

 25 Oct 1995

cfl1993 BELYAEV A.S., BOOS E.E EXCITED NEUTRINO AT NEXT LINEAR COLLIDERS

NUCLEAR PHYSICS INSTITUTE, MOSCOW STATE UNIVERSITY

119899 MOSCOW, RUSSIA

The possibility of single and pair excited neutrino production in high energy e+e

\Gamma ; fle and flfl collisions on

linear colliders is studied. The integrated cross sections of these subproceses are calculated. Special attention is paid to search for excited neutrino in fle

\Gamma ! W\Gamma W+e\Gamma process. Lower limits for the compositeness parameter

estimated which will be available on the experiments at VLEPP, SLAC, JLC and DESY future linear colliders.

1. Introduction Standard Model (SM) at present is in a good agreement with present experimental data. But from the theoretical point of view SM has a number of shortcomings and thus can not be considered as a complete theory of elementary particles.

The natural scale of the possible "new" physics wich comes, in particular, from the analysis of W and Z longitudinal components scattering amplitudes, from the analysis of the g \Gamma 2 properties of electron and muon, and from the estimation of quark and lepton radii (high energy e+e\Gamma and qq collisions) is a value of \Lambda 1 TeV.

At present great attention is paid to study of possible compositeness of leptons and quarks. One of the signals of compositeness independent of concrete model should be the existing of the excited fermion states. Masses of the excited quark and lepton states are expected to be of order \Lambda and can be in the interval 0:1 \Gamma 1 TeV.

Analysis of experiments at present energies gives restrictions on the possible scale of the compositeness of the excited leptons shown in Table 1 (see [1] ):

Table 1: Scale limits for contact interactions. Type Value(TeV) Cl(%) collab. \Lambda +LL(eeee) ? 1:4 95 88 TASSO \Lambda \Gamma LL(eeee) ? 3:3 95 88 TASSO \Lambda +LL(ee__) ? 4:4 95 86 JADE \Lambda \Gamma LL(ee__) ? 2:1 95 86 JADE \Lambda +LL(eeo/ o/ ) ? 2:2 95 86 JADE \Lambda \Gamma LL(eeo/ o/ ) ? 3:2 95 86 JADE \Lambda \Sigma LR(_*_e*e) ? 3:10 90 86 LBL,NWES

TRIUMF \Lambda +LL(eeqq) ? 1:7 95 91 CDF \Lambda \Gamma LL(eeqq) ? 2:2 95 91 CDF \Lambda +LL(__qq) ? 1:4 95 92 CDF \Lambda \Gamma LL(__qq) ? 1:6 95 92 CDF \Lambda (qqqq) ? 0:825 95 91 UA2

On the other hand analysis of experiments at LEP imposes restrictions on the masses of the excited charged leptons [1] given in Table 2.

There is a large number of papers which consider the excited lepton production in e+e\Gamma collisions (for example, [2, 3]). But it is necessary to point out that colliders of alternative type - fle and flfl colliders - give new possibilities for investigation of some physical phenomena (production of excited leptons and quarks, color excitation of Z bosons, Higgs production, polarization phenomena) compared to e+e\Gamma colliders. In particular, the most preferable reaction for search of the excited electron is fle ! e\Lambda [3]. This type of colliders based on using of the high energy photons generated by Compton back-scattering of laser light [4]. Practical realization of fle and flfl colliders based on the corresponding e+e\Gamma linear colliders is under consideration in the framework of VLEPP, JLC and SLAC projects.

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Table 2: Mass limits for excited charged leptons. (* = ml\Lambda =\Lambda ) Type Value(GeV) Cl(%) Comment *Z e(e\Lambda ) ? 91:0 95 e+e\Gamma ! Z ! e\Lambda e, 92 ALEPH ? 1

? 44:6 95 e+e\Gamma ! Z ! e\Lambda e\Lambda , 92 ALEPH ? 1 ? 116 95 from e+e\Gamma ! e\Lambda (t \Gamma channel) ! ee, ? 1

91 OPAL(indirect effect) ? 1 _(_\Lambda ) ? 91:0 95 e+e\Gamma ! Z ! _\Lambda _, 92 ALEPH ? 1

? 46:1 95 e+e\Gamma ! Z ! _\Lambda _\Lambda , 92 ALEPH ? 1 o/ (o/ \Lambda ) ? 90:0 95 e+e\Gamma ! Z ! o/ \Lambda o/ , 92 ALEPH ? 1

? 46:0 95 e+e\Gamma ! Z ! o/ \Lambda o/ \Lambda , 92 ALEPH ? 0:18

Some theoretical papers consider excited lepton production at e+e\Gamma , pp [3], fle and flfl [5] future colliders. The main results of [3, 5] are the following: if compositeness of leptons is realized at a scale ^ O(10 TeV), excited lepton states can be found in e+e\Gamma and fle collisions with masses up to maximal available energy ps. In [3] it is also said that the lower limit for excited charged leptons at LHC can be reached up to 4 TeV (ps = 16 TeV; \Lambda ^ 10 TeV). Interesting aspects of excited neutrino production at Z pole (Z ! *e*\Lambda e , LEP I) was a subject of paper [6]. This paper gives the following upper limit on the possible masses of the excited neutrino: up to 90 GeV if * = ml\Lambda =\Lambda = 0:09.

Here we consider the least studied (compared to charged lepton production) excited neutrino production in more detail in e+e\Gamma ; fle and flfl collisions in the TeV energy region. These excited neutral states are supposed to be the isospin 1=2 partners to the much studied excited charged leptons and have spin 1=2 in the most simple realization of models (higher spin and isospin assignments have been also discussed elsewhere [7]). Transition between the ordinary light fermions and the excited ones and also between both excited fermions are described in SU(2)\Omega U(1) invariant form by the following effective Lagrangian [8]:

L1eff = _`\Lambda fl_(g o/2 W _ + g0 Y2 B_)`\Lambda ; (1)

L2eff = 12\Lambda _`\Lambda Roe_* (fg o/2 W _* + f0g0 Y2 B_*)`L + h:c:; (2) where g and g0 are the usual SU(2) and SU(1) weak couplings; o/ denotes the Pauli matrices; `\Lambda and ` are isodoublets of the excited and usual leptons respectively; constants f and f0 are supposed to be of order unity.

Using this model we consider the following processes of single and pair production of the excited neutrino:

e+e\Gamma ! *\Lambda _* (3) fle\Gamma ! *\Lambda W\Gamma (4)

e+e\Gamma ! *\Lambda _*\Lambda (5)

flfl ! *\Lambda _*\Lambda (6)

For processes (3), (4) and (5) we put f = f0 = 1, while for process (6) we put f = 1, f0 = \Gamma 1, because the (f \Gamma f0) factor for the vertex fl*e_*\Lambda e eliminates it in the case of f = f0 = 1. Moreover, the analysis of the future experiments on flfl collisions would be very important for the determination of f and f0, because the cross section in this case is proportional to (f \Gamma f0)2.

The main question which is discussed here is the sensitivity of the future experiments in the TeV region to the signals from the excited neutrino certainly it is connected with the limits on the values of \Lambda and m*

e\Lambda .It should be pointed out that all calculations here both analytical and numerical have been done with the aid of

CompHEP software package [9], the present version of which performs the following principal operations: 1. analytic calculations of squared matrix elements (with the aid of Feynman rules) of the process 1 ! 2, 2 ! 2, 2 ! 3 in the first order of any input model; 2. numeric integration of such processes and graphic presentation of the final results (for 2 ! 3 proceses with the help of BASES integrated pakage wich is connected with CompHEP through special interface).

2

e+e

\Gamma ! *\Lambda _*

@@

@

e+

\Gamma \Gamma \Gamma e \Gamma

. .^

Z \Gamma \Gamma \Gamma

*

\Lambda

e

@@

@ _*e

@@

@

e+

) )(

W+

\Gamma \Gamma

\Gamma

_*

\Lambda

e

\Gamma \Gamma \Gamma e \Gamma @@@ *e

fle

\Gamma ! *\Lambda W\Gamma

@@

@

e

\Gamma

) )(

W

\Gamma

\Gamma \Gamma

\Gamma

*

\Lambda

e

\Psi \Psi ffff fl

\Phi \Phi \Omega

\Omega W

\Gamma

@@

@

e

\Gamma

@@

@ *

\Lambda

e

\Psi \Psi ffff fl

\Psi \Psi ffff

W

\Gamma

@@

@

e

\Gamma

\Psi \Psi ffff fl

e

\Gamma ; e\Lambda \Gamma

\Gamma \Gamma

\Gamma

*

\Lambda

e

\Phi \Phi \Omega

\Omega W

\Gamma

e+e

\Gamma ! *\Lambda _*\Lambda

@@

@

e+

\Gamma \Gamma \Gamma e \Gamma

. .^

Z \Gamma \Gamma \Gamma

*

\Lambda

e

@@

@ _*

\Lambda

e

@@

@

e+

) )(

W+

\Gamma \Gamma

\Gamma

_*

\Lambda

e

\Gamma \Gamma \Gamma e \Gamma @@@ *\Lambda

e

flfl ! *

\Lambda _*\Lambda

\Phi \Phi \Omega

\Omega fl

\Gamma \Gamma

\Gamma

*

\Lambda

e

_*e \Psi \Psi ffff fl

@@

@ _*

\Lambda

e

3

2. Decay modes Decay widths and thus the branching ratios for excited neutrino which could be obtained by straightforward calculations from (2) and represented by the following expression :

\Gamma (*\Lambda e ! *e(e)V) = ff4 m

3*

e\Lambda

\Lambda 2 f

2 V 1 \Gamma M

2V

m2*

e\Lambda !

2

1 + M

2V

2m2*

e\Lambda !

; (7)

where

V = fl; Z or W; ffl = f \Gamma f

0

2 ; fZ =

fc2W + f0s2W

2sWcW ; fW =

fp 2sW ; sW and cW being sin and cos of Weinberg angles. In Tables 3 we present decay modes and the corresponding branching ratios of the excited neutrino *\Lambda e (for m*

e\Lambda =0.1, 0.5 and 1.0 TeV) when f = 1, f

0 = 1 and f = 1, f0 = \Gamma 1.

Table 3: Branching ratios for the excited neutrino decay (f = 1).

Branching ratios Total

decay m*

e\Lambda *

\Lambda e ! eW *

\Lambda e ! *Z *

\Lambda e ! *fl width(GeV)(GeV)

f = f

0 f = \Gamma f0 f = f0 f = \Gamma f0 f = f0 f = \Gamma f0 f = f0 f = \Gamma f0

100 0.866 0.268 0.134 0.012 0 0.720 0.00084 0.0027 500 0.610 0.602 0.390 0.115 0 0.283 0.85 0.86 1000 0.608 0.606 0.392 0.117 0 0.277 7.0 7.1

It is seen from Table 3 that dominating decay channel is *\Lambda e ! eW. So the more preferable method of searching of the excited neutrino through its decay into electron and W-boson, which decay then in two jets (it is dominating decay channel of W-boson with branching 80 %).

3. Pair and single excited neutrino production

1. General remarks It is worth noting that for e+e\Gamma colliders with c.m. energies 0.5, 1.0 and 2.0 TeV the respective effective energies for efl and flfl collisions will be approximately the following: 0.375, 0.750, 1.5 TeV for efl collisions (i.e. psefl = 0:75pse+e\Gamma ) and 0.350, 0.700, 1.4 TeV for flfl collisions (i.e. psflfl = 0:7pse+e\Gamma ). Of course strictly speaking it is necessary to fold the cross section with the real fl-beam energy spectrum and it will be done in future, but in the main approximation it is convenient to use such rescaling of ps.

The dependence of the calculated integrated cross section oe on m*

e\Lambda or \Lambda when one of the alternative variables isfixed is shown in Figs. 1, 2 (ps

efl = 0:75pse+e\Gamma and psflfl = 0:7pse+e\Gamma ).From the point of view of building a realistic model more preferable case is m

*e\Lambda , \Lambda . The case when m*e\Lambda o/ \Lambda requires considering some special mechanisms to explain such difference of m*

e\Lambda from \Lambda and thus to make this modelnatural. It is assumed that \Lambda is of order of one TeV. But we should not disregard the case when excited lepton mass

is of order of one hundred GeV, because we know the mechanism by which the possible lepton constituents could be bound.

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2. Single excited neutrino production Let us consider the processes of single production of the excited neutrino -- e+e\Gamma ! *\Lambda _* and fle\Gamma ! *\Lambda W\Gamma (5) processes and compare the behavior of oe which dependes on \Lambda and m*

e\Lambda in these two cases. The corresponding totalcross sections are :

oe(e+e\Gamma ! *\Lambda _*) = ssff

2f2

4\Lambda 2 fi(

1 s4W ^(2w + fi) log(1 +

fi w ) \Gamma 2fi*

+ 1 \Gamma 2s

2 W

(1 \Gamma z)s4Wc2W ^w(1 +

w

fi ) log(1 +

w

fi ) \Gamma

1 2(fi + 2w)* +

1 + (1 + 4s2W)2 16(1 \Gamma z)2s4Wc4W fi(1 \Gamma

2 3 fi)); (8)

oe(fle\Gamma ! *\Lambda W\Gamma ) = ssff2f2 8s2W\Lambda 2 "4 log

a \Gamma R \Gamma w \Gamma 1 a + R \Gamma w \Gamma 1i\Gamma 2a

3 + (3w + 2)a2 \Gamma (w + 4)a \Gamma w3 \Gamma w2 + 4w + 2

1 \Gamma a j

+ Ri\Gamma 14a2 + (7w \Gamma 2)a + (7w2 + 13w \Gamma 26) + (14w \Gamma 16)a \Gamma 18w + 8a2 \Gamma 2a + 1 j*; (9) where a = m2*

e\Lambda =s (m*e\Lambda = me\Lambda ), fi = 1 \Gamma m

2*

e\Lambda =s,

w = M 2w=s ; z = M 2z =s ; R = p1 + a2 + w2 \Gamma 2aw \Gamma 2a \Gamma 2w: Dependence of the integrated cross section oe on \Lambda obviously looks like (1=\Lambda )2 (Figs. 1a, 1b). The dependence of oe on the excited neutrino mass m*

e\Lambda is shown on Figs. 2a, 2b. Of course, the maximum available m*e\Lambda is higher in case(3), because of the effective c.m. energy would be slightly higher in the case of e+e\Gamma collisions (ps

efl = 0:75pse+e\Gamma ). But if we consider e+e\Gamma ! *\Lambda _* and e+e\Gamma ! *\Lambda _*\Lambda and compare values of oe in the range of m*

e\Lambda not very closeto the kinematical limit ps

fle, then for (5) oe is about one order higher then for (3). This is due to the fact that in(5) the vertex factor for flWW is proportional to the momenta of the particles in the vertex and thus gives a higher

contribution to the integral compared to that of the eW*. For instance, oe = 0:6 pb for (5) and oe = 0:08 pb for (3), when \Lambda = 3 TeV and m*

e\Lambda = 0:5 TeV at pse+e\Gamma = 1:5 TeV (me\Lambda = 2 TeV in the s-channel). In terms of the number ofevents we shall have 3600 for (5) and 480 for (3) events of the excited neutrino decay taking into account the dominant

decay branching Br(*\Lambda e ! eW) ' 0:6 at the luminosity 104pb\Gamma 1. Therefore the maximum detectable value of \Lambda is higher in the case (5).

One can see that in case (5) oe depends much stronger on ps and on \Lambda compared to case (3). It is necessary to point out that all analytical expressions considered above coincide with the formulas in the independent parallel paper [10].

3. Excited neutrino pair production Now let us turn to the pair production of the excited neutrino. Analytical expressions for total cross section for these processes are given by

oe(e+e\Gamma ! *\Lambda _*\Lambda ) = ssff

2s

96s4Wc4W(1 \Gamma z)2 fi(3 \Gamma fi

2)((4s2

W \Gamma 1)

2 + 1); (10)

oe(flfl ! *\Lambda _*\Lambda ) = ssff

2f2s

4\Lambda 4 fi

2^(1 \Gamma fi2)2 log 1 + fi

1 \Gamma fi + 2fi(

5 3 \Gamma fi

2)*(f = \Gamma f0); (11)

where fi = q1 \Gamma m2*

e\Lambda =s.

For process e+e\Gamma ! *\Lambda _*\Lambda we present the cross section only for s-channel Z-boson exchange (which gives the main contribution ) in order not to overload this paper with comparatively large expressions.

It is seen from Fig. 1c that oe for e+e\Gamma ! *\Lambda _*\Lambda becomes independent of \Lambda at \Lambda ? ps. while for flfl ! *\Lambda _*\Lambda it behaves like (1=\Lambda )4 (Fig. 1d). This happens because at large \Lambda the main contribution to the cross section for (5) is given by the vertex with two excited neutrinos: Z*\Lambda _*\Lambda (which is independent on \Lambda ). Dependence of the cross section on the excited neutrino mass for both processes is shown in Figs. 2c, 2d. One can see that oe is much higher for e+e\Gamma ! *\Lambda _*\Lambda compared to flfl ! *\Lambda _*\Lambda . Hence the sensitivity of the experiment on excited neutrino pair production will be higher in the case of e+e\Gamma collisions and thus the achievable values of m*

e\Lambda and \Lambda in the case (4) are higher.

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4. Numerical results Our numerical results which show measurable values of \Lambda for different energies of planned colliders are summarized in Table 4 (here we assume the integrated luminosity per year as high as 104 pb\Gamma 1 and 100 events excited neutrino production per year with decay channel *\Lambda e ! eW as a criterion for observability of the effect). Note that oe for e+e\Gamma ! *\Lambda _*\Lambda becomes independent on \Lambda and so we do not present corresponding values.

Table 4: The values of \Lambda which are measurable when pse+e\Gamma = 0:5; 1 and 2 TeV.

e+e\Gamma ! *\Lambda _* fle\Gamma ! *\Lambda W\Gamma e+e\Gamma ! *\Lambda _*\Lambda flfl ! *\Lambda _*\Lambda ps

e+e\Gamma m*e\Lambda \Lambda m*e\Lambda \Lambda m*e\Lambda \Lambda m*e\Lambda \Lambda (Gev) (GeV) (TeV) (GeV) (TeV) (GeV) (TeV) (GeV) (TeV)

100 6.4 100 9.1 100 0.7 500 200 5.5 200 7.4 ! 175 I 200 X

400 2.0 400 X 400 X

100 8.5 100 22 100 1.0 1000 200 8.2 200 21 ! 350 I 200 0.95

400 7.0 400 19 400 X

100 10.5 100 92 100 1.4 2000 200 10.2 200 91 ! 350 I 200 1.3

400 9.7 400 86 400 1.2

In this table X means that the corresponding particle can not be produced while I means the cross section independent on \Lambda and thus the respective values of compositeness parameter are'not presented. The tables and analysis considered above clearly show that fle\Gamma ! *\Lambda W\Gamma process is more preferable for single excited neutrino production studies in comparison with e+e\Gamma ! *\Lambda _* while for the pair production e+e\Gamma ! *\Lambda _*\Lambda is more profit then flfl ! *\Lambda _*\Lambda .

It is obvious that our estimations are quite rough and for more precise analysis of (3)-(6) processes it is necessary to consider the main modes of decay of the exited neutrino in 2 ! 3 processes, to fold the subprocesses cross sections with the real photon spectrum and to compare total cross sections with the standard model predictions. All this for the fle\Gamma ! W\Gamma *\Lambda ! W+e\Gamma process we try to do in the next section of this paper.

4. fl e\Gamma ! W\Gamma W+e\Gamma process: searching for signal from excited neutrino In this section we present more realistic analysis of excited neutrino production. The main contribution to the deviation of integrated cross section for considered process from Standard Model comes from diagrams fle\Gamma ! W\Gamma *\Lambda ! W+e\Gamma . So, it is necessary to consider invariant mass distribution doe=dM , where M - invariant mass of outgoing e\Gamma and W+. Results of the numerical calculations are presented in Fig. 3. These calculation performed at \Lambda = 3 TeV, ps = 0:5, 1, 1.5 and 2 TeV. There are two pair distributions in the Fig. 3. First kind represented calculation without folding oe with the photon spectra: dot-dashed line shows invariant mass distribution according to the Standard Model while

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Table 5: The main characteristic values for fl e\Gamma ! W\Gamma W+e\Gamma process and presented at Figure 3 histograms

c.m. energy(TeV) 0.5 1.0 1.5 2.0

m*

e\Lambda (TeV) 0.3 0.6 1.0 1.4

energy resolution

(GeV) ' 5 ' 9 ' 15 ' 20

bin width of histogram(GeV) 10 10 20 50

number of events

in resonance bin

for processes:

without *\Lambda e 200 170 220 400

with *\Lambda e 240 320 500 750

\Gamma (*\Lambda e ! eW) (f = f0)(GeV) 0.03 0.3 0.8 2.0

dotted histogram show distribution when excited neutrino is produced. Dashed line and solid line histogram represent respective distributions which are folded with photon spectra (m*

e\Lambda = 0:3; 0.6, 1 and 1:4 TeV for ps= 0.5 (Fig. 3a),1 (Fig. 3b), 1.5 (Fig. 3c) and 2 (Fig. 3d) TeV respectively). The widths of histogram bins are equal to 10 GeV

for ps = 0:5 and 1 TeV; 20 GeV for ps =1.5 TeV and 50 GeV for ps =2 TeV. The bins outside resonance region are merged. The choice of such bin width seems reasonable because the energy resolution (for example for JLC) is planned as following:

oeEp

E =

15%p

E + 1% : (12) In Table 5 we represented the main characteristic values of the considered process and presented histograms. Shown in Fig. 3 is the case when resonance hits the middle of the bin. The signal exceeds 3 standard deviations from Standard model background (we assume integrated luminosity 104 pb\Gamma 1 per year). In the worst case when the mass of resonance coincide with the border of bins the excess would be two standard deviations. But it is expected that real resolution will be of order of 1 GeV. So , in any case we would have a clear signal from excited neutrino.

In our calculations we made cut of the scattering angle of the electron: 10o ! ` ! 170o. It is worth mentioning that signal from the excited neutrino would be more clear if one optimize the angular cuts.

We have presented here results only fore \Lambda = 3 TeV just to demonstrate observability of the signal from excited neutrino. To learn the upper limits on \Lambda which would be practically achievable at definite collider it is necessary to take into account specific properties of the specific experiment.

We are grateful to G. Jikia, Yu. Pirogov, P. Zerwas and A. Djouadi for fruitful discussions. We also wish to thank authors of the CompHEP system for valuable advice.

References 1 Review of particle properties // Phys. Rev. 1992. V. D45 2 Martinez M. and Miquel R. // Z. Phys. 1990. V. C46. P. 637

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3 Kleis R. and Zerwas P.M. // report CERN 87-07 1987. V. 2. P. 277 4 Ginsburg I.F. et al. // Nucl. Instr. and Meth. 1983. V. 205. P. 47 5 Ginzburg I.F. and Ivanov D.Y. // preprint TP 29(183) Russia, 1990 6 Boudjema F. and Djouadi A. // Phys. Lett. 1990. V. B240. P. 485 7 Kuhn J.H. and Zerwas P.M. // Phys.Lett. 1984. V. B147. P. 189;

Kuhn J.H., Thoel H.D. and Zerwas P.M. // Phys. Lett. 1985 . V. B158. P. 270

8 Cabibbo N., Maiani L. and Strivastava Y. // Phys. Lett. 1984. V. B139. P. 459;

Renard F.M. // Phys. Lett. 1983. V. B126. P. 59, ibid 1984. V. B139 P. 449; Hagiwara K., Komamiya S. and Zeppenfeld D. // Z. Phys. 1988. V. C29. P. 265

9 Boos E.E et al. // Moscow State Univ., Nucl. Phys. Inst., preprint 89-63/140, 1990;

Boos E.E et al. // preprint DESY, 91-114, 1991

10 Boudjema F., Djouadi A. and Kneur J. // preprint DESY 92-116, 1992

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a) b) c) d) Figure 1: Total cross section versus \Lambda (pse+e\Gamma = 0:5; 1.0, 2:0 TeV) for the processes: e+e\Gamma ! *\Lambda _*(a), fle\Gamma ! *\Lambda W\Gamma (b) (me\Lambda =2 TeV in the s-channel), e+e\Gamma ! *\Lambda _*\Lambda (c), flfl ! *\Lambda _*\Lambda (d)

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a) b) c) d) Figure 2: Total cross section versus parameter of compositeness \Lambda (pse+e\Gamma = 0:5; 1.0, 2:0 TeV) for the processes: e+e\Gamma ! *\Lambda _*(a), fle\Gamma ! *\Lambda W\Gamma (b) (me\Lambda =2 TeV in the s-channel), e+e\Gamma ! *\Lambda _*\Lambda (c), flfl ! *\Lambda _*\Lambda (d)

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a) b) c) d) Figure 3: Invariant mass of outgoing e\Gamma and W+ distribution for fle\Gamma ! W\Gamma W+e\Gamma process. Calculation without folding with the photon spectra: dot-dashed line -- invariant mass distribution according to the Standard Model; dotted histogram -- distribution when excited neutrino is produced. Dashed line and solid line histogram represent respective distributions which are folded with photon spectra (m*

e\Lambda = 0:3; 0.6, 1 and 1:4 TeV for ps= 0.5 (Fig. 3a),1 (Fig. 3b), 1.5 (Fig. 3c) and 2 (Fig. 3d) TeV respectively)

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