Search for TeV-scale gravity signatures in high-mass final states with leptons and jets with the ATLAS detector at $\sqrt{s}=13$ TeV

A search for physics beyond the Standard Model, in final states with at least one high transverse momentum charged lepton (electron or muon) and two additional high transverse momentum leptons or jets, is performed using 3.2 fb$^{-1}$ of proton--proton collision data recorded by the ATLAS detector at the Large Hadron Collider in 2015 at $\sqrt{s}=13$ TeV. The upper end of the distribution of the scalar sum of the transverse momenta of leptons and jets is sensitive to the production of high-mass objects. No excess of events beyond Standard Model predictions is observed. Exclusion limits are set for models of microscopic black holes with two to six extra dimensions.


Introduction
Models of TeV-scale gravity postulate that the fundamental scale of gravity, M D , in a higher-dimensional space-time is much lower than is measured in our four-dimensional space-time. In large extra-dimensional models (e.g. the model proposed by Arkani-Hamed, Dimopoulos and Dvali (ADD) [1,2]) there are n additional flat extra dimensions, assumed to be compactified on a torus with a common radius much larger than 1/M D . Another class of models (e.g. that of Randall and Sundrum (RS) [3,4]) uses one extra dimension in a highly warped anti-de-Sitter space. Both of these types of model can address the large difference between the scale of electroweak interactions, O(0.1 TeV), and that of gravity, the Planck scale, M Pl = O(10 16 TeV), in a natural way. Interesting signatures are expected in these models in the form of non-perturbative gravitational states such as microscopic black holes [5,6]. Such final states could be produced in proton-proton (pp) interactions at the Large Hadron Collider (LHC) [7]. In the absence of a full theory of quantum gravity, predictions for production cross-sections and decays of black holes rely on semi-classical approximations which are expected to be valid if the mass of the black hole is well above M D and also higher than the Hawking temperature [8]. A strong rise in the production rate of such states is expected when the energy scale of the interactions reaches the order of M D . Since the gravitational interaction couples to the energy-momentum tensor rather than gauge quantum numbers, final states are expected to be populated "democratically", according to the number of available Standard Model degrees of freedom. For this reason, it is expected that a significant fraction of final states would contain leptons. This search exploits this feature to enhance the signal contribution in comparison with the dominant background at the LHC, which arises from quark and gluon scattering processes forming hadronic final states. Final states with at least three high transverse momentum (p T ) objects are selected, of which at least one must be an electron or muon (leptons in what follows) and the others can be either leptons or hadronic jets. The discriminating variable used in this search, p T , is the scalar sum of the transverse momenta of high p T objects in an event. The signal is expected to appear at high p T . Searches by ATLAS [9][10][11][12] and CMS [13,14] during Run 1 of the LHC did not reveal any significant excesses over expected background levels. An ATLAS analysis [15] of Run-2 data at 13 TeV also found no evidence of new effects in multijet final states. This work extends the reach of the analysis in Ref. [12], performed at a centre-of-mass energy of 8 TeV, with 3.2 fb −1 of data recorded by ATLAS in 2015 at 13 TeV. This search is potentially sensitive to other forms of new physics at high-mass and involving the electroweak sector. ATLAS [16] is a multipurpose detector with a forward-backward symmetric cylindrical geometry and nearly 4π coverage in solid angle. 1 The inner detector (ID) utilises fine-granularity pixel and microstrip detectors over the pseudorapidity range |η| < 2.5 to provide precise track parameter and secondary vertex measurements. For Run 2 of the LHC, a new pixel layer has been added at a radius of 3.3 cm [17]. A gas-filled straw-tube tracker complements the silicon tracker at larger radii. The tracking detectors are immersed in a 2 T magnetic field produced by a thin superconducting solenoid. The electromagnetic 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam direction. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam direction. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Object separations are measured using ∆R = (∆φ) 2 + (∆η) 2 .

ATLAS detector
(EM) calorimeters employ lead absorbers and use liquid argon as the active medium. The barrel EM calorimeter covers |η| < 1.5 and the end-cap EM calorimeters cover 1.4 < |η| < 3.2. Hadronic calorimetry in the region |η| < 1.7 is performed using steel absorbers with scintillator tiles as the active medium. Liquid-argon calorimetry with copper absorbers is used in the hadronic end-cap calorimeters, which cover the region 1.5 < |η| < 3.2. The forward calorimeters (3.1 < |η| < 4.9) use copper and tungsten as absorber with liquid argon as active material. The muon spectrometer (MS) measures the deflection of muon trajectories in the region |η| < 2.7, using three stations of precision drift tubes (with cathode strip chambers in the innermost station for |η| > 2.0) located in a toroidal magnetic field of approximately 0.5 T and 1 T in the central and end-cap regions, respectively. The muon spectrometer is also instrumented with separate trigger chambers covering |η| < 2.4. Events are selected using a first-level trigger implemented in custom electronics, which reduces the event rate with a design value of 100 kHz using a subset of detector information [18]. Software algorithms with access to the full detector information are then used to yield a recorded event rate of about 1 kHz.

Signal simulation
Signal samples are generated by using the Charybdis2 1.0.4 generator [19] to simulate the production and decay of rotating black holes in models with n = 2, 4 and 6 extra dimensions and values of M D ranging from 2 TeV to 5 TeV. Black holes are assumed to be produced over a continuous range of mass values above a threshold M th , set so as to avoid the theoretical uncertainties associated with the region close to M D . The analysis is guided by two benchmark signal models, the first of which has M D = 2 TeV and M th = 7 TeV, resulting in a cross-section of 0.72 pb. The second has M D = 4 TeV, M th = 6 TeV, and a cross-section of 0.93 pb. In these simulations, no initial-state gravitational radiation is permitted, while the final decay of the black-hole remnant produces a variable number of particles, whose multiplicity is drawn from a Poisson distribution in accordance with the Charybdis2 default. The CTEQ6L1 parton distribution functions (PDFs) used are taken from Ref.
[20], while the final-state fragmentation and parton showering is modelled using Pythia8 [21]. The detector response is modelled using a fast simulation of the response of the calorimeters [22] and Geant4 [23] for other parts of the detector. Events from minimum-bias interactions are also simulated with Pythia8. They are overlaid on the simulated signal and background events according to the luminosity profile of the recorded data. Interactions within the same bunch crossing as the hard-scattering process and in neighbouring bunch crossings are both simulated and are referred to as pile-up.

Event selection
Events are selected from a sample with an integrated luminosity of 3.2±0.2 fb −1 . The luminosity estimate is derived following the same methodology as that detailed in Ref.
[24], from a calibration of the luminosity scale using a pair of x-y beam-separation scans performed in August 2015. The event selection uses the lowest-threshold single-lepton triggers available in each data-taking period with good operational conditions. The single-electron trigger uses a minimum threshold of E T = 60 GeV. The minimum threshold used for the single-muon trigger is p T = 50 GeV. All the final-state objects are required to satisfy basic criteria to ensure that they are well reconstructed and originate from the primary interaction. Candidate electrons and muons are required to have p T > 10 GeV and pseudorapidity |η| < 2.47 (electrons) or |η| < 2.5 (muons). They are also required to satisfy baseline identification criteria (the "Loose" operating point of Ref

Backgrounds
The dominant backgrounds originate from W and Z boson production associated with hadronic jets (W+jets and Z+jets) and from tt production. For these backgrounds, the distributions in kinematic quantities are predicted by Monte Carlo (MC) simulations, which are normalised to data in dedicated control regions (CRs . The detector response is modelled using Geant4. The electron channel also contains background events from hadronic jets which are incorrectly reconstructed as electrons. This background, called "multijet", is estimated from the data using a sample of events selected with loosened identification criteria using the Matrix Method [42]. The rate of background muons from hadronic jets is negligible.
The background CR selection criteria are summarised in Table 1. All of the CRs select events with 750 < p T < 1500 GeV, including at least three objects with p T > 60 GeV of which one is required to be a lepton. The Z+jets CR additionally requires exactly two leptons with the same flavour and opposite charge and an invariant mass m ℓℓ in the range 80-100 GeV. The W+jets CR requires events with exactly one lepton and a missing transverse momentum E miss T [43] exceeding 60 GeV. In this CR, in order to suppress background from top quark production, none of the jets may be b-tagged. The tt CR also requires exactly one lepton, but there must be at least four jets of which at least two are b-tagged. In order to use information about the shape of the p T distribution to more accurately constrain the normalisation of the W+jets, Z+jets and tt backgrounds in the SRs, each control region is divided into three 250-GeV-wide bins.

Systematic uncertainties
The systematic uncertainties in the signal and backgrounds include those due to the limited numbers of simulated events and to the measurement of integrated luminosity. Experimental uncertainties arising from the trigger efficiencies, lepton identification and reconstruction procedures, the b-tagging algorithm and the energy calibration of leptons and jets, as well as effects from the jet energy resolution, are also taken into account. Potential mismodelling by the MC simulations of the W+jets, Z+jets and tt backgrounds is quantified by comparing the nominal against alternative simulated samples and PDF sets.

Results
Results are extracted from profile likelihood fits using three background normalisation parameters for the W+jets, Z+jets and tt backgrounds. These normalisation parameters are freely floating in the fits. Nuisance parameters are included in the fits to describe the systematic uncertainties, taking into account the correlations across the processes and regions involved in each fit. A background likelihood fit to all control regions of both lepton channels, assuming no signal contribution, is used to predict the expected yields in validation regions (VRs) and to test the hypothesis that the data is well described with no signal in these regions. The VRs are defined using the same event selections as the signal regions, but in the range 1500 < p T < 2000 GeV. As in the CRs, any signal contamination in the VRs is expected to be small, based on previous analyses [12] and on signal simulations. Comparisons between the data and the predictions in the control regions, where the background predictions are adjusted by the background likelihood fit, may be seen in Figure 1. The MC simulation provides a good description of the CR data, with scale factors of 0.81±0.07, 1.01±0.08 and 0.95±0.08 for W+jets, Z+jets and tt respectively. No significant deviation from the background prediction is observed in the VRs. Figure 2 shows the data and background predictions for p T in the electron and muon channels following the background likelihood fit, with two signal models overlaid. This figure uses the SR selection except for the final requirement on p T . The data are in good agreement with the background prediction across the range of p T which can be tested with the present data, with the size and pattern of deviations between data and background prediction being consistent with statistical fluctuations and the size of the systematic uncertainties. Table 2 presents the data and background predictions in the signal regions. The number of events observed in SR-3TeV is higher than the background estimate in the electron channel with a p-value of 1% when tested against the background-only hypothesis. The excess is not sufficiently significant to be considered as evidence of any new physics effect. The final results are therefore derived from the combination of the two channels. The observed numbers of events in SR-2TeV and SR-3TeV are 192 and 13 respectively for the combination of the electron and muon channels, to be compared with fitted background predictions of 181 ± 11 and 9.9 ± 1.4.
Model-independent cross-section upper limits on any potential new physics contribution are obtained from fits to all control regions and to signal regions combining the electron and muon channels, with potential signal contributions included via a freely-floating parameter in those signal regions. Modelindependent upper limits of 12.1 fb (3.4 fb) at the 95% confidence level (CL) are set on the maximum observable cross-section (defined as cross-section × acceptance × efficiency) allowed for any form of new physics in the SR-2TeV (SR-3TeV) region which produces a lepton in conjunction with at least two other objects, each with p T > 100 GeV.
Fits including predicted signal yields in all control and signal regions simultaneously are used to extract exclusion limits for specific black-hole signal models. Since the signal regions overlap in p T , these exclusion fits are performed for p T > 3 TeV, combining the electron and muon data. Confidence levels are evaluated using the CL s procedure [45]. The results are shown in Figure 3, together with the corresponding limit from the Run 1 analysis at √ s = 8 TeV [12]. The impact on the M th limit for n = 6 due to the PDF-induced uncertainties in the signal cross-section varies from ±200 GeV to ±100 GeV as M D varies from 2 TeV to 5 TeV. The limit on M th is more stringent than that from the Run 1 search by almost 3 TeV at M D = 2 TeV and by more than 2 TeV at M D = 4 TeV. For a model of rotating black holes with two extra dimensions, the 95% CL lower limit on the threshold mass M th is set at 7.8 TeV for M D = 2 TeV. For a model with six extra dimensions, the limit is set at 7.4 TeV for M D = 5 TeV.

Conclusion
A search has been performed for signatures of TeV-scale gravity in high-mass final states including at least one lepton in conjunction with at least two other leptons or hadronic jets each with p T > 100 GeV, using 3.2 fb −1 of proton-proton collisions recorded by the ATLAS detector at the LHC at a centre-of-mass energy of 13 TeV. No significant deviation from the background predictions is observed. Upper limits are therefore set on the possible contribution of new physics processes in this class of final states at 12.1 fb (3.4 fb) at 95% CL for p T > 2 TeV (3 TeV). Constraints are placed on production of microscopic black holes in models with two to six extra space dimensions which substantially extend the excluded range of model parameters. The results of this analysis could potentially be used to constrain other models predicting new phenomena at the TeV scale involving decays to leptons and jets. [