This letter presents a study of prospects of searching for excited leptons
during RunII of the Fermilab Tevatron. We concentrate on single and pair
production of excited electrons in the photonic decay channel in one CDF/DO
detector equivalent for 2 fb^{-1}. By the end of RunIIa, the limits should be
easily extended beyond those set by LEP and HERA for excited leptons with mass
above about 190 GeV.Comment: 4 pages, 8 figure

A. Semenov

A. Vologdin

B. Abbott

C. Adloff

D. Toback

E. Boos

F. Abachi

F. Abe

F. Boudjema

G. Abbiendi

G. Zech

H. Baer

H.L. Lai

J. Breitweg

J. Gaspard

J. Smith

K. Hagiwara

M. Acciarri

P. Abreu

R. Barate

S. Belyaev

S. Mrenna

T. Appelquist

T. Huber

T. LeCompte

T. Sjöstrand

U. Baur

Physical Review D

English

arXiv

Boos, E.

Vologdin, A.

Toback, D.

Gaspard, J.

Texas A&M University

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1
Prospects for Searching for Excited Leptons during
Run II of the Fermilab Tevatron
June 5, 2018
E. Boos1, A. Vologdin1, D. Toback2, and J. Gaspard2
1Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia
2Texas A&M University, College Station, TX 77843 USA
Abstract
This letter presents a study of prospects of searching for excited leptons during
Run II of the Fermilab Tevatron. We concentrate on single and pair production of
excited electrons in the photonic decay channel in one CDF/DØ detector equivalent
for 2 fb−1. By the end of Run IIa, the limits should be easily extended beyond those
set by LEP and HERA for excited leptons with mass above about 190 GeV.
1
The Standard Model (SM) of particle physics is known to give results that match the
current experimental data with a high precision. However, because of well known theoretical
problems and disadvantages, it is widely believed it can not be a complete theory of elemen-
tary particles, but rather, likely a kind of effective theory at energies below some scale of the
order of a TeV. While many models of “new physics” beyond the SM have been suggested
over the years, one of the most straight-forward ideas proposes that quarks and leptons are
composite particles. Such a scenario is a recurring theme in nature; molecules are composed
of atoms, which are in turn composed of nuclei, which are in turn composed of nucleons and
so on. Furthermore, composite models can explain, in principle, family replication, mixing
in the quark and lepton sectors, and even make the fermion masses and weak mixing angles
calculable.
In most composite models fermions possess an underlying substructure which is char-
acterized by a scale Λ [1] with Λ about 1 TeV or higher [2]. While there is no unified
model of compositeness, a model-independent effective Lagrangian for excited leptons, orig-
inally proposed in [3], can be used to model single and pair production in experiments. The
Lagrangian:
Ll∗l∗ = l
∗
γµ(
τ
2
Wµ + g
′Y
2
Bµ)l
∗ (1)
Ll∗l =
1
2Λ
l
∗
Rσ
µν(fg
τ
2
Wµν + f
′
g
′Y
2
Bµν)lL + h.c. (2)
where f and f ′ are coupling constants, has been used extensively in a number of phenomeno-
logical papers which presents ideas on searching for excited fermion production and decay
to final state gauge bosons in e+e−, pp¯, ep, and eγ collisions [4, 5, 6]. Direct searches for
lepton compositeness has been done extensively at LEP [7] and HERA [8], each with no
discovery, but with ever more sensitive limits. Unfortunately, only direct searches for quark
compositeness have been done at the Fermilab Tevatron [9].
In this Letter we present a study for searching for excited lepton production and decay
for the upcoming Run II of CDF and DØ detectors. We begin with an updated simulation of
excited lepton production, and optimize the sensitivity by studying the kinematics of excited
lepton production and decay. With these results we estimate the mass reach and compare
to the recent results from LEP and HERA.
To study the mass reach of the Tevatron, we simulated single and pair production and
decay of excited leptons using the upgraded Fermilab accelerator (1.8→ 2.0 TeV), and CDF
and DØ detectors for Run II. The Feynman rules from the effective Lagrangian (Eqn. 1)
are implemented into CompHEP [10] using the LanHEP [11] software package. We have
included into this simulation a complete tree-level calculation which takes into account all
the spin correlations between excited states production, subsequent decays, and incorporate
the known NLO corrections. All the partial width and known 2→ 2 cross-section have been
cross-checked at the symbolic level. Events on parton level generated by means ofCompHEP
have been used as an external process for pythia with the help of the CompHEP-pythia
interface [12]. The underlying event, jet fragmentation, ISR and FSR are modeled using
the pythia [13] Monte Carlo with the cteq4l [14] structure functions. Since Drell-Yan
production of excited leptons production is similar to that of Supersymmetric leptons, we
2
take the K-factors given in [15], which only depend on the masses of final particles, and vary
between 1.23 and 1.24 in the mass range of the search.
While excited leptons can come in three flavors: e∗, µ∗ and τ ∗, we chose to concentrate
on the electron since the result of µ∗ expected to be similar to e∗, and τ ’s at the Tevatron are
still difficult to trigger on and identify. Excited electrons can decay via: e∗ → eγ, e∗ → eZ,
and e∗ → Wν channels with the branching ratios shown in Fig. 1. The backgrounds to the
W and Z decay channels in the hadronic channels are fairly large and the leptonic branching
fractions needed to identify the W and Z channels are small; however, the backgrounds
to the photonic final states are relatively small in comparison making them a gold-plated
signature.
In the case of the single excited electron production mode, there are two possible signal
pp → e∗e → e+e−γ and pp → e∗ν → eνγ. Similarly, pair production gives pp → e∗+e∗− →
e+e−γγ and pp → e∗ν∗ → eνγγ. For simplicity we concentrate on inclusive eeγ final state
for both single and pair production as it covers most of the production in both single and
pair production cases. Before taking into account the branching ratio to photons, the total
production cross section is shown in Fig. 2 for the case f/Λ = 10−2 GeV−1 and f = f
′
.
There are a number of backgrounds to the eeγ channel. The dominant backgrounds are
Wγ+jets and Zγ+jets production. Others includeW+jets and Z+jets, and multijets, where
jets can fake leptons and/or photons. Studies have shown [16] that the fake backgrounds
can be modeled by the kinematics of the irreducible backgrounds. The backgrounds are
modeled using the same CompHEP simulation structure described above. Since there is
an infrared singularity at pγT = 0, we require P
γ
T > 10 GeV and ∆Rij > 0.1, where ∆Rij ≡√
(∆η)2 + (∆ϕ)2, and at the generator level, i and j are any lepton-photon combination.
We take the K-factor, which has a value of about 1.36 depending on pγT , for the background
processes from the literature [17].
For both signal and backgrounds, we use a parametric simulation to model the detector
response. The SHW detector simulation [18] has been shown to be an effective averaging
between the CDF [19] and DØ [20] detectors for Run II. After detector simulation the
kinematic distributions for both the signal and estimated backgrounds are shown in Figs 3
and 4. We find acceptances at about the 0.3 level for signal.
To maximize our sensitivity we assume, for simplicity, that taking a set of cuts which
minimizes the expected cross section limit also maximizes our sensitivity to calculate these
limits. To calculate these limits, we use the signal acceptance and background estimates from
the simulations above. We add in a single detector with 2 fb−1 of luminosity and we assume
the experimental parameters of Table 1 for systematic uncertainties. We use a frequentist
method [21] to incorporate the errors and assume that all errors on acceptance, background
and luminosity are uncorrelated. To determine the expected limit as a function of a given
cut using Run II data, under the assumption of no observed signal, the 95% confidence
level (C.L.) cross section upper limit, for a given cut, is uniquely determined by number of
events observed in the data. With no signal, the number of events observed in the data, N ,
fluctuates around the mean number of expected events, M , according to Poisson statistics.
Thus, an average expected cross section limit is given by:
3
Luminosity (fb−1) 2.0 ± 0.1
Background error δNback
Nback
0.1
Acceptance error δA
A
0.1
Table 1: Parameters used to calculate the 95% C.L. cross section upper limits.
Me∗ σ
prod B (e∗ → eγ) Cut Nback σ
expected
95% C.L σ
expected
95% C.L · B
(GeV) (fb) (GeV) (fb) (fb)
150 712 0.400 140.0 42.0 41.3 16.5
200 312 0.334 185.0 18.0 30.9 10.3
250 160 0.309 230.0 7.64 23.7 7.3
300 87 0.297 275.0 4.36 20.0 5.9
Table 2: Values for f
Λ
= 1
100
GeV−1 optimized points.
σcut95 =
∞∑
N=0
σ95(N, cut)
e−MMN
N !
(3)
In this way we get an average expected cross section limits as a function of each cut. We
can then optimize for each mass point as a function of the cuts.
After a study of multi-dimensional distributions for background and signal, we deter-
mined that the e+e−γ final state has the best signal to background ratio and kinematical
distributions. Furthermore, we find that applying a single cut on the kinematical variable
Meγ (where e is the electron with highest pT ) gives the best relation between acceptance
and N to find minimal value of σ95 for a given mass of the excited electron. This is read-
ily apparent using Figs. 3 and 4 which shows that the best separation between signal and
background is the Meγ variable.
Figure 5 shows the expected 95% C.L. cross section upper limit, σ95, as a function of the
Meγ cut for different masses of e
∗ for f
Λ
= 1
100
GeV−1. Placing our cut at the minimum of
the curve gives our optimization, and final expected cross section limit. These results are
shown in Fig. 6. Using the Feynman rules for the Lagrangian in Eqn. 1 leads to a simple
relation between cross-section and f
Λ
for signal:
(Λ1)
2σ(
f
Λ1
,Me∗) = (Λ2)
2σ(
f
Λ2
,Me∗) (4)
f
Λ
=
σ95
104σ(10−2,Me∗)
(5)
Taking into account this equation, numerical values of signal cross-sections (where f
Λ
=
10−2 GeV−1) and results for σ95 we can make an exclusion plot in the
f
Λ
vs. Me∗ plane. This
result is shown in Fig. 7. We compare our results to those of LEP and HERA in Fig. 8 which
would give the most stringent limits, to date, for masses above 190 GeV.
4
The prospects for searching for excited electrons at the upgraded Fermilab Tevatron are
excellent. We expect that with a single detector and 2 fb−1 of data should significantly
extend the mass reach, especially in the low f
Λ
region and large masses. We also point out
that similar results are obtained for excited muons which significantly improve on the current
limits which are not producible at HERA.
The authors would like to thank John Hobbs for the use of his limit calculator, Bruce
Knuteson for his relation in Eqn. 3, and Bhaskar Dutta for helpful discussions. We would also
like to thank the DØ collaboration for the use of their computers to do the simulation work.
We also would like to thanks the Institute of Nuclear Physics of Moscow State University,
the University of Maryland and Texas A&M University for their support. Finally we would
like to thank the US DOE and Russian Ministry of Industry, Science and Technology for
their support during this project. The work of E.B. and A.V. was partly supported by
the RFBR-DFG 99-02-04011, RFBR 00-01-00704, CERN-INTAS 99-377, and Universities of
Russia 990588 grants.
5
Figure 1: The branching ratios for excited leptons as a function of the mass of the excited
lepton.
6
Figure 2: Total cross section for the sum of both single and pair production and decay of
excited electrons in the eeγ final state.
7
Figure 3: A comparison of the kinematic distributions of the final state electrons and photons
for excited electron and standard model background processes. The figures show the results
for single and pair production of e∗e→ eeγ and e∗e∗ → eeγ.
8
Figure 4: A comparison of some of the variables studied which gave good separation between
excited leptons and standard model background processes in the eeγ final state. Note that
the Meγ variable gives the best separation between signal and background for Me∗ = 200
GeV at Meγ > 185 GeV.
9
Figure 5: The expected 95% C.L. cross section upper limit as a function of the Meγ cut
for different masses of e∗. There the cross section is defined as σ(pp¯ → ee∗ → eeγ) +
σ(pp¯→ e∗e∗ → eeγ) and L = 2 fb−1.
10
Figure 6: Optimized expected 95% C.L. for e∗ → eeγ production using the eeγ final state
and 2 fb−1 of data with a single detector.
11
Figure 7: Exclusion plot for f
Λ
as a function of e∗ mass using 2 fb−1 worth of data and a
single detector.
12
10
-4
10
-3
10
-2
50 100 150 200 250
H1 Exclu
ded
Expected
Tevatron
Exclusion
(2fb-1)
L3 Exclud
ed
 f = f ,
Mass e* (GeV)
f/Λ
 
(G
eV
-
1 )
Figure 8: For masses above about 190 GeV, we expect that the Tevatron should, with 2 fb−1
of data, and one detector, produce the most stringent limits.
13
References
[1] On the other hand an existence of the excited states may be a results of a presence of
extra dimensions. This may occur if the quark, lepton and boson fields can propagate
in extra dimensions. However in that case one would expect an appearance of excited
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D 64, 035002 (2001).
[2] Current experimental constraints come from the analysis of the g − 2 properties of
muon and electron, and from the estimate of quark and lepton radii. See A. Czarnecki,
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national Workshop on Advanced Computing and Analysis Technics in Physics Research
(ACAT2000, Fermilab, October 16-20, 2000).
[13] T. Sjo¨strand, Comp. Phys. Comm. 82, 74 (1994); S. Mrenna, Computer Phys. Commun.
101, 232 (1997); T. Sjo¨strand, P. Eden, C. Friberg, L. Lonnblad, G. Miu, S. Mrenna
and E. Norrbin, Comp. Phys. Comm. 135, 238 (2001).
14
[14] H. L. Lai et al.. Phys. Rev. D 55, 1280 (1997).
[15] H. Baer et al., Phys. Rev. D 57, 5871 (1998).
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[17] J. Smith et al., Z. Phys. C 44, 267 (1989).
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2709 (1990).
15


Prospects of searching for excited leptons during run II of the Fermilab Tevatron

OAKTrust Digital Repository (Texas A&M Univ)

arXiv:hep-ph/0111034v2  5 Nov 2001Prospects for Searching for Excited Leptons duringRun II of the Fermilab TevatronJune 5, 2018E. Boos1, A. Vologdin1, D. Toback2, and J. Gaspard21Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia2Texas A&M University, College Station, TX 77843 USAAbstractThis letter presents a study of prospects of searching for excited leptons duringRun II of the Fermilab Tevatron. We concentrate on single and pair production ofexcited electrons in the photonic decay channel in one CDF/DØ detector equivalentfor 2 fb−1. By the end of Run IIa, the limits should be easily extended beyond thoseset by LEP and HERA for excited leptons with mass above about 190 GeV.1The Standard Model (SM) of particle physics is known to give results that match thecurrent experimental data with a high precision. However, because of well known theoreticalproblems and disadvantages, it is widely believed it can not be a complete theory of elemen-tary particles, but rather, likely a kind of effective theory at energies below some scale of theorder of a TeV. While many models of “new physics” beyond the SM have been suggestedover the years, one of the most straight-forward ideas proposes that quarks and leptons arecomposite particles. Such a scenario is a recurring theme in nature; molecules are composedof atoms, which are in turn composed of nuclei, which are in turn composed of nucleons andso on. Furthermore, composite models can explain, in principle, family replication, mixingin the quark and lepton sectors, and even make the fermion masses and weak mixing anglescalculable.In most composite models fermions possess an underlying substructure which is char-acterized by a scale Λ [1] with Λ about 1 TeV or higher [2]. While there is no unifiedmodel of compositeness, a model-independent effective Lagrangian for excited leptons, orig-inally proposed in [3], can be used to model single and pair production in experiments. TheLagrangian:Ll∗l∗ = l∗γµ(τ2Wµ + g′Y2Bµ)l∗ (1)Ll∗l =12Λl∗Rσµν(fgτ2Wµν + f′g′Y2Bµν)lL + h.c. (2)where f and f ′ are coupling constants, has been used extensively in a number of phenomeno-logical papers which presents ideas on searching for excited fermion production and decayto final state gauge bosons in e+e−, pp¯, ep, and eγ collisions [4, 5, 6]. Direct searches forlepton compositeness has been done extensively at LEP [7] and HERA [8], each with nodiscovery, but with ever more sensitive limits. Unfortunately, only direct searches for quarkcompositeness have been done at the Fermilab Tevatron [9].In this Letter we present a study for searching for excited lepton production and decayfor the upcoming Run II of CDF and DØ detectors. We begin with an updated simulation ofexcited lepton production, and optimize the sensitivity by studying the kinematics of excitedlepton production and decay. With these results we estimate the mass reach and compareto the recent results from LEP and HERA.To study the mass reach of the Tevatron, we simulated single and pair production anddecay of excited leptons using the upgraded Fermilab accelerator (1.8→ 2.0 TeV), and CDFand DØ detectors for Run II. The Feynman rules from the effective Lagrangian (Eqn. 1)are implemented into CompHEP [10] using the LanHEP [11] software package. We haveincluded into this simulation a complete tree-level calculation which takes into account allthe spin correlations between excited states production, subsequent decays, and incorporatethe known NLO corrections. All the partial width and known 2→ 2 cross-section have beencross-checked at the symbolic level. Events on parton level generated by means ofCompHEPhave been used as an external process for pythia with the help of the CompHEP-pythiainterface [12]. The underlying event, jet fragmentation, ISR and FSR are modeled usingthe pythia [13] Monte Carlo with the cteq4l [14] structure functions. Since Drell-Yanproduction of excited leptons production is similar to that of Supersymmetric leptons, we2take the K-factors given in [15], which only depend on the masses of final particles, and varybetween 1.23 and 1.24 in the mass range of the search.While excited leptons can come in three flavors: e∗, µ∗ and τ ∗, we chose to concentrateon the electron since the result of µ∗ expected to be similar to e∗, and τ ’s at the Tevatron arestill difficult to trigger on and identify. Excited electrons can decay via: e∗ → eγ, e∗ → eZ,and e∗ → Wν channels with the branching ratios shown in Fig. 1. The backgrounds to theW and Z decay channels in the hadronic channels are fairly large and the leptonic branchingfractions needed to identify the W and Z channels are small; however, the backgroundsto the photonic final states are relatively small in comparison making them a gold-platedsignature.In the case of the single excited electron production mode, there are two possible signalpp → e∗e → e+e−γ and pp → e∗ν → eνγ. Similarly, pair production gives pp → e∗+e∗− →e+e−γγ and pp → e∗ν∗ → eνγγ. For simplicity we concentrate on inclusive eeγ final statefor both single and pair production as it covers most of the production in both single andpair production cases. Before taking into account the branching ratio to photons, the totalproduction cross section is shown in Fig. 2 for the case f/Λ = 10−2 GeV−1 and f = f′.There are a number of backgrounds to the eeγ channel. The dominant backgrounds areWγ+jets and Zγ+jets production. Others includeW+jets and Z+jets, and multijets, wherejets can fake leptons and/or photons. Studies have shown [16] that the fake backgroundscan be modeled by the kinematics of the irreducible backgrounds. The backgrounds aremodeled using the same CompHEP simulation structure described above. Since there isan infrared singularity at pγT = 0, we require PγT > 10 GeV and ∆Rij > 0.1, where ∆Rij ≡√(∆η)2 + (∆ϕ)2, and at the generator level, i and j are any lepton-photon combination.We take the K-factor, which has a value of about 1.36 depending on pγT , for the backgroundprocesses from the literature [17].For both signal and backgrounds, we use a parametric simulation to model the detectorresponse. The SHW detector simulation [18] has been shown to be an effective averagingbetween the CDF [19] and DØ [20] detectors for Run II. After detector simulation thekinematic distributions for both the signal and estimated backgrounds are shown in Figs 3and 4. We find acceptances at about the 0.3 level for signal.To maximize our sensitivity we assume, for simplicity, that taking a set of cuts whichminimizes the expected cross section limit also maximizes our sensitivity to calculate theselimits. To calculate these limits, we use the signal acceptance and background estimates fromthe simulations above. We add in a single detector with 2 fb−1 of luminosity and we assumethe experimental parameters of Table 1 for systematic uncertainties. We use a frequentistmethod [21] to incorporate the errors and assume that all errors on acceptance, backgroundand luminosity are uncorrelated. To determine the expected limit as a function of a givencut using Run II data, under the assumption of no observed signal, the 95% confidencelevel (C.L.) cross section upper limit, for a given cut, is uniquely determined by number ofevents observed in the data. With no signal, the number of events observed in the data, N ,fluctuates around the mean number of expected events, M , according to Poisson statistics.Thus, an average expected cross section limit is given by:3Luminosity (fb−1) 2.0 ± 0.1Background error δNbackNback0.1Acceptance error δAA0.1Table 1: Parameters used to calculate the 95% C.L. cross section upper limits.Me∗ σprod B (e∗ → eγ) Cut Nback σexpected95% C.L σexpected95% C.L · B(GeV) (fb) (GeV) (fb) (fb)150 712 0.400 140.0 42.0 41.3 16.5200 312 0.334 185.0 18.0 30.9 10.3250 160 0.309 230.0 7.64 23.7 7.3300 87 0.297 275.0 4.36 20.0 5.9Table 2: Values for fΛ= 1100GeV−1 optimized points.σcut95 =∞∑N=0σ95(N, cut)e−MMNN !(3)In this way we get an average expected cross section limits as a function of each cut. Wecan then optimize for each mass point as a function of the cuts.After a study of multi-dimensional distributions for background and signal, we deter-mined that the e+e−γ final state has the best signal to background ratio and kinematicaldistributions. Furthermore, we find that applying a single cut on the kinematical variableMeγ (where e is the electron with highest pT ) gives the best relation between acceptanceand N to find minimal value of σ95 for a given mass of the excited electron. This is read-ily apparent using Figs. 3 and 4 which shows that the best separation between signal andbackground is the Meγ variable.Figure 5 shows the expected 95% C.L. cross section upper limit, σ95, as a function of theMeγ cut for different masses of e∗ for fΛ= 1100GeV−1. Placing our cut at the minimum ofthe curve gives our optimization, and final expected cross section limit. These results areshown in Fig. 6. Using the Feynman rules for the Lagrangian in Eqn. 1 leads to a simplerelation between cross-section and fΛfor signal:(Λ1)2σ(fΛ1,Me∗) = (Λ2)2σ(fΛ2,Me∗) (4)fΛ=σ95104σ(10−2,Me∗)(5)Taking into account this equation, numerical values of signal cross-sections (where fΛ=10−2 GeV−1) and results for σ95 we can make an exclusion plot in thefΛvs. Me∗ plane. Thisresult is shown in Fig. 7. We compare our results to those of LEP and HERA in Fig. 8 whichwould give the most stringent limits, to date, for masses above 190 GeV.4The prospects for searching for excited electrons at the upgraded Fermilab Tevatron areexcellent. We expect that with a single detector and 2 fb−1 of data should significantlyextend the mass reach, especially in the low fΛregion and large masses. We also point outthat similar results are obtained for excited muons which significantly improve on the currentlimits which are not producible at HERA.The authors would like to thank John Hobbs for the use of his limit calculator, BruceKnuteson for his relation in Eqn. 3, and Bhaskar Dutta for helpful discussions. We would alsolike to thank the DØ collaboration for the use of their computers to do the simulation work.We also would like to thanks the Institute of Nuclear Physics of Moscow State University,the University of Maryland and Texas A&M University for their support. Finally we wouldlike to thank the US DOE and Russian Ministry of Industry, Science and Technology fortheir support during this project. The work of E.B. and A.V. was partly supported bythe RFBR-DFG 99-02-04011, RFBR 00-01-00704, CERN-INTAS 99-377, and Universities ofRussia 990588 grants.5Figure 1: The branching ratios for excited leptons as a function of the mass of the excitedlepton.6Figure 2: Total cross section for the sum of both single and pair production and decay ofexcited electrons in the eeγ final state.7Figure 3: A comparison of the kinematic distributions of the final state electrons and photonsfor excited electron and standard model background processes. The figures show the resultsfor single and pair production of e∗e→ eeγ and e∗e∗ → eeγ.8Figure 4: A comparison of some of the variables studied which gave good separation betweenexcited leptons and standard model background processes in the eeγ final state. Note thatthe Meγ variable gives the best separation between signal and background for Me∗ = 200GeV at Meγ > 185 GeV.9Figure 5: The expected 95% C.L. cross section upper limit as a function of the Meγ cutfor different masses of e∗. There the cross section is defined as σ(pp¯ → ee∗ → eeγ) +σ(pp¯→ e∗e∗ → eeγ) and L = 2 fb−1.10Figure 6: Optimized expected 95% C.L. for e∗ → eeγ production using the eeγ final stateand 2 fb−1 of data with a single detector.11Figure 7: Exclusion plot for fΛas a function of e∗ mass using 2 fb−1 worth of data and asingle detector.1210-410-310-250 100 150 200 250H1 ExcludedExpectedTevatronExclusion(2fb-1)L3 Excluded f = f ,Mass e* (GeV)f/Λ (GeV-1 )Figure 8: For masses above about 190 GeV, we expect that the Tevatron should, with 2 fb−1of data, and one detector, produce the most stringent limits.13References[1] On the other hand an existence of the excited states may be a results of a presence ofextra dimensions. 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