Search for Dark Matter and Large Extra Dimensions in pp Collisions Yielding a Photon and Missing Transverse Energy

Results are presented from a search for new physics in the final state containing a photon and missing transverse energy. The data correspond to an integrated luminosity of 5.0 inverse femtobarns collected in pp collisions at sqrt(s) = 7 TeV by the CMS experiment. The observed event yield agrees with standard-model expectations for the photon-plus-missing-transverse-energy events. Using models for production of dark-matter particles (chi), we set 90% confidence level (C.L.) upper limits of 13.6--15.4 femtobarns on chi production in the photon-plus-missing-transverse-energy state. These provide the most sensitive upper limits for spin-dependent chi-nucleon scattering for chi masses between 1 and 100 GeV. For spin-independent contributions, the present limits are extended to chi masses below 3.5 GeV. For models with 3--6 large extra dimensions, our data exclude extra-dimensional Planck scales between 1.65 and 1.71 TeV at 95% C.L.

collected using a two-level trigger system, with Level-1 (L1) seeding High Level Triggers (HLT). The single-photon triggers comprising this search are not prescaled, and are fully efficient within the selected signal region of |η γ | < 1.44 [8] and p γ T > 145 GeV. To optimize the analysis for single high-p T photons accompanied by large E T / , photon candidates are restricted to be in the central barrel region, where purity is highest. To distinguish photon candidates from jets, we apply additional calorimetric selections. The ratio of energy deposited in the HCAL to that in the ECAL within a cone of ∆R = 0.15 is required to be less than 0.05, where ∆R = (∆φ) 2 + (∆η) 2 is defined relative to the photon candidate and the azimuthal angle φ is measured in the plane perpendicular to the beam axis. Photon candidates must also have a shower distribution in the ECAL consistent with that expected for a photon [8].
Isolation requirements on photon candidates impose upper limits on the energy deposited in the detector around the axis defined by the EM cluster position and the primary vertex [8].
In particular, the scalar sum of p T depositions in the ECAL within a hollow cone of 0.06 < ∆R < 0.40, excluding depositions within |∆η| = 0.04 of the cluster center, must be <4.2 GeV + 0.006×p γ T , the sum of scalar p T depositions in the HCAL within a hollow cone of 0.15 < ∆R < 0.40 must be <2.2 GeV + 0.0025×p γ T , and the scalar sum of track p T values in a hollow cone of 0.04 < ∆R < 0.40, excluding depositions that are closer to the cluster center than |∆η| = 0.015, must be <2.0 GeV + 0.001×p γ T (with p T in GeV units). The vetoes defined by the |∆η| cutoffs are needed to maintain high efficiency for photons that initiate EM showers within the tracker. The tracker isolation requirement is based on tracks that originate from the primary vertex.
Since the high luminosity of the LHC yields multiple pp interactions per bunch crossing, there are several reconstructed vertices per event. The primary vertex is defined as the vertex that corresponds to the largest sum of the squares of the associated track-p T values. However, to ensure that photon candidates are isolated from charged particle tracks in events with multiple vertices, the tracker isolation requirement must be passed by all reconstructed vertices, or the event is rejected.
The E T / is defined by the magnitude of the vector sum of the transverse energies of all of the reconstructed objects in the event, and is computed using a particle-flow algorithm [9]. The candidate events are required to have E T / > 130 GeV.
All events are required to have the energy deposited in the crystal containing the largest signal within the photon to be within ±3 ns of the time expected for particles from a collision. This requirement reduces instrumental background arising from showers induced by bremsstrahlung from muons in the beam halo or in cosmic rays. Spurious signals embedded within EM showers that otherwise pass selection criteria are eliminated by requiring consistency among the energy deposition times for all crystals within an electromagnetic shower. Photon candidates are removed if they are likely to be electrons, as inferred from characteristic patterns of hits in the pixel detector, called "pixel seeds," that are matched to the EM clusters [10]. In addition, a veto applied to events that contain muon candidates, including those that do not emanate from the collision point, prevents bremsstrahlung from muons in cosmic rays and the beam halo from being reconstructed as prompt photons balanced by E T / . Finally, events are vetoed if they contain significant hadronic activity, defined by: (i) a track with p T > 20 GeV that is ∆R > 0.04 away from the photon candidate, or (ii) a jet that is reconstructed with p T > 40 GeV using the anti-k T [11] particle-flow algorithm [9], within |η| < 3.0 and ∆R < 0.5 of the axis of the photon.
After applying all of the selection criteria, 75 candidate events are found.
Backgrounds that are out of time with the collisions are estimated from data by examining the transverse distribution of energy in the EM cluster and the time-of-arrival of the signal in the crystal with the largest energy deposition. Templates for anomalous signals [12], cosmic-ray muons, and beam halo events are fitted to a candidate sample that has no timing requirement, which reveals that the only significant residual contribution to the in-time sample arises from halo muons, with an estimated 11.1 ± 5.6 events.
Electrons misidentified as photons arise mainly from W → eν events. The matching of electron showers to pixel seeds has an efficiency of = 0.9940 ± 0.0025, as estimated with Monte-Carlo simulated events (MC) and verified with Z → ee events in data. Scaling a control sample of electron candidates by (1 − )/ yields an estimated contribution of 3.5 ± 1.5 W → eν events in the candidate sample.
The contamination from jets misidentified as photons is estimated by using a control sample of EM-enriched QCD events to calculate the ratio of events that pass the signal photon criteria relative to those that pass looser photon criteria but fail an isolation requirement. Since the EM-enriched sample also includes production of direct single photons, this additional contribution to the ratio is estimated by fitting templates of energy-weighted shower widths from MC-simulated γ+jets events to an independent QCD data sample, and used to subtract the γ+jets contribution. This corrected ratio is applied to a subset of the EM-enriched jet events that passes loose photon identification and additional single-photon event selection criteria, providing a background contribution of 11.2 ± 2.8 jet events.
Backgrounds from (Zνν)γ, (W ν)γ, γ+jet, and diphoton events are estimated from MC samples processed through the full GEANT4-based simulation of the CMS detector [13,14], trigger emulation and event reconstruction used for data. The Wγ → νγ samples are generated with MADGRAPH5 [15], and the cross section is corrected to include next-to-leading order (NLO) effects through a K-factor calculated with MCFM [16]. The Zγ → ννγ, γ+jet, and diphoton samples are obtained using the PYTHIA 6.424 generator [17] at leading order (LO) and CTEQ6L1 [18] parton distribution functions (PDF). The Zγ → ννγ sample is also scaled up to reflect NLO contributions given in Ref. [19]. Good agreement between data and the rescaled MC for the Zγ → γ channel has been obtained in previous CMS studies [20]. The uncertainty on Zγ → ννγ and the other backgrounds takes into account several sources: theoretical uncertainties on the LO cross section and K-factors; the uncertainty on the scale factor that models the data-MC difference in the efficiency; and systematic uncertainties on the photon-vertex assignment, modeling of pile-up, and the accuracy of the energy calibration and resolution for photons, jets, and E T / . The expected contribution from the Zγ → ννγ process to the background is 45.3 ± 6.8 events. The combined expected background from (W ν)γ, γ+jet, and diphoton events is 4.1 ± 1.0.
The 73 observed events in data agree with the total expected background of 75.1 ± 9.4 events. Distributions in photon p T for the selected candidate events and for those estimated from background are shown in Fig. 1. The spectra expected from ADD for M D = 1 TeV and n = 3 are superimposed for comparison. Based on these results, exclusion limits are set for the DM and ADD models.
The limits on the cross sections are calculated by dividing the difference between the number of events in data and the predicted number of background events by the product A × × L, where A is the geometric and kinematic acceptance of the selection criteria, is the selection efficiency for signal, and L is the integrated luminosity. A × is calculated by estimating A × MC from the MC and multiplying it by a scale factor to account for the difference in efficiency between MC and data. for axial-vector couplings, respectively. The spectra for ADD MC events are generated using PYTHIA 8.145 [21], requiring p γ T > 130 GeV, and scaled to NLO using a K-factor from Ref. [22]. The factor A × MC for ADD is in the range of 26.5-28.5% in the parameter space spanned by n = 3-6 and M D = 1-3 TeV.
Systematic uncertainties that contribute to the A × MC calculation are from the choice of PDF [18,23,24]; the selection of the primary vertex for the photon, modeling of pile-up, and the energy calibration and resolution for photons [8]; jets [25]; and E T / [26]. The total systematic uncertainty on A × MC is +4.8% and −4.9%.
As mentioned above, A × MC is multiplied by a scale factor (SF) to account for the difference in efficiency between data and MC. The calculated SF of 0.90 ± 0.11 combines contributions from the trigger, photon reconstruction, consistency of cluster timing, and vetoes. The photon HLT is determined to be essentially 100% efficient for our selection criteria in data and in MC, but is assigned a 2% uncertainty due to small L1 trigger inefficiencies. Since the photon identification requirements have similar efficiencies for photons and electrons, the electron efficiency of 0.96 ± 0.02, as measured in Z → ee decays is used as the SF. Corrections for photon reconstruction are described in Ref. [20]. The photon clusters in MC always have consistent timing among individual crystals, and the SF in data is found to be 0.983 ± 0.009 based on a sample of electron events. The track and jet-veto efficiency is studied in samples of W → eν data and MC, and confirmed with Zγ → eeγ data. Since the efficiencies measured in these samples agree within their uncertainties, the SF is set to unity and assigned a systematic uncertainty of ±0.10. The SF for the cosmic-ray muon veto is determined to be 0.95 ± 0.01 by comparing its efficiency in MC and data in a sample of Z → ee events.
Upper limits are placed on the DM production cross sections, as a function of M χ , assuming vector and axial-vector operators, summarized in Table 2a. These are converted into the corresponding lower limits on the cutoff scale Λ, also listed in Table 2a. The Λ values are then translated into upper limits on the χ-nucleon cross sections, calculated within the effective theory framework. These are displayed in Fig. 2 as a function of M χ [2]. The 90% CL limits are presented in Table 2a. Superposed are the results from selected other experiments. Previously inaccessible χ masses below ≈3.5 GeV are excluded for a χ-nucleon cross section greater than  ≈3 fb at 90% CL. For spin-dependent scattering, the upper limits surpass all previous constraints for the mass range of 1-100 GeV. The results presented are valid for mediator masses larger than the limits on Λ, assuming unity for the couplings g χ and g q . The specific case of light mediators is discussed in Ref. In summary, the agreement between single-photon production in pp collisions at 7 TeV and standard-model expectations was used to derive significant upper limits on the vector and axial-vector contributions to the χ-nucleon scattering cross section. This search was complementary to searches for elastic χ-nucleon scattering or χχ annihilation. In addition, through greater sensitivity to the ADD model, the analysis attained the most stringent limits on an effective extra-dimensional Planck scale obtained in the γ+E T / production channel.