Search for Large Extra Dimensions in the Diphoton Final State at the Large Hadron Collider

A search for large extra spatial dimensions via virtual-graviton exchange in the diphoton channel has been carried out with the CMS detector at the LHC. No excess of events above the standard model expectations is found using a data sample collected in proton-proton collisions at sqrt(s) = 7 TeV and corresponding to an integrated luminosity of 36 inverse picobarns. New lower limits on the effective Planck scale in the range of 1.6-2.3 TeV at the 95% confidence level are set, providing the most restrictive bounds to date on models with more than two large extra dimensions.

where √ŝ is the center-of-mass energy of the hard parton-parton collision. We note that the HLZ convention contains an explicit dependence on the number of extra dimensions.
Searches for extra dimensions via virtual-graviton effects have been conducted at HERA, LEP, and the Tevatron (Refs. [3,8] contain recent reviews of these searches). The most stringent previously published limits on M S come from the D0 measurements in the dijet [9] and diphoton plus dielectron [10] channels, which exclude values of M S lower than 1.3−2.1 TeV at 95% confidence level (CL), depending on n ED .
In this paper, we present a search for virtual-graviton contributions in the diphoton final state, using a data sample corresponding to an integrated luminosity of 36 pb −1 , collected in pp collisions at √ s = 7 TeV at the CERN Large Hadron Collider (LHC) with the Compact Muon Solenoid (CMS) detector.

Event Reconstruction and Selection
We first require that an event be consistent with a pp collision and have at least one wellreconstructed primary vertex [13]. We then reconstruct photons with E T > 30 GeV in the ECAL barrel fiducial region (|η| < 1.44) by clustering electromagnetic energy depositions in the ECAL. The ECAL clusters are five crystals wide in η and a variable length in φ to capture associated electromagnetic energy from possible photon conversions in the tracker. If hits are present in the pixel detector consistent with an electron track whose momentum and location is similar to the energy and location of the ECAL cluster, then the cluster is rejected as a photon candidate. In 2010 collision data, the ECAL has an energy resolution better than 1% in the barrel for unconverted photons with E T > 20 GeV [14].
Hadronic jets can be misidentified as photons when their leading hadron is a hard π 0 or η. We reduce the misidentification rate by placing the following restrictions on the isolation of the cluster: (i) the hadronic energy within ∆R < 0.15 of the cluster must be less than 5% of its electromagnetic energy; (ii) the scalar sum of the transverse momentum of tracks, Σp T , associated with the primary event vertex surrounding the cluster within a hollow cone of 0.04 < ∆R < 0.40 must be less than 2.0 GeV + 0.001E T , where E T is the photon transverse energy (a rectangular strip of ∆η × ∆φ = 0.015 × 0.400 is excluded from the track p T summation to allow for photons that convert into e + e − pairs); (iii) the ΣE T of ECAL energy surrounding the cluster within 0.06 < ∆R < 0.40 (and excluding a strip of ∆η × ∆φ = 0.04 × 0.400) must be less than 4.2 GeV + 0.006E T ; and (iv) the ΣE T of HCAL energy surrounding the cluster within 0.15 < ∆R < 0.40 must be less than 2.2 GeV + 0.0025E T . Here We also require that the shower shape in η, σ ηη , be consistent with a photon. The σ ηη variable is a modified second moment of the electromagnetic energy cluster about its mean η position, defined in Ref. [15]. Topological and timing criteria suppress noise present in the ECAL [14, 16].
We reconstruct two photons using the selection described above and require that the invariant mass of the two photons satisfies M γγ > 60 GeV. The invariant mass and photon pseudorapidity selection criteria are optimized to produce the highest sensitivity for values of M S and n ED to which the present data is sensitive. Alternating between fixing the M γγ requirement and floating the |η| requirement-and vice versa-results in a final choice of |η| < 1.44 and M γγ > 500 GeV. The optimal choice for |η| was very close to the ECAL barrel-endcap boundary, so we chose the edge of the transition region into the boundary for simplicity. This defines the signal region. The intervals 60 < M γγ < 200 GeV and 200 < M γγ < 500 GeV define the control and intermediate regions of the data, respectively.
The photon reconstruction and identification efficiency is measured in Monte Carlo (MC) simulation and corrected using a data/MC scale factor of 1.010 ± 0.012 derived from studying Z → e + e − events. The final efficiency is roughly constant as a function of the photon E T and η. The efficiency for an E T > 30 GeV photon with |η| < 1.44 is (87.8 ± 2.3)%, where the dominant systematic uncertainty is chosen to cover the variation as a function of E T and η. Therefore, the corresponding diphoton reconstruction and identification efficiency is (77.1 ± 4.5)%.

Signal and Background Estimation
We simulate ED in the ADD model using the SHERPA (v1. 1.2) [17] MC generator, which samples different operating points in M S and n ED , followed by a fast parametric simulation of the CMS detector [18]. A fast simulation is adequate for describing multiphoton final states and has been extensively validated using full simulation of the detector via GEANT4 [19]. The simulation includes both SM diphoton production and signal diphoton production via KK-graviton exchange, in order to account for the interference effects. We use CETQ6L1 [20] parton distribution functions (PDF) in the simulation. The leading order (LO) SHERPA cross sections are multiplied by a next-to-leading order (NLO) K factor of 1.3 ± 0.1 [21], where the systematic uncertainty covers the variation of the K factor with the diphoton mass. Additionally, a 1.5% relative uncertainty on the signal acceptance is included to account for uncertainty due to the PDF.
Backgrounds due to the mimicking of a photon signal by a jet are small in the signal region. There are two sources of these backgrounds from isolated photon misidentification which we consider: multijet production and prompt photon production (i.e., photons from γ + jets). In particular, we measure a misidentification rate, defined as the ratio of the number of isolated photons to non-isolated photons in a sample, where the non-isolated photons are selected similarly to the isolated photons except that they fail one of the isolation or shower-shape criteria. The definition of the numerator and denominator are given so that the two sets are exclusive to each other. The misidentification rate is measured in an EM enriched sample and is then applied to the observed events with one or more non-isolated photons, resulting in a prediction of the dijet and γ + jet backgrounds.
Because a given control sample in which we measure the misidentification rate may contain some number of real, isolated photons that "contaminate" the misidentification-rate numerator, we correct for the numerator purity on a sample-by-sample basis. This is done by releasing the σ ηη requirement and fitting the numerator sample for the fraction of prompt photons us-ing one-dimensional probability density histograms ("templates") in σ ηη . The signal template is constructed from MC simulation, and the background template is constructed by using inverted isolation criteria. The measured misidentification rate falls from 28% at E T = 30 GeV to 2% at E T = 120 GeV. We use two other complementary techniques (using converted photons and an isolation template to estimate prompt-photon contamination) to bound the misidentification rate and apply a conservative 20% systematic uncertainty, which is the dominant uncertainty on the background estimation.
The diphoton background is computed with the SHERPA MC program and then rescaled by an NLO K factor of 1.3 [21,22]. This K factor is alternatively derived with DIPHOX [23], wherein we observe that the K factor decreases slowly as a function of diphoton invariant mass and stabilizes in the range of interest. We therefore use a K factor of 1.3 ± 0.3 for the diphoton background to cover its variation as a function of M γγ throughout the control, intermediate, and signal regions (M γγ > 60 GeV). We observe (expect) 440 (374 ± 51) events with M γγ > 60 GeV and zero (0.30 ± 0.07) with M γγ > 500 GeV.    Fig. 2. In the control region, we find that the data are consistent with the background expectation within the systematic uncertainty. The systematic uncertainty on the the total background takes into account the correlations between dijet and γ + jet backgrounds arising because both depend on the same misidentification rate. The relative combined uncertainty on the backgrounds in the signal region is 22%, due nearly entirely to the diphoton NLO K-factor uncertainty.

Results
We perform a counting experiment in the signal region (M γγ > 500 GeV) and set 95% CL upper limits on the quantity where σ total represents the total diphoton production cross section (including both signal, SM, and interference effects), and σ SM represents the SM diphoton production cross section, only. We indicate the signal branching fraction to diphotons by β and the signal acceptance by A. We utilize a standard Bayesian approach [3,24] with a flat prior chosen for the signal cross section and log-normal priors for the nuisance parameters (integrated luminosity, signal efficiency, and background). The likelihood is constructed from the Poisson probability to observe N events, given S, the signal efficiency of (77.1 ± 4.5)%, the expected number of background events (0.30 ± 0.07), and the integrated luminosity L = (36 ± 1) pb −1 [12]. Table 2 summarizes the systematic uncertainties used as inputs to the limit calculation.
The observed (expected) 95% CL upper limit on S is 0.11 (0.13) pb. We translate the limit on S into a limit on the parameters of the ADD model using the following technique. Because the effects of virtual-graviton exchange interfere with the SM diphoton production, generally, we expect the total diphoton cross section to have the following form: where σ int and σ ED refer to the contributions to the total cross section from interference and direct ED effects, respectively. Here, the dimensionful η G parameter specifies the strength of the ED effects and is related to M S through Eqs. (1-3). Consequently, we parameterize S as a function in the parameter η G . For the HLZ n ED = 2 case, η G depends on the signal spectrum due to an explicitŝ dependence in Eq. (2). Therefore, in this case we parameterize S as a function of 1/M 4 S and translate the limit on this parameter into a limit on M S . The observed 95% CL upper limit on S together with the parameterization of S as a function of η G and 1/M 4 S are shown in the left pane of Fig. 3. The intersection of the limit on S with the curves determines the upper 95% CL upper limits on the parameters η G and 1/M 4 S . As seen from these plots, the upper limits are equal to 0.070 TeV −4 for η G and 0.078 TeV −4 for 1/M 4 S (for n ED = 2). We further translate these limits, by means of Eq. (2), into lower bounds  Table 3: 95% CL limits on M S (TeV), as a function of the convention and number of ED. A comparison of the limits with a truncation of the production cross section above √ŝ > M S is also shown. The two limits for the Hewett convention correspond to positive and negative interference effects.

GRW
Hewett HLZ Pos. Neg. n ED = 2 n ED = 3 n ED = 4 n ED = 5 n ED = 6 n ED = 7 Full  Table 3. This is calculated trivially for n ED = 2 and for n ED > 2 by using Eq. (2). The limits in convention [5] are identical to the HLZ limits for n ED = 4; the limit for the Hewett convention with constructive interference is 1.74 TeV and is close to the HLZ limit for n ED = 5.
We note that the LO signal cross section calculations become non-perturbative when the value ofŝ in the 2 → 2 process exceeds M 2 S . This effect is not taken into account in the SHERPA cross section calculations used in this analysis, or in previous studies of this process at the Tevatron [10], where the effect is not expected to be important due to the lower collider energy. Because the energy of the LHC is significantly higher than the limits on M S we are able to set in this analysis, we take this effect into account by conservatively assuming that the signal cross section is zero for √ŝ > M S . Under these assumptions, the limits on M S decrease by 5% for n ED = 2 (1.80 TeV) and 15% for n ED = 7 (1.31 TeV). A summary of the limits under the assumption of a truncated production cross section is also shown in Table 3.
In addition to setting limits on a specific model of large extra dimensions, we can also set a model-independent limit on any new physics model which results in central, high-E T diphotons, either resonant or non-resonant (e.g., Kaluza-Klein gravitons in the Randall-Sundrum model [25]). We measure a 95% CL exclusion on the cross section times branching fraction times acceptance of 0.110 pb, for diphoton pairs with M γγ > 500 GeV and the following kinematic requirements on each of the two photons: E T > 30 GeV and |η| < 1.44.

Conclusions
In conclusion, we have performed a search for large extra dimensions [1,2] in the diphoton final state with a data sample collected in pp collisions at √ s = 7 TeV corresponding to an integrated luminosity of 36 pb −1 . We optimize the signal selection to reach maximum sensitivity in a counting experiment in a one-sided mass window by selecting events with centrally produced photons and large diphoton invariant mass. Given the absence of an excess over the SM direct diphoton background, we set lower limits on the cutoff scale M S in the range 1.6-2.3 TeV. While this analysis was being finalized, a phenomenological interpretation of the dijet angular distribution results from the CMS and ATLAS experiments appeared [26] and suggested even stronger limits on M S . However, a dedicated experimental analysis and interpretation of the dijet data in the models with large extra dimensions has yet to be conducted. The results presented in this Letter extend the current limits reached at the Tevatron [9, 10] in all but the n ED = 2 case.