Excited Leptons at the CERN Large Hadron Collider
? O. J. P. Eboli1 , S. M. Lietti1 and Prakash Mathews2
de F?sica da USP, ? C.P. 66.318, S?o Paulo, SP 05389-970, Brazil. a
arXiv:hep-ph/0111001v2 14 Feb 2002
of Physics, University of Hyderabad, Hyderabad 500 046, India.
We analyze the potential of the CERN Large Hadron Collider (LHC) to search for excited spin- 1 electrons and neutrinos. Assuming an SU (2)L ? 2 U (1)Y invariant model, we study in detail the single production of excited electrons and neutrinos and respective backgrounds through the reactions pp → e+ e? V and e± νV with V = γ, W , or Z. We show that the LHC will be able to tighten considerably the direct constraints on these possible new states, probing excited lepton masses up to 1–2 TeV depending on their couplings to fermions and gauge bosons.
The standard model (SM) of electroweak interactions explains very well the available experimental data . Notwithstanding, some important questions are still left unanswered, in particular, the proliferation of fermionic generations and their complex pattern of masses and mixing angles are not explained by the model. A rather natural explanation for the replication of the fermionic generations is that the known leptons and quarks are composite  and they should be regarded as the ground state of a rich spectrum of fermions. Therefore, the observation of excited quarks and leptons would be an undeniable signal for compositeness . Up to now all direct searches for compositeness have failed. At the DESY ep collider HERA , operating in the e+ p mode, no evidence of excited fermions was found which leads to 95% C.L. bounds O(200) GeV on the excited lepton mass for m? = Λ, where we denote by Λ the strong dynamics scale. The direct search for single and pair productions of excited leptons at the CERN e+ e? collider LEP leads to 95% C.L. constraints on m? of the order O(100) GeV for m? = Λ . In this work, we reexamine the single production of excited spin- 1 electrons (e? ) and 2 neutrinos (ν ? ) at the LHC via the reactions 1
pp → e± e?? → e+ e? V , pp → νe?± + ν ? e± → e± νV ,
where V stands for γ, W ± or Z. We carefully analyze the SM backgrounds and signals for an SU(2)L ? U(1)Y invariant model, which is described below. We show that the strongest limits are obtained for V = γ and that the CERN Large Hadron Collider (LHC) will be able to probe for excited electrons and neutrinos with masses up to 1 TeV, assuming that m? = Λ. The outline of this paper is the following. In section II we review the model used in our analysis. Section III contains our results while the conclusions are presented in Section IV.
The strong dynamics of the lepton constituents is unknown, therefore, we employ a model-independent analysis of the e?ects of fermion compositeness based on e?ective Lagrangian techniques. In this work, we assume that the excited fermions have spin and isospin 1 since the last assignment allows the excited fermions to acquire their masses prior 2 to SU(2) ? U(1) breaking, avoiding dangerous bounds coming from the precise determinations of ?ρ. In the case of the ?rst generation leptons, the assumed lightest particle spectrum is lL = νe e ; eR
? νe e?
? νe e?
The Lagrangian describing the transition between ordinary and excited fermions should exhibit chiral symmetry in order to protect the light leptons from acquiring radiatively a large anomalous magnetic moment . The SU(2) ? U(1) invariant Lagrangian describing the interaction between excited and ordinary leptons is  Lll? = 1 ? ?ν τ Y gf W?ν + g ′ f ′ B?ν lL + h.c. , LR σ 2Λ 2 2 (4)
where Λ is the compositeness scale while g and g ′ are, respectively, the SU(2)L and U(1)Y coupling constants. Here the constants f and f ′ are weight factors which can be interpreted as di?erent scales Λi = Λ/fi for the gauge groups. As usual, the tensors W?ν and B?ν represent the ?eld-strength tensors. Notice that our hypothesis implies that only the righthanded part of the excited fermions takes part in the generalized magnetic interaction with the known leptons. In the physical basis, the Lagrangian (4) can be written as Lll? = e0 e0 ? ? ? ? (f ? f ′ )N?ν f l? σ ?ν lL + Θl ,l l? σ ?ν l′ L + h.c. , 2Λ 2Λ l,l′=νe ,e ?ν l=νe ,e (5)
? where ? (?? ) stands for νe or e (νe or e? ) and e0 is the proton electric charge. The ?rst term contains only triple vertices with N?ν = ?? Aν ? (sw /cw )?? Zν and it vanishes for f = f ′ . On the other hand, the second term contains triple as well as quartic vertices with
νe Θ?ν,νe =
Θe ,e ?ν Θνe ,e ?ν
? ? ? ?
e + ? 1 ?? Zν ? i 2 W? Wν , sw cw sw c2 ? s2 e + ? w = ? 2?? Aν + w ?? Zν ? i 2 W? Wν sw cw sw √ 2 cw + + = , ?? Wν ? ieW? Aν + Zν sw sw √ 2 cw ? ? ?? Wν + ieW? Aν + Zν . = sw sw
Adding all the contributions, the chiral V l? l vertex is
V Γ? f ?? f
e0 ν q σ?ν (1 ? γ5 )fV , 2Λ
with V = W , Z,or γ and q being the incoming V momentum. The weak and electric charges, fW , fZ , and fγ are fW = √ 1 f , 2sw 4I3L (c2 f + s2 f ′ ) ? 4ef s2 f ′ w w w , fZ = 4sw cw fγ = ef f ′ + I3L (f ? f ′ ) ,
where ef is the excited fermion charge in units of the proton charge, I3L is its weak isospin, and sw (cw ) is the sine (cosine) of the weak mixing angle. We present our results using the two complementary coupling assignments f = f ′ and f = ?f ′ . For example, for the case f = f ′ (f = ?f ′ ), the coupling of the photon to excited neutrinos (electrons) vanishes. In order to illustrate the changes in the phenomenology when we vary f and f ′ we display in Table I the branching ratios for excited electrons and neutrinos for the above choices of couplings.
III. SIGNALS AT LARGE HADRON COLLIDERS
In this paper we analyze the potentiality of the LHC to directly search for excited electrons and neutrinos via the reactions (1) and (2). The signal and backgrounds were simulated at the parton level with full tree level matrix elements, taking into account interference e?ects between the SM and excited lepton contributions. This was accomplished by numerically evaluating helicity amplitudes for all subprocesses using MADGRAPH  in the framework of HELAS , with the new interactions being implemented as additional Fortran routines. In our calculations we used the Martin–Roberts–Stirling Set G [MRS (G)]  proton structure functions with the factorization scale Q2 = s. ? Let us, initially, concentrate on the case in which the produced vector boson is a γ, that is, the reactions pp → e+ e? γ and pp → e± νγ. At tree level, these ?nal states can be obtained through the single production of excited leptons via the Drell–Yan mechanism, followed by their radiative decays, i.e. 3
q q → Z ? /γ ? → e± e? ? → e± e? γ , ? qq ′ → W ?± → νe? ± + e± ν ? → νe± γ . We applied to the above processes the following acceptance cuts pT > 20 GeV , |ηe± ,γ | < 2.5 , ?R(e+ e? ),(e+ γ),(e? γ) > 0.4 ,
where pT is the transverse momentum of the visible particle or the missing transverse momentum when a neutrino is produced. η stands for the pseudo-rapidity of the visible particles √ and ?R (= ?η 2 + ?φ2 ) is the separation between two of them. After applying these initial cuts, the SM cross sections are σpp→e+e? γ = 1.29 pb , σpp→e±νγ = 2.88 pb . A natural way to extract the excited electron signal, and at the same time suppress the SM backgrounds, is to impose a cut on the eγ invariant mass. For instance, Fig. 1(a) [(b)] contains the eγ invariant distribution in the reaction pp → e+ e? γ [e± νγ] for the SM and with the inclusion of an excited electron with mass m? = 250 GeV and f /Λ = f ′ /Λ = 5 TeV?1 . From these ?gures we can see that it is convenient to collect the data in eγ invariant mass bins since the signal is concentrated in a small region of this invariant mass spectrum. Therefore, we introduced the cut |Me± γ ? M| < 25 GeV , (12)
where M is the center of a 50 GeV invariant mass bin. Certainly this cut is ideal for excited electrons of mass m? = M . However, the cut (12) is e?cient only for excited electron masses up to 1250 GeV since heavier excited electrons are rather broad resonances and we also run out of statistics. Consequently, we only considered M ≤ 1500 GeV. To search for heavier excited electrons (m? > 1500 GeV), we performed a new analysis replacing the cut (12) by Me± γ > 1250 GeV . (13)
To further reduce the SM background, we also vetoed events exhibiting Z’s decaying into e+ e? pairs through the cut Me+ e? > 120 GeV. (14)
Excited neutrinos contribute only to the e± νγ production and they can be identi?ed by the γ/T transverse mass (MT ) distribution; see Fig. 2. Analogously to the excited electron p case, we looked for an excess of events in MT bins of 50 GeV via the additional cut |MT + 15 GeV ? M | < 25 GeV , 4 (15)
where M is a variable parameter. This cut enhances the signal of excited neutrinos whose mass is M . Once again, the cut (15) is e?cient only for excited neutrino masses up to 1250 GeV so we restricted M ≤ 1500 GeV. For higher masses (m? > 1500 GeV), the decay width of the excited neutrino is so large that we performed a di?erent study replacing the cut (15) by MT > 1250 GeV . (16)
The above cuts (12)–(16) reduce the SM background drastically. For instance, assuming an excited lepton mass of 250 GeV (= M ) the SM background for the processes (1) and (2) is reduced to
eγ σpp→e+e? γ = 3.55 fb , eγ σpp→e± νγ = 51.7 fb ,
MT σpp→e± νγ = 12.3 fb ,
where we applied cuts (11-14) to the ?rst two results and (11), (15) and (16) to the last one. Tables II–IV contain the cross sections of the irreducible background after cuts for several excited lepton masses where we can see that the background diminishes very fast with the increase of m? . At this point, it is important to consider other possible sources of background to these ?nal states since the irreducible background has been largely reduced. For example, additional backgrounds are pp → e+ e? jet and pp → e± ν jet, where a jet is misidenti?ed as a photon. Taking the jet faking photon probability at the LHC to be ffake = 1/5000 , we present also in Tables II–IV the expected cross section for these processes. Another possible reducible background for the process pp → e± νγ is the reaction pp → e+ e? γ with one of the charged leptons escaping undetected, that leads to missing transverse momentum. We also evaluated this processes, however, its cross section turns out to be negligible. In order to quantify the LHC potential to search for excited leptons, we de?ned the statistical signi?cance S of the signal S= |σtotal ? σback | √ L , √ σback (17)
where L is the LHC integrated luminosity, that we assumed to be 100 fb?1 . S can be easily evaluated using Tables II–IV and the expected signal cross section. In order to derived the attainable limits at the LHC, we assumed that the observed number of events is the one predicted by the SM. Let us start our analysis by the search for excited electrons. In this case, we assumed that f = f ′ in order to reduce the number of free parameters, and we imposed the cuts (11) – (14) with M = m? to maximize the sensitivity for excited fermions of mass m? . We display in Figure 3(a) the 95% C.L. bounds on the coupling |f /Λ|, coming from the process pp → e+ e? γ (e± νγ), as a function of the excited electron mass. As we can see, the e+ e? γ production leads to slightly better limits on excited electrons except at small m? . The 5
combined results of these two processes are also presented in this ?gure and these bounds turn out to be at least an order of magnitude more stringent than the present best limits coming from the HERA experiments. Moreover, the LHC will be able to extend considerably the range of excited electron masses that can be probed (up to 2 TeV). In the study of the excited neutrino production, we assumed f = ?f ′ that leads to a ? non-vanishing νe νe γ coupling. The 95% C.L. limits on |f /Λ| that can be obtained from the reaction pp → e± νγ, where we imposed the cuts (11) and (15) – (16), are shown in Figure 3(b). Notice that the limits on excited neutrinos from this process are looser (stronger) than the ones derived for excited electrons for m? < 1400 (> 1400) GeV. Furthermore, these bounds are orders of magnitude more stringent than the presently available ones and they span a much larger range of excited neutrino masses. It is also interesting to obtain a bound on the excited electron mass assuming that f = f ′ and f /Λ = 1/m? . In this scenario, the LHC will be able to rule out excited electrons with masses smaller than 1 TeV, at 95% C.L., through the study of either the e+ e? γ or e± νγ productions, while their combined results increase this limit by 40 GeV. This limit improves the present HERA bound (233 GeV)  by a factor of roughly 5. In the case of excited neutrinos, assuming f = ?f ′ and f /Λ = 1/m? , the analysis of the e± νγ ?nal state leads to m? > 838 GeV at 95% C.L.. Again, this limit is much more restrictive than the available HERA one (? 150 GeV). Note that for the choice f = f ′ (f = ?f ′ ), the coupling of excited neutrinos (electrons) to photons vanishes. In this way, the production of a pair of leptons ee or eν with a photon can probe only the excited electron (neutrino) production if f = f ′ (f = ?f ′ ). Therefore, we should also consider the excited lepton decay into a W or a Z and an ordinary lepton in these cases. Taking into account only the leptonic decay of the weak gauge bosons, we also analyzed the processes pp → e+ e? e+ e? and e+ e? e± ν. Notice that excited electrons can contribute to both reactions, while excited neutrinos only to the second one. In order to look for excited electrons in the e+ e? e+ e? and e+ e? e± ν productions, we applied initially the acceptance cut (11) and then required Me+ e? > 20 GeV (18)
for all possible e+ e? pairs. This cut reduces the SM contribution due to photon exchange. The SM background to the e+ e? e+ e? production receives a large contribution from the Z pair production and it can be further suppressed by vetoing events that exhibit two e+ e? pairs compatible with being a Z, i.e. |Me+ e? ? mZ | < 25 GeV and |Me+ e? ? mZ | < 25 GeV
1 1 2 2
or ? mZ | < 25 GeV and |Me+ e? ? mZ | < 25 GeV,
where e± (e± ) is the electron/positron with the highest (smallest) energy. 1 2 The SM background for the excited neutrino search in the e+ e? e± ν channel can be depleted by requiring that the transverse mass calculated using all charged leptons satisfy 6
MTeν > 20 GeV.
Another important SM contribution to this reaction is W Z production with the Z decaying into a pair e+ e? and the W decaying into a pair eν. In order to reject this process, we vetoed events displaying a pair e+ e? compatible with being a Z and the invariant mass of the remaining e± close to the W mass, i.e. |Me± e? ? mZ | < 25 GeV and |MTe± ν ? mW + 15 GeV | < 25 GeV. (21)
Moreover, the excited electron signal in this topology originates from its charged current production in association with a neutrino. Therefore, the three charged leptons in the ?nal state come from the decays of the excited electron. To further enhance the signal we performed the analysis considering bins in the invariant mass of the three charged leptons in the ?nal state Meee , i.e. we demanded that |Meee ? M | < 25 GeV, where the center of the bin M is again a variable parameter. We present in Figure 4(a) the attainable 95% C.L. limits on excited electrons coming from the e+ e? e+ e? and e+ e? e± ν reactions, assuming that f /Λ = f ′ /Λ and f /Λ = ?f ′ /Λ. As we can see, the bounds for f /Λ = f ′ /Λ are an order of magnitude weaker than the ones originating from the decay of the excited electron into a photon–electron pair. Notwithstanding, these processes are important when this decay channel is closed. As expected, the four lepton bounds for f /Λ = ?f ′ /Λ are O(20)% more restrictive than the ones for f /Λ = f ′ /Λ. The charged current production of excited neutrinos can contribute only to the e+ e? e± ν ?nal state. The decay of the excited neutrino either in eW or in νZ leads to e+ e? ν once we consider the W and Z decay into ?rst family leptons. Therefore, the transverse mass of the e+ e? MTeeν = 2(pTee pTmiss ? pTee · pTmiss ) , (23) (22)
where pee = pe+ +pe? and pTee is its transverse momentum, characterizes the excited neutrino production. In order to isolate the excited neutrino signal in the e+ e? e± ν topology, we initially applied the cuts (11), (18), and (20) and then we required the event to present an e+ e? pair with a transverse mass in the bin |MTeeν + 15 GeV ? M | < 25 GeV, (24)
with M being a variable parameter that enhances the search for excited neutrinos with mass m? = M . We present in Figure 4(b) the attainable 95% C.L. limits on excited neutrinos coming from the e+ e? e± ν reaction, assuming that f /Λ = f ′ /Λ and f /Λ = ?f ′ /Λ. As we can see, these bounds are an order of magnitude weaker than the ones coming from the decay of the excited neutrino into a photon-neutrino pair for f = ?f ′ . 7
IV. SUMMARY AND CONCLUSIONS
We analyzed the potential of the LHC to unravel the existence of excited leptons through the study of the processes (1) and (2). We assumed a center-of-mass energy of 14 TeV and an integrated luminosity of 100 fb?1 in our calculations. The ?nal states containing a photon (e+ e? γ or e± νγ) lead to the most stringent bounds, as can be seen in Figure (3), provided the excited lepton (?? ) has a sizable branching ratio into pairs ?γ. Otherwise, the search for excited leptons should be carried out studying the ?nal states e+ e? e+ e? and e+ e? e± ν where our results are presented in Figure (4). We also considered the possibility of the V boson in the processes (1) and (2) decaying into muons, however the improvement in the bounds is marginal. < For light excited leptons (m? ? 200 GeV), the attainable limits at the LHC are less stringent than the bounds originating from LEP , but they are comparable to the limits obtained by HERA . Notwithstanding, the LHC bounds are much stronger than the presently available ones for a large range of excited lepton masses (up to 2 TeV), being at least one order of magnitude better. Furthermore, assuming f = f ′ and f /Λ = 1/m? , the LHC will be able to exclude the existence of excited leptons with masses up to 1 TeV. A similar sensibility can be reached at the Next Linear Collider (NLC) . In our analysis, we assumed that the excited leptons interact with the SM particles via the e?ective operator (4). This is a conservative assumption since it is possible that excited fermions may also couple to ordinary quarks and leptons via contact interactions originating from the strong constituent dynamics. In this case, the production cross section should be enhanced . However, the contact interactions also modify the Drell-Yan process and can be strongly constrained if no deviation from the SM predictions is observed in this process.
This work was supported by Conselho Nacional de Desenvolvimento Cient? ??co e Tecnol?gico (CNPq), by Funda??o de Amparo ` Pesquisa do Estado de S?o Paulo (FAPESP), o ca a a and by Programa de Apoio a N? cleos de Excel?ncia (PRONEX). u e
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m? (GeV) 100 250 500 750 1000 e? → eγ e? → eZ e? → νW ν ? → νγ ν ? → νZ ν ? → eW
0.728 0.317 0.289 0.284 0.282
(0.) (0.) (0.) (0.) (0.)
0.012 0.103 0.111 0.113 0.113
(0.137) (0.381) (0.391) (0.393) (0.393)
0.260 0.580 0.600 0.603 0.605
(0.863) (0.619) (0.609) (0.607) (0.607)
0. 0. 0. 0. 0.
(0.728) (0.317) (0.289) (0.284) (0.282)
0.137 0.381 0.391 0.393 0.393
(0.012) (0.103) (0.111) (0.113) (0.113)
0.863 0.619 0.609 0.607 0.607
(0.260) (0.580) (0.600) (0.603) (0.605)
TABLE I. Branching ratios of excited leptons with the coupling constant assignment ′ = 0 (f = ?f ′ = 0). Notice that the branching ratios do not dependent on the value f = f of Λ.
M (GeV) 100 250 500 750 1000 1250 1500 - 2500
pp → e+ e? γ 31.43 3.55 0.279 0.051 0.0139 0.0048 0.0243
pp → e+ e? jet 0.18 0.04 0.004 0.001 0.0002 0.0001 0.0004
total 31.61 3.59 0.283 0.052 0.0141 0.0049 0.0247
TABLE II. Cross sections in fb of the irreducible and jet faking photon backgrounds for the process pp → e+ e? γ after cuts (11) and (14). For M up to 1500 GeV, the invariant mass cut (12) was also imposed while for higher M the invariant mass cut (13) was applied.
M (GeV) 100 250 500 750 1000 1250 1500 - 2500
pp → e± νe± γ 768.0 51.65 3.54 0.74 0.23 0.087 0.54
pp → e± νe± jet 53.9 2.94 0.17 0.03 0.01 0.002 0.01
total 821.9 54.59 3.71 0.77 0.24 0.089 0.55
TABLE III. Cross sections in fb of the irreducible and jet faking photon backgrounds for the process pp → e± νe± γ after the cuts (11). For M up to 1500 GeV, the invariant mass cut (12) was also applied while for higher M the invariant mass cut (13) was imposed.
M (GeV) 100 250 500 750 1000 1250 1500 - 2500
pp → e± νe± γ 857.3 12.25 0.57 0.08 0.017 0.004 0.029
pp → e± νe± jet 68.3 2.20 0.13 0.02 0.005 0.001 0.007
total 925.6 14.45 0.70 0.10 0.022 0.005 0.036
TABLE IV. Cross sections in fb of the irreducible and jet faking photon backgrounds for the process pp → e± νe± γ after the cuts (11). For M up to 1500 GeV, the invariant mass cut (15) was also used, while for higher M the invariant mass cut (16) was applied.
FIG. 1. Invariant mass distribution of the pair eγ in the process pp → e+ e? γ (a) and pp → e± νγ (b). The full line stands the SM background and the dashed line for the excited electron signal, assuming m? = 250 GeV and f /Λ = f ′ /Λ = 5/TeV.
FIG. 2. Transverse mass distribution in the reaction pp → eνγ at LHC. The full line represents the SM background while the dashed line stands for an excited neutrino signal, assuming m? = 250 GeV and f /Λ = f ′ /Λ = 5/TeV.
FIG. 3. 95% C.L. limits on the coupling |f /Λ| of excited electrons (a) and excited neutrinos (b). In (a) the dotted (dashed) line stands for the bounds coming from the pp → e± νγ (e+ e? γ) reaction while the solid line represents the combined results. In (b), the solid line displays the bounds coming from the process pp → e± νγ.
FIG. 4. 95% C.L. limits on the coupling |f /Λ| of excited electrons (a) and excited neutrinos (b) obtained by combining the searches in the reactions pp → e+ e? e± ν and pp → e+ e? e+ e? . The solid (dashed) line stands for the coupling assignment f = f ′ (f = ?f ′ ).