Search for Branons at LEP

We search, in the context of extra-dimension scenarios, for the possible existence of brane fluctuations, called branons. Events with a single photon or a single Z-boson and missing energy and momentum collected with the L3 detector in e^+ e^- collisions at centre-of-mass energies sqrt{s}=189-209$ GeV are analysed. No excess over the Standard Model expectations is found and a lower limit at 95% confidence level of 103 GeV is derived for the mass of branons, for a scenario with small brane tensions. Alternatively, under the assumption of a light branon, brane tensions below 180 GeV are excluded.


Introduction
The possible existence of additional space dimensions was suggested by Kaluza and Klein [1] more than eighty years ago. In the original theory, the fundamental scale of gravitation, M F , coincides with the Planck scale, M P ≈ 10 19 GeV. Since then, several theories have used this idea as an alternative way to solve some fundamental problems of physics, particularly those related with gravitation and the unification of all forces. One of the most attractive models is proposed in Reference 2. This model assumes the restriction of the dynamics of the Standard Model to a three-dimensional spatial brane, leaving the gravitation and perhaps some other exotic particles the freedom to propagate in the extra dimensions. If these extra dimensions have a large size, M F is of the order of the electroweak scale and the existence of extra dimensions could manifest at present and future colliders with detection of gravitons, as described by an effective theory with couplings of order M F .
A different scenario is considered in this Letter. In this approach, the presence of a threedimensional brane as an additional physical body in the theory, with its own dynamics, leads to the appearance of additional degrees of freedom. These manifest as new scalar particles, π, called branons. Branons are associated to brane fluctuations along the extra-dimensions [3] and are also natural dark-matter candidates [4]. Their dynamics is determined by an effective theory with couplings of the same order as the brane tension, f .
Searches for gravitons and branons are in a sense complementary [5]. If the brane tension is above the gravity scale, f ≫ M F , the first evidence for extra dimensions would be the discovery of gravitons, giving information about the fundamental scale of gravitation and the characteristics of the extra dimensions. If the brane tension is below the gravity scale, f ≪ M F , then the first signal of extra dimensions would be the discovery of branons, allowing a measurement of the brane tension scale, the number of branons and their masses [6].
Many experimental results were reported on direct searches for gravitons at LEP [7][8][9] and at the TEVATRON [10]. This Letter describes a search for branons in data collected at LEP. Branons couple to Standard Model particles by pairs, suggesting the study of two production mechanisms in e + e − collisions: e + e − →ππγ and e + e − →ππZ. They proceed via the diagrams shown in Figure 1. The experimental signature for branon production at LEP is the presence of either a photon or a Z boson together with missing energy and momentum. This is due to the two branons which do not interact in the detector and are hence invisible. In the following, only decays of the Z boson into hadrons are considered. For a given centre-of-mass energy, only the lighter branons give a significant contribution to the cross sections of the e + e − →ππγ and e + e − →ππZ processes. For simplicity, we will assume a scenario with only one light branon species of mass M.

Data and Monte Carlo Samples
Data collected by the L3 detector [11] at LEP in the years from 1998 through 2000 are considered. They correspond to an integrated luminosity of about 0.6 fb −1 at centre-of-mass energies, √ s, from 188.6 to 209.2 GeV.
The efficiencies for branon production through the processes e + e − →ππγ and e + e − → ππZ →ππqq are determined by reweighting Monte Carlo events of the processes e + e − → ννγ(γ) and e + e − → ννZ → ννqq, respectively, with the differential cross sections of Reference 6. Events from the first process are generated with KK2f and events from the second process with EXCALIBUR, through W-boson fusion.
The L3 detector response is simulated using the GEANT program [21], which describes effects of energy loss, multiple scattering and showering in the detector. Time-dependent detector inefficiencies, as monitored during the data-taking period, are included in the simulation.

Search in the e + e − →ππZ →ππqq channel
The single-Z signature for branon production at LEP is similar to the signature of the associated production of a Z boson and a graviton which was previously studied in data collected by L3 at √ s = 188.6 GeV [8]. The events selected for that search are re-analysed in this Letter to search for branons, and the same analysis procedure is used to select candidate events at √ s = 191.6 − 209.2 GeV. The integrated luminosities considered for each value of √ s are listed in Table 1.
Unbalanced hadronic events with a visible mass compatible with that of the Z boson are selected. The large background from e + e − → qqγ events with a low-angle high-energy photon is reduced by requiring the missing momentum vector to point in the detector. Cuts on event-shape and jet-shape variables are applied to suppress other backgrounds: Z-boson pair-production with one of the Z bosons decaying into neutrinos and the other into hadrons, W-boson pair-production with one of the W bosons decaying into hadrons and the other into a low-angle undetected charged lepton and a neutrino, and single-W production through the e + e − → Weν process, followed by a hadronic decay of the W boson. Table 1 summarises the yield of the selection at the different centre-of-mass energies. In total, 455 events are observed while 470 events are expected from several Standard Model processes. The dominant background is W-boson pair-production (47%). Other sources of background are single-W production (25%), Z-boson pair-production (13%) and the e + e − → qqγ process (12%).
Expectations for a branon signal with M = 0 and f = 40 GeV are also listed in Table 1. The efficiency to detect such a signal is 55%. Two variables are most sensitive to discriminate a possible signal from the Standard Model background: the reduced energy of the Z boson,

Search in the e + e − →ππγ channel
Events with a single photon and large missing energy and momentum, selected by L3 at √ s = 188.6 − 209.2 GeV [7], are re-analysed for the presence of a signal due to the e + e − →ππγ process in addition to the Standard Model contributions from the e + e − → ννγ(γ) and e + e − → e + e − γ(γ) processes. A breakdown of the integrated luminosities as a function of √ s is given in Table 2. Two different energy regimes are considered, depending on the value of the transverse momentum of the photon, p t , relative to the beam energy, E beam , and its polar angle, θ γ . Highp t events, 0.04E beam < p t < 0.60E beam , are selected in both the barrel, | cos θ γ | < 0.73, and endcap, 0.8 < | cos θ γ | < 0.97, regions of the electromagnetic calorimeter. The selection of low-p t events, 0.016E beam < p t < 0.04E beam , relies on a single-photon energy trigger with a threshold around 900 MeV which is active only in the barrel region [22]. Table 2 lists the number of observed data events together with the Standard Model expectations for different values of √ s. The high-p t analysis selects e + e − → ννγ(γ) events with purity above 99% and efficiency above 80%. In total, 838 events are observed in data while 811 are expected from Standard Model processes. Figures 3a and 3b show the measured differential cross sections for the e + e − → ννγ(γ) processes as a function of x γ = E γ /E beam , the fraction of the beam energy carried by the photon and of | cos θ γ |. Data obtained by the highp t selection are corrected for detector acceptance and integrated over the polar-angle fiducial region | cos θ γ | < 0.97. The measured differential cross sections are in good agreement with the Standard Model expectations. The criteria of the low-p t selections are much more stringent in order to be sensitive to very low photon energies while minimizing the huge e + e − → e + e − γ(γ) component. In total, 543 events are observed in data and 554 are expected from Standard Model processes. The main contribution is from e + e − → e + e − γ(γ) events and the e + e − → ννγ(γ) purity is around 24%. The event selection is described in detail in Reference 7. Figures 4a and 4b compare the distributions of x γ and | cos θ γ | observed in data with the expectations of the Standard Model processes. A good agreement is observed.
The presence of a branon leads to an increase in the differential cross sections which is a function of the branon mass M and the brane tension f [6]: where α is the electromagnetic coupling constant. Figures 3 and 4 show the typical distortion in the differential cross sections expected in the presence of a branon signal.

Results
Evidence for branon production was found neither in the e + e − →ππZ →ππqq nor in the e + e − →ππγ channels and the data are interpreted in terms of bounds on the possible production of branons. For each centre-of-mass energy, the data and the expectations are compared in bins of the two-dimensional distributions of x Z vs. cos θ Z for the e + e − →ππZ →ππqq channel and of x γ vs. cos θ γ for the e + e − →ππγ channel. Assuming a Poisson probability distribution for each bin, 95% confidence level exclusion limits are derived according to the method described in Reference 23. Systematic uncertainties are taken into account in the calculation of the limit. For the e + e − →ππZ →ππqq channel, they are similar to those encountered in the study of Z-boson pair-production when one of the bosons decays into hadrons and the other into neutrinos [24] and are dominated by uncertainties on the background normalisation, on the detector energy scale and modelling and from limited Monte Carlo statistics. The main systematic uncertainties for the e + e − →ππγ channel [7] are the modelling of Standard Model process, the determination of the trigger efficiency and the treatment of photons which convert in electron-positron pairs in the detector material in front of the electromagnetic calorimeter.
The bounds from the e + e − →ππZ analysis are shown in Figure 5. For massless branons, the brane tension f must be greater than 47 GeV. There is no sensitivity for branon masses near and beyond the kinematic limit (M ( √ s − m Z )/2) and no bounds on f can be derived for M > 54 GeV. The sensitivity in the e + e − →ππγ channel is larger than that of the e + e − →ππZ →ππqq channel. This is due to two factors: the different coupling of the Z boson and the photon to electrons and a larger phase space available in the presence of a photon in the final state, as opposed to a massive Z boson. The limits obtained from the e + e − →ππγ analysis are also shown in Figure 5. For M = 0, the brane tension f must be greater than 180 GeV. For very elastic branes (f → 0) a lower branon mass bound of M > 103 GeV is obtained. These bounds are the most stringent to date on the possible existence of branons. The bounds for M > 0 GeV complement and improve those deduced from astrophysical observations [4].