Search for an exotica particle µ (e ) in the µ(e) + γ channel in CMS detector at 10 TeV

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1 Available on CMS information server CMS AN 9/xxx The Compact Muon Solenoid Experiment Analysis Note The content of this note is intended for CMS internal use and distribution only 4 April 9 Search for an exotica particle µ (e ) in the µ(e) + γ channel in CMS detector at TeV M. Gataullin, V. Litvin, H. Newman, A. Yen, Y. Yang, R.Y. Zhu California Institute of Technology, Pasadena, CA 9, USA Abstract One of the open questions in Standard Model particle physics is the observed mass hierarchy of fermion generations. The Compositeness model was proposed to give an answer by assuming constituent particles in quarks and leptons, which in turn gives rise to a large number of excited states. Discovery of such an excited state would indicate the existence of substructure of quarks and leptons. In this note, we present the studies of a search for such an excited state of the muon and the electron, in the µ (e) + γ decay channel in the CMS detector, assuming an integrated pb data collected from TeV center-of-mass pp collisions at the LHC. We show that such an excited state could be discovered with mass up to TeV if the compositeness scale is about 3 TeV.

2 Introduction The Standard Model of particle physics has been successfully tested experimentally. However, there are a number of open questions which the SM has not solved. One such question is the observed mass hierarchical structure of fermion generations. The compositeness model (or preon model) was proposed by assuming the existence of sub-particles for quarks and leptons. In this approach, a quark or lepton is a bound state of three fermions, or one fermion and one gauge boson. The proposed sub-particles are usually called preons which are bounded by a new strong interaction. Compositeness model gives rise to a large number of excited states. Discovery of such an excited state would give strong evidence for a sub-structure of quarks and leptons, though all experimental searches have been unsuccessful so far. In proton-proton collision at the LHC, the production of excited fermions is dominated by the contact interaction (Figure ) which is usually described by an effective four-fermion Lagrangian [] where Λ is the compositenss scale and J µ is the fermion current L CI = g Λ J µ J µ () J µ = η L fl γ µ f L + η L f L γµ f L + η L f L γµ f L + H.c. + (L R) () f and f refer to the ordinary and excited fermion, respectively. g is chosen to be 4π, and the η factors of lefthanded currents are set to be unity and the right-handed currents are neglected for simplicity. Transition between ordinary and excited fermion is described by the effective Lagrangian L trans = Λ f R σµν (g f f s λ a Ga µν + gf τ W µν + g f Y B µν) + H.c. (3) This would allow electroweak decay of excited fermions. The partial width for the decay channels are Γ(f f + γ) = 4 αf γ m 3 Λ (4) where V refers to the W or Z gauge boson and Γ(f f + V ) = gv 8 4π f V m 3 Λ ( m V m ) ( + m V ) () m f γ = ft 3 + f Y (6) f Z = ft 3 cos θ W + f Y sin θ W (7) f W = f (8) where T 3 denotes the third component of the weak isospin and g W = 4πα/sinθ W and g Z = g W /cosθ W, θ is the electroweak coupling constant. f and f are parameters determined by the composite dynamics. In this analysis, they are set to be unity. The decay of excited fermion could also be mediated by the four-fermion contact interaction, the decay width is given by Γ(f f + f f ) = m 96π (m Λ )4 N c S (9) where N c is the number of colors of the fermion and S is an additional combinational factor, S = for f f, S = for f = f and meanwhile f is a lepton. Various decay channels of excited leptons are shown in Figure and the branching ratios as a function of m /Λ are shown in Figure 3.

3 The production of a single excited lepton by contact interaction depends on both the scale Λ and the mass of the excited lepton, ˆσ(q q µµ, µ µ) = π 6ŝ ( ŝ Λ ) ( + m m (ŝ ))( 3 ŝ + m ŝ ) ( + m ŝ ) () In this analysis, we consider the process of pp µ + µ and pp e + e, with µ (e ) µ(e) + γ. Therefore, there are two energetic leptons and one energetic photon in the event. The primary irreducible Standard Model background with this event topology is the production of Z/γ lepton pairs associated with one photon, primarily from Initial State Radiation of quarks (ISR) or Final State Radiation of leptons (FSR). Other reducible backgrounds mainly come from fake photons from electromagnetic jets. Data Sets The background data sets used in this analysis are listed in Table. Signal samples for excited electrons are listed in Table ). Signal samples for excited muons are privately produced ). A customized version of the PYTHIA event generator is used since no process for excited muon production is available in the version 6.4. Table : Background datasets used in this study. Dataset Events σ (pb) /Zmumu/Summer8 IDEAL V9 v/gen-sim-reco /Zee/Summer8 IDEAL V9 v/gen-sim-reco /Zgamma/Summer8 IDEAL V9 v/gen-sim-reco 3.96 /ZJets-madgraph/Fall8 IDEAL V9 reco-v/gen-sim-reco /TTJets-madgraph/Fall8 IDEAL V9 v/gen-sim-reco /WZ incl/summer8 IDEAL V9 v/gen-sim-reco /ZZ/Summer8 IDEAL V9 v/gen-sim-reco 64. /InclusiveMuPt/Summer8 IDEAL V9 v/gen-sim-reco E /QCDpt/Summer8 IDEAL V9 v3/gen-sim-reco E9 Table : Signal datasets for excited electron used in this study. Dataset Events σ (pb) /Exotica Estar M/Summer8 IDEAL V9 v/gen-sim-reco 398.8E /Exotica Estar M4/Summer8 IDEAL V9 v/gen-sim-reco 6.66E /Exotica Estar M6/Summer8 IDEAL V9 v/gen-sim-reco 69.39E /Exotica Estar M8/Summer8 IDEAL V9 v/gen-sim-reco 3.4E /Exotica Estar M/Summer8 IDEAL V9 v/gen-sim-reco 364.E /Exotica Estar M/Summer8 IDEAL V9 v/gen-sim-reco 66.4E /Exotica Estar M/Summer8 IDEAL V9 v/gen-sim-reco 889.E /Exotica Estar M/Summer8 IDEAL V9 v/gen-sim-reco E- /Exotica Estar M3/Summer8 IDEAL V9 v/gen-sim-reco E-6 3 Selection for µ µ + γ 3. Selection cuts For the selection of muons, the standard global muon is used. Two leading muons are required to have P T greater than GeV. The following requirements are imposed on both muons. First, they should be compatible with ) In the version 6.4 of PYTHIA used, there are only electroweak decay channels of excited electron. The cross section listed in the Table is the production cross section times the true branching ratio of e e + γ, with Λ = TeV. ) Those samples can be found here. About k events for each mass point is generated in CMSSW..7 (gen+hlt) and..8 (RECO). 3

4 prompt muons produced from primary vertex, in order to suppress muons from b decays as well as cosmic muons. The transverse impact parameter of the muon inner track with respect to the primary event vertex is required to be less than. cm. Secondly, at least rechits in the muon inner track is required to reject decay-in-flight and punch through. Thirdly, track isolation criteria is imposed. The total P T of reconstructed tracks in a cone. < R <.3 ( R φ + η ) around the direction of the muon inner track is required to be less than 6 GeV. To be added into the sum, the track is required to have P T greater than GeV, and the difference between the z component of the vertices of the track and the muon inner track is required to be less than. cm, and the transverse impact parameter of the track vertex with respect to beam spot is required to be less than. cm. Lastly, the invariant mass of the two muons is required to be greater than 6 GeV, above the cut of 4 GeV applied in event generation. If the two leading muons meet the selection criteria, we search for a photon candidate. First, it must have P T above GeV and it must be separated with both muons by R at least.. The one with highest P T is selected if more than one photon candidate satisfies the P T and R requirements. The following selection cuts are then applied to this photon candidate. First, the total hadronic energy in the calorimeter towers in a cone R =. around the direction of the supercluster of this photon candidate is required to be less than % of the supercluster energy. Secondly, the total P T of reconstructed tracks in a cone. < R <.3 around the direction of the photon candidate over the P T of photon candidate is required to be less than.4. Similar requirements for muon track isolation are applied for tracks to be added into the sum, except that the primary event vertex is used intead of the vertex of the muon inner track. Thirdly, the sum of total E T of hadronic energy in the calorimeter towers in a cone. < R <.3 and the total E T in all ECAL rechits in a cone R =.3 around the direction of the supercluster over the supercluster E T is required to be less.. Only ECAL rechits with R >.6 and η >.4 around the supercluster direction and with energy above.8 GeV in barrel or.3 GeV in endcap are used. Lastly, the total energy deposited in a 3x3 crystal matrix around the crystal with maximum energy in the seed cluster of the supercluster over the supercluster energy is required to be greater than.9. The single muon trigger HLT Mu is used and found to have trigger efficiency about 97% for selected signal samples. After all previous selection cuts, the invariant mass from each pair of muon and photon candidate is calculated. Figure 6 left shows the invariant mass distribution for various backgrounds and three low mass signals, for an integrated luminosity of pb. The invariant mass of µ µ + γ decays is fitted with a crystal ball function (Figure 8 left); the resultant peak width for each mass point is shown in Figure 6 right. No event passed in the InclusiveMuPt sample, therefore its contribution is estimated by factorizing the selections as follows. First, events with two leading muons with P T greater than GeV with an invariant mass above 6 GeV and a photon with P T above GeV and separated with both muons by R at least. are selected. This is namely to get the efficiency of the kinematic cuts. In those events, only muon or photon selection cuts are applied, to get the efficiency separately. In this way, the estimated rate is about.3 ±.(stat) events/ pb. Selection efficiencies for various backgrounds and signals are listed in Table 3. Table 3: Selection efficiency (%) for two muons and one photon in signal and background samples. Efficiency in each column is with respect to previous selection. The last column shows the total efficiency. M µ (GeV ) kinematic cuts muon selections photon selections trigger cumulative 7.9 ± ±. 8. ± ±.. ± ± ±. 87. ± ±. 6.8 ± ± ± ±. 97. ±. 7. ± ±. 9. ±. 9.6 ±. 97. ±. 7. ± ±. 9. ±. 9.9 ± ±. 73. ± ± ±. 93. ± ±. 7.4 ± ±.3 9. ±. 93. ± ±. 7. ± ±. 94. ±. 9. ± ±. 74. ±.3 Z µµ.9 ± ±. 3. ±. 96. ±.6 8.7E- ±.9E-3 TTbar.8 ± ±.6. ±.. ±..8E-3 ± 4.E-4 ZW.6 ±. 93. ±.7 7. ± ±.9 3.6E- ± 3.8E-3 ZZ. ± ±..8 ±. 9.8 ±.9.6E- ±.3E-3 WW. ±. 77. ± ±.3. ±..E-3 ±.E-3 4

5 After all previous selection cuts, the major Standard Model background is from inclusive Z µµ events. Therefore, the invariant mass distribution of two muons could be used as an effective tool for data-mc comparision. The invariant mass distribution of two muons and one photon has also a peak around M Z, due to the fact that a significant fraction of selected photons in inclusive Z µµ events are actually from FSR of muons. 3. Search potential For each excited muon mass point, the final signal efficiency (ɛ S ) is calculated using pairs of muon and photon with invariant mass around the mass peak, in the range from M σ M to M + 3σ M. An asymmetric window is used due to the non-gaussian invariant mass distribution of µ µ + γ decays (Figure 8 left). At most one pair per event is counted, though both pairs of muon and photon are used for entries into the M(µγ) spectrum. The invariant mass spectrum from standard model backgrounds is fitted with an function p /x p (Figure 8 right), and the number of background for each mass point is estimated to be the integral of the fitted function in the same range as used for the final signal efficiency estimation. The discovery potential (namely the upper reach on the scale Λ) for each mass point for a given integrated luminosity is estimated by requiring the corresponding signal significance to be five, calculated by the formula [] S = ( S + B B + σb (sys) B) B + σb (sys) + σb (stat) () σ B (stat) is estimated from the statistical errors of fitting the background distribution. Two systematic uncertainties are considered. First, % error of the integrated luminosity is assumed. Secondly, the contribution from errors of the Parton Distribtuion Fuction (PDF) and variations of factorization scale (Q ) used for event generation is estimated by the reweighting method [3]. For different PDF set or Q, a weight is assigned to each selected event, wt = f S i (x, Q, flav )f Si (x, Q, flav ) f S (x, Q, flav )f S (x, Q, flav ) () where S i is the PDF set number i, S is the best-fit set. Symmetric error from 4 error sets of PDF cteq6m is calculated by the formula [4], X = Σ i= (X(S+ i ) X(S i )) (3) where X is the observable, and X(S i ± ) are the predictions for X based on the PDF set S± i. In our case, X is the signal efficiency ɛ S or number of background. The factorization scale Q is scaled down and up by a factor of, and the biggest difference is taken as the systematic uncertainty due to the variations of factorization scale. The systematic uncertainties for each signal mass point due to errors of the PDF set and variations of Q is shown in Figure 9. Figure left shows the discovery reach on Λ for each mass point of excited muon, with an integrated luminosity of pb. The error bars in this Figure correspond to variations of signal efficiency by ±σ ɛs. Assuming the observed number of data follows a Poisson distribution of the expected number of background, we could set the expected 9% confidence level upper limit on the excited muon production cross section times the branching ratio into µ + γ. A Bayesian technique [] is used, taking into account all uncertainties. For each possible observed number of data N obs, one corresponding upper limit value is obtained. The expected limit is then calculated as the weighted sum of all possible values with weight to be the possibility of observing N obs with expecation B. Figure right shows the expected exclusion limit of Λ for each mass point of excited muon, with an integrated luminosity of pb.

6 Table 4: The final signal efficiency (%) and the number of estimated background for each excited muon mass point, for an integrated luminosity of pb. M µ (GeV ) signal efficiency (ɛ S ± σ ɛs (stat)) number of background (B ± σ B (stat) ± σ B (syst)) 47. ±.4.9E+ ±.E+ ± 3.9E ±.3.E+ ±.4E- ±.3E ±.3 6.E- ± 3.E- ± 7.3E ±.3 4.E- ±.E- ± 4.8E- 67. ±.3 3.E- ±.6E- ± 3.6E- 69. ±.3.8E- ± 9.6E- ±.E- 68. ±.4.3E- ± 7.E- ±.4E- 67. ±.3 9.6E- ±.E- ±.E- 4 Selection for e e + γ 4. Selection cuts For the selection of electrons, the standard GsfElectron is used. The following selection cuts are employed for selecting events with two electrons and one photon. Two leading electrons are required to have P T above GeV. The following requirements are applied to both electrons. First, compatibility with event vertex is required to suppress electrons from b decays. The transverse impact parameter of the electron track with respect to the primary event vertex is required to be less than. cm. Secondly, the total P T of reconstructed tracks in a cone. < R <.3 around the direction of the electron is required to be less than 3 GeV. To be added into the sum, the track needs to satisfy similar requirements for photon track isolation. Thirdly, the same cut of calorimeter isolation as photon is applied. Fourthly, two electrons are required to pass electron identification cuts, as shown in Figure. Lastly, the invariant mass of the two electrons is required to be greater than 6 GeV. After the two leading electrons are selected, a photon candidate is selected in a similar way in previous section. The photon candidate is required to have P T above GeV and to be separated from both electrons by R at least.. In addition, the photon candidate is rejected if its supercluster is also associated with any of the leading two electrons. Again, if more than one photon candidate satisfies, the one with largest P T is selected. The same photon selection cuts used for selecting excited muon are then applied to this selected photon candidate. The photon trigger HLT Photon LR is used and found to be very close to % efficient for selected signal samples. Figure 3 left shows the invariant mass distributions for various backgrounds and three low mass signals, for an integrated luminosity of pb. Figure 3 right shows the peak width of the reconstructed invariant mass of e e + γ decays. No event passed in the QCDpt sample, and its contribution is estimated as follows. First, the efficiency of kinematic cuts are obtained, as in previous section. Due to limited statistics, the electron selection efficiency in this sample is estimated by applying all selection cuts to all reconstructed electron candidates with P T greater than GeV, without imposing requirements of kinematic cuts. Similarly for photon selection efficiency. The estimated rate is about. ±.6(stat) events/ pb. Selection efficiencies for various backgrounds and signal samples are listed in Table. After all previous selection cuts, the major Standard Model background left is from inclusive Z ee events. Figure 4 left show the invariant mass distribution of the two electrons, and Figure 4 right shows the invariant mass distribution of the two electrons and the photon. 4. Search potential Following the same way described in Section 3., the final signal selection efficiency as well as the number of background for pb is estimated and is shown in Table 6. Figure 6 shows the systematic uncertainties for each signal mass point due to errors of the PDF set and variations of Q. Figure 7 shows the discovery reach and the expected exclusion limit for each mass point of excited electron, with an integrated luminosity of pb. 6

7 Table : Selection efficiency (%)for two electrons and one photon in signal and background samples. Efficiency in each column is with respect to previous selection. The last column shows the total efficiency. M e (GeV ) kinematic cuts electron selections photon selections trigger cumulative 64.3 ±. 78. ± ±.. ±. 4. ± ± ± ±.. ±.. ± ±. 8.3 ± ±.. ±..7 ± ±. 8.9 ±. 9.9 ±.. ±. 9.6 ±. 8.7 ±. 8. ±. 9.8 ± ±. 6.7 ± ±. 8. ±. 93. ± ± ±. 8.8 ±. 8. ±. 93. ± ±. 64. ±. 86. ±. 8.4 ±. 9.3 ± ± ± ± ±. 9. ± ±. 6.4 ±. Z ee.9 ±. 6.3 ± ±.. ±. 3.9E- ±.9E-3 TTbar 3.9 ±. 4.7 ±..4 ±.. ±. 7.8E-4 ±.8E-4 ZW.9 ± ±. 6.4 ±.9. ±..E- ±.9E-3 ZZ. ± ±.. ±.7. ±. 3.E- ± 3.9E-3 WW.4 ±..7 ±.9 ± ± ± Table 6: The final signal efficiency (%) and the number of estimated background for each excited electron mass point, for an integrated luminosity of pb. M e (GeV ) signal efficiency (ɛ S ± σ ɛs (stat)) number of background (B ± σ B (stat) ± σ B (syst)) 36.4 ±..E+ ± 6.6E- ±.4E ±..7E- ±.7E- ± 3.E ±..3E- ± 8.E- ±.6E- 8.8 ±. 7.E- ± 4.6E- ± 8.8E ±. 4.9E- ± 3.E- ±.8E-3.6 ±..4E- ±.6E- ±.8E ±..6E- ±.E- ±.8E ±..E- ± 7.4E-3 ±.E-3 3. ±. 8.4E-3 ± 6.E-3 ± 9.4E-4 Summary In this analysis, we studied the discovery potential for an exotica particle excited muon and electron in the decay channel with photon, for an integrated luminosity of pb at TeV pp collisions at the LHC. We showed that such a particle could be discovered with mass up to TeV if the compositeness scale is about 3 TeV. We expect to set a more stringent limit on the parameter space of Λ and M than the most recent limit set by D collaboration with fb data[6]. 6 Acknowledgments We are grateful to Toyoko Orimoto, and XXX( to be added). 7

8 References [] U. Baur et al., Excited-quark and -lepton production at hadron colliders, Phys. Rev. D 4, 8 (9). [] S. Bityukov, bityukov/durham/scpv.cc. [3] CMS Collaboration, CMS Physics Technical Design Report, Volume II, CERN/LHCC 6-. [4] J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, hep-ph/9 [] J. Heinrich et al., Interval estimation in the presence of nuisance parameters.bayesian approach,physics/499. [6] D Collaboration, Search for excited electrons in ppbar collisions at sqrt(s) =.96 TeV, hep-ex/

9 q µ q µ Figure : Production of single excited muon by contact interaction. µ, µ, ν µ µ µ γ, Z, W f f Figure : Decay channels of excited muon by electroweak and contact interactions. 9

10 Branching Ratio µ* µ+γ µ* µ+z µ* ν+w µ* µ+ff M µ* /Λ Figure 3: Relative contribution of decays of excited muon via electroweak and contact interactions as a function of M/Λ.. TeV µ* µγ Z/γ* µµ pp µx. TeV µ* µγ Z/γ* µµ pp µx nd Pt of leading µ µ inner track d w.r.t. event vertex.4 (cm) xy. TeV µ* µγ Z/γ* µµ pp µx. TeV µ* µγ Z/γ* µµ pp µx Number of inner tracker hits Σ Pt track ( R <.3) Figure 4: Selection variables and cuts for muons.

11 selected γ,. TeV µ* selected γ, Z µµ γ (µ* decay). TeV µ* γ (ISR/FSR) Z µµ γ (Fake) pp µx PT Σ E tower HCAL ( R <.) / E sc γ (µ* decay). TeV µ* γ (ISR/FSR) Z µµ γ (Fake) pp µx γ (µ* decay). TeV µ* γ (ISR/FSR) Z µµ γ (Fake) pp µx Σ Et calo. ( R <.3) / Et sc Σ Pt track ( R <.3) / PT γ (µ* decay). TeV µ* γ (ISR/FSR) Z µµ γ (Fake) pp µx / E E 3x3 raw SC Figure : Selection variables and cuts for photon.

12 Events pb / GeV Z µµ TTbar ZZ + ZW + WW Λ = 4 TeV M(µ,γ) (TeV) σ M M µ* Figure 6: Left, invariant mass distribution of selected muons and photon, for standard model backgrounds and three low-mass excited muons. Right, reconstructed peak width of excited muons for different mass points. Events pb / 4 GeV Z µµ TTbar WZ + ZZ + WW. TeV µ* (Λ = 4 TeV) Events pb / 4 GeV Z µµ TTbar WZ + ZZ + WW. TeV µ* (Λ = 4 TeV) M(µ,µ) M(µ,µ,γ) Figure 7: M(µ, γ) and M(µ, µ, γ) of selected muons and photon.

13 Events χ / ndf. / 83 norm. ± 4.7 mean 994. ±.3 sigma. ±. alpha.99 ±.476 n 7.6 ± 6.66 Events pb / GeV 3 χ / ndf.464 / 3 p.7 ±.8 p.73 ± M(µ,γ) M(µ,γ) (TeV) Figure 8: Left, invariant mass distribution of TeV signal µ µ + γ decays, fitted with a crystal ball function. Right, invariant mass distribution of standard model background, fitted with an function p /x p. Systematic uncertainties (%) 3 PDF sets cteq6m PDF Q M µ* Figure 9: Systematic uncertainties for different mass points of excited muon, due to errors of the PDF set and variations of factorization scale. 3

14 Λ (TeV) σ discovery pb Λ (TeV) % C.L. exclusion pb M µ* M µ* Figure : Search limits for different mass points of excited muon, for an integrated luminosity of pb. signal e,. TeV e* signal e,. TeV e* Σ E tower HCAL ( R <.)/E sc Σ Et calo. ( R <.3) / Et sc signal e,. TeV e* signal e,. TeV e* Σ Pt track ( R <.3) electron track d xy w.r.t event vertex (cm) Figure : selection cuts for electron candidates. 4

15 signal e,. TeV e* signal e,. TeV e* σ ηη barrel σ ηη endcap signal e,. TeV e* signal e,. TeV e* η barrel in η endcap in signal e,. TeV e* signal e,. TeV e* φ barrel in φ endcap in Figure : electron ID cuts for selecting electron candidates, in barrel and endcap.

16 Events pb / GeV 3 Z ee TTbar ZZ && ZW && WW Λ = 4 TeV M(e,γ) (TeV) σ M M e* Figure 3: Left, invariant mass distribution of selected electrons and photon, for standard model backgrounds and three low-mass excited electrons. Right, reconstructed peak width of excited electrons for different mass points. Events pb / 4 GeV Z ee TTbar WZ + ZZ + WW. TeV e* (Λ = 4 TeV) Events pb / 4 GeV Z ee TTbar WZ + ZZ + WW. TeV e* (Λ = 4 TeV) M(e,e) M(e,e,γ) Figure 4: M(e, γ) and M(e, e, γ) of selected electrons and photon 6

17 Events 3 χ / ndf 7.6 / 3 norm 349 ±.9 mean ±. sigma.477 ±.6 alpha.6349 ±.4 n 3.93 ±.37 Events pb / GeV χ // ndf.93 / / 3 p.8. ± p ± ± M(e,γ) M(e,γ) (TeV) Figure : Left, invariant mass distribution of TeV signal e e + γ decays, fitted with a crystal ball function. Right, invariant mass distribution of standard model background, fitted with an function p /x p Systematic uncertainties (%) 3 PDF sets cteq6m PDF Q Figure 6: Systematic uncertainties for different mass points of excited electron, due to errors of the PDF set and variations of factorization scale. M e* 7

18 Λ (TeV) σ discovery pb Λ (TeV) % C.L. exclusion pb M e* 3 M e* Figure 7: Search limits for different mass points of excited electron, for an integrated luminosity of pb. 8