Search for Higgs and $Z$ Boson Decays to $\phi\,\gamma$ with the ATLAS Detector

A search for the decays of the Higgs and $Z$ bosons to a $\phi$ meson and a photon is performed with a $pp$ collision data sample corresponding to an integrated luminosity of 2.7 fb$^{-1}$ collected at $\sqrt{s}=$13 TeV with the ATLAS detector at the LHC. No significant excess of events is observed above the background, and 95% confidence level upper limits on the branching fractions of the Higgs and $Z$ boson decays to $\phi\,\gamma$ of 1.4$\times$10$^{-3}$ and 8.3$\times$10$^{-6}$, respectively, are obtained.

The data sample used in this analysis was collected with a dedicated trigger, commissioned in September 2015, requiring an isolated photon with a transverse momentum p T greater than 35 GeV and an isolated pair of tracks with an invariant mass loosely consistent with the φ meson mass of 1019. 5 MeV [34], one of which must have a transverse momentum greater than 15 GeV. The trigger efficiency for both the Higgs and Z boson signals is around 80% with respect to the offline selection. Events are retained for analysis if collected under stable LHC beam conditions and the detector was operating normally.
For this analysis, in the absence of particle identification capabilities in the relevant momentum range, every reconstructed charged particle satisfying the following requirements is assumed to be a K ± meson. Events are selected if there are at least two tracks with p T > 400 MeV originating from the primary vertex, which is defined as the vertex with the largest p 2 T in the event. The charged kaons are reconstructed from inner-detector tracks that satisfy quality requirements, including a requirement on the number of hits in the silicon detectors [35]. The K ± candidates are required to have pseudorapidity 1 |η| < 2.5 and p T > 15 GeV. The φ → K + K − decays are reconstructed from pairs of oppositely charged inner detector tracks. The higher-p T track in a pair, denoted the leading track, is required to have p T > 20 GeV. The experimental resolution in m K + K − is around 4 MeV, comparable to the natural width of the φ meson, Γ φ = 4.266 ± 0.031 MeV [34]. Track pairs with a mass m K + K − within ±20 MeV of the φ meson mass [34] are selected as φ → K + K − candidates. Selected φ → K + K − candidates are required to satisfy an isolation requirement: the sum of the p T of the reconstructed inner detector tracks from the main vertex within ∆R = (∆φ) 2 + (∆η) 2 = 0.2 of the leading track (excluding both tracks constituting the φ → K + K − candidate) is required to be less than 10% of the p T of the φ candidate, Photons are reconstructed from clusters of energy in the electromagnetic calorimeter. Clusters without matching tracks are classified as unconverted photon candidates while clusters matched to tracks consistent with the hypothesis of a photon conversion into an e + e − pair are classified as converted photon candidates [36]. Reconstructed photon candidates are required to have transverse momentum p and trigger and reconstruction efficiencies) is 18% and 8% for the Higgs and Z boson decays, respectively. The difference in efficiencies primarily arises due to the softer p γ T and p K + K − T distributions in the case of Z → φ γ production. The m K + K − γ resolution is around 1.8% for both the Higgs and Z boson decays. The m K + K − distribution for selected φ γ candidates, with no m K + K − requirement applied, is shown in Figure 1 and exhibits a clear peak at the φ meson mass.  The main source of background to the search comes from events involving inclusive multijet or photon + jet processes where a φ → K + K − candidate is reconstructed from tracks associated with a jet. The normalization of this inclusive background is extracted directly from a fit to data. The selection criteria discussed earlier shape the m K + K − γ distribution for background such that it exhibits a threshold structure near 100 GeV, and falls then smoothly towards higher mass values. Given the nontrivial shape of this background, these processes are modeled with a nonparametric data-driven approach using templates to describe the kinematic distributions. A similar procedure was used in the search for Higgs and Z boson decays to J/ψ γ and Υ(nS ) γ described in Ref. [14]. The approach exploits a sample of around 4000 K + K − γ candidate events passing all of the kinematic selection requirements described previously, except that the photon and φ → K + K − candidates are not required to satisfy the nominal isolation requirements. The events satisfying this selection are collected in a generation region (GR). The contamination of this sample from signal events is expected to be negligible and is verified not to affect the shape of the background model. Probability density functions (pdfs) that model the p K + K − T , p γ T , ∆η(K + K − , γ), and ∆φ(K + K − , γ) distributions of this sample are constructed using a Gaussian kernel density estimation [39]. Correlations between these variables and p γ T in the event were studied and accounted for in the background model by deriving separate pdfs in 13 exclusive regions of p γ T . In the case of the φ → K + K − and photon isolation variables, correlations are accounted for by using two-dimensional histograms derived in the same 13 exclusive regions of p γ T . Values of m K + K − are sampled from the corresponding distribution in the GR. The pdfs of these kinematic and isolation variables are sampled to generate an ensemble of pseudocandidates, each with a complete K + K − γ four-vector and an associated pair of φ → K + K − and photon isolation values. The nominal selection requirements are imposed on the ensemble and the surviving pseudocandidates are used to construct templates for the m K + K − γ distribution.
To validate this background model with data, the m K + K − γ distributions in several validation regions, defined by kinematic and isolation requirements looser than the nominal signal requirements, are used to compare the prediction of the background model with the data. The m K + K − γ distribution in one of these validation regions, defined by the GR selection with the addition of the nominal photon isolation requirement, is shown in Figure 2. The background model is found to describe the data well, and within the observed statistical uncertainties. A consistency test of the background modelling procedure has been performed with a sample of simulated photon + jet events in place of the data; similarly good agreement is observed. The robustness of the background model is further validated by splitting the data into highand low-p subsets, that exhibit different threshold structures, and confirming that the background model describes the shapes of both m K + K − γ distributions. Further exclusive background contributions from Z → γ decays have been studied but are found to represent a negligible contribution for the selection requirements and dataset used in this analysis.
[GeV] Trigger and identification efficiencies for photons are determined from samples enriched with Z → e + e − events in data [36,40]. The systematic uncertainty on the expected signal yield associated with the trigger efficiency is estimated to be 2%. The photon identification efficiency uncertainties, for both the converted and unconverted photons, are estimated to be 2.4% and 2.6% for the Higgs and Z boson signals, respectively. An uncertainty of 6% is assigned to the track reconstruction efficiency and includes effects associated with the material budget of the inner detector and the behavior of the track reconstruction algorithm if a nearby track is present. The integrated luminosity of the data sample has an uncertainty of 5% derived using the method described in Ref. [41]. The photon energy scale uncertainty, determined from Z → e + e − events and validated using Z → γ events [42], is propagated through the simulated signal samples as a function of η γ and p γ T . The uncertainty associated with the description of the photon energy scale in the simulation is found to be less than 0.3% of the three-body invariant mass while the uncertainty associated with the photon energy resolution is found to be negligible relative to the overall three-body invariant mass resolution. Similarly, the systematic uncertainty associated with the track momentum measurement is found to be negligible.
The uncertainty on the shape of the inclusive multijet and photon + jet background is estimated through the study of variations in the background modeling procedure. The shape of the background model is allowed to vary around the nominal shape within an envelope associated with shifts in the p K + K − T distribution, tilts of the ∆φ(K + K − , γ) distribution, and by neglecting the weakest correlation accounted for in the nominal background model.
Results are compared to background and signal predictions using an unbinned maximum-likelihood fit to the m K + K − γ distribution. The fit uses the selected events with m K + K − γ < 300 GeV. The systematic uncertainties described above result in a 3% deterioration of the sensitivity to the H → φγ decay. For the Z boson decay the reduction is larger, 13%, mainly due to the systematic uncertainty in the background shape. The expected and observed numbers of background events within the m K + K − γ ranges relevant to the Higgs and Z boson signals are shown in Table 1.
On the basis of the observed data, upper limits are set on the branching fractions for the Higgs and Z boson decays to φ γ using the CL s modified frequentist formalism [43] with the profile-likelihood ratio test statistic [44]. The result of the background-only fit is shown in Figure 3; a small excess of two standard deviations is observed in the Z boson mass region, estimated using the asymptotic approximation for the distribution of the test statistic. The expected SM production cross section is assumed for the Higgs boson while the ATLAS measurement of the inclusive Z boson cross section is used for the Z boson signal [30]. The results are summarized in Table 2. The observed 95% confidence level (CL) upper limits on the branching fractions for H → φ γ and Z → φ γ decays are around 600 and 700 times the expected SM branching fractions, respectively. Table 2: Expected and observed branching fraction limits at 95% CL for 2.7 fb −1 of pp collision data at √ s = 13 TeV. The ±1σ intervals of the expected limits are also given.

Branching Fraction Limit (95% CL) Expected Observed
In conclusion, a search for the decay of Higgs or Z bosons to φ γ has been performed with a pp collision data sample at √ s = 13 TeV corresponding to an integrated luminosity of 2.7 fb −1 collected with the