\times10^{-2}$& $8.33\times10^{-3}$& 12.7800& $4.57\times10^{-3}$& $5.02\times10^{-4}$& 62.3& $3.03\times10^{-3}$& $2.45\times10^{-3}$& 3.71200& $7.50\times10^{-4}$& $1.64\times10^{-4}$& 17.1& $5.49\times10^{-4}$& $7.13\times10^{-4}$& 1.91600& $1.65\times10^{-4}$& $3.66\times10^{-5}$& 7.9& $-$& $-$& $-$2000& $4.15\times10^{-5}$& $9.96\times10^{-6}$& 3.8& $-$& $-$& $-$

![Statistical significance depending on the excited neutrino mass for the process $pp\rightarrow W^+e^{-}e^{+} X$ with different couplings $f(=f')$ at the LHC.\[fig11\]](fig11.eps)

Conclusion
==========

In our analysis, we assumed that the excited neutrino interact with the SM particles via the effective Lagrangian (1). We restrict ourselves to the gauge interactions since the aim of this paper is to compare the potential of three types of colliders within the similar sets of cuts. Our results coincide with @Boudjema where similar analysis was performed for the LC, and essentially coincide with @Belyaev where the mass range accessible with LHC was obtained. Finally, our analysis show that for relatively small masses ($m_*<450$ GeV) LC is more promising than LC$\otimes$LHC and the LHC for the processes considered. The LHC can probe higher masses of excited neutrinos and smaller couplings than the LC and LC$\times$LHC can do.

We may conclude from Table \[table4\] that the $W^+e^-\nu$ final state in $e^+e^{-}$ and $pp$ collisions has both excited neutrino and excited electron contribution. However, $W^+e^-q$ and $W^+e^-e^+$ final state in $e^{-}p$ and $pp$ collisions isolate the excited neutrino contribution. Focusing on the $2j$+opposite sign leptons signal in $pp$ collision and $3j$+a lepton signal (by requiring a peak in the $ejj$ invariant mass distribution and reconstructing $W$-mass from two jets) excited neutrino can be probed at the detectors built on the future colliders.

We give the realistic estimates for excited neutrino signal and the corresponding background at three-type of colliders with the availability of higher center of mass energies and higher luminosities. Since the cross section for the signal is proportional to $1/\Lambda^{2}$, various choices of the $\Lambda$, i.e., in this study we have choosen $\Lambda=m_{*}$, will lead to the changes in the cross sections as $(m_{*}/\Lambda)^{2}.$ For $\Lambda=1$ TeV, we need to multiply the signal cross sections by a factor <span>\[</span>$m_{*}$(TeV)<span>\]</span>$^{2}$ at every mass values of excited neutrinos. Our analysis show that for $f=f^{'}=1$ the LC can discover excited neutrino in $\nu^{*}\rightarrow W^+e^-$ decay mode up to the kinematical limit, while LC$\otimes$LHC and LHC can reach much higher mass values, namely 1300 GeV and 1850 GeV, respectively. For $f=f^{'}=0.1$ discover limits are: 450 GeV at LC, 275 GeV at LC$\otimes$LHC and 350 frodriguez@example.org.

This work is partially supported by Turkish State Planning Committee under the Grants No 2003K120190.

<span>99</span> H. Terazawa, Y. Chikashige and K. Akama, Phys. Rev. D **15**, 480 (1977); Y. Ne'eman, Phys. lett. B **82**, 69 (1979); H. Terazawa, M. Yasue, K. Akama and M. Hayashi, Phys. Lett. B **112**, 387 (1982); F. M. Renard, Il Nuovo Cimento A **77**, 1 (1983); E.J. Eichten, K.D. Lane and M.E. Peskin, Phys. Rev. D **50**, 811 (1983); A. De Rujula, L. Maiani and R. Petronzio, Phys. Lett. B **140**, 253 (1984); J. Kühn and P.M. Zerwas, Phys. Lett. B 147, 189 (1984). K. Hagiwara, S. Komamiya, and D. Zeppenfeld, Z. Phys. C **29**, 115 (1985). U. Baur, M. Spira and P.M. Zerwas, Phys. Rev. D **42**, 815 (1990). K. Hagiwara et al., Particle Data Group, Phys. Rev. D **66**, 010001 (2002). M. Acciarri et al., L3 Coll., Phys. Lett. B **502**, 37 (2001). C. Adloff et al., H1 Coll., Eur. Phys. J. C **17**, 567 (2000). F. Boudjema, A. Djouadi and J.L. Kneur, Z. Phys. C **57**, 425 (1993); F. Boudjema, A. Djouadi, Phys. Lett. B **240**, 485 (1990). O.J.P. Eboli, S.M. Lietti and P. Mathews, Phys. Rev. D **65**, 075003 (2002). S. Sultansoy, Eur. Phys. J. C **33**, s1064 (2004). O. Cakir *et al.*, Eur. Phys. J. C **30**, d01, 005 (2003). O. Cakir, A. Yilmaz and S. Sultansoy, hep-ph/0403307. J. Kuhn, P.M. Zerwas, Phys. Lett. B **147**, 189 (1984). A. Pukhov *et al.*, hep-ph/9908288 (1999). H.L. Lai et al., CTEQ Collab., Phys. Rev. D **51**, 4763 (2000). A. Belyaev, C. Leroy and R. Mehdiyev, hep-ph/0401066.

[^1]: frodriguez@example.org

[^2]: frodriguez@example.org

[^3]: frodriguez@example.org

{'source': 'arXiv_out/hep-ph0408171_extract_excited_neutrino_v2'}