Search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV in the diphoton final state in proton-proton collisions at $\sqrt{s}=$ 8 and 13 TeV

The results of a search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV decaying into two photons are presented. The analysis uses the data set collected with the CMS experiment in proton-proton collisions during the 2012 and 2016 LHC running periods. The data sample corresponds to an integrated luminosity of 19.7 (35.9) fb$^{-1}$ at $\sqrt{s}=$8 (13) TeV. The expected and observed 95% confidence level upper limits on the product of the cross section and branching fraction into two photons are presented. The observed upper limit for the 2012 (2016) data set ranges from 129 (161) fb to 31 (26) fb. The statistical combination of the results from the analyses of the two data sets in the common mass range between 80 and 110 GeV yields an upper limit on the product of the cross section and branching fraction, normalized to that for a standard model-like Higgs boson, ranging from 0.7 to 0.2, with two notable exceptions: one in the region around the Z boson peak, where the limit rises to 1.1, caused by the presence of Drell-Yan dielectron production where both electrons are misidentified as isolated photons, and a second due to an observed excess with respect to the standard model prediction, which is maximal for a mass hypothesis of 95.3 GeV with a local (global) significance of 2.8 (1.3) standard deviations.


Introduction
Within the standard model (SM) of particle physics [1][2][3], particle masses arise from the spontaneous breaking of electroweak symmetry, which is achieved through the Brout-Englert-Higgs mechanism [4][5][6][7][8][9].In its minimal version, electroweak symmetry breaking is realized through the introduction of a doublet of complex scalar fields.At the end of the process, only one scalar field remains and the corresponding quantum, the Higgs boson, should be experimentally observable.In 2012, both the ATLAS [10] and CMS [11,12] Collaborations observed a new boson with a mass of approximately 125 GeV whose properties are at present compatible with those of the SM Higgs boson.The analyses of data in the diphoton final state leading to this discovery probed an invariant mass range extending from 110 to 150 GeV.However, physics beyond the SM (BSM) can also provide a Higgs boson that is compatible with the observed 125 GeV boson.The extended parameter space of several BSM models, for example the next-to-minimal supersymmetric model (NMSSM) [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and generalized models containing two Higgs doublets (2HDM) [33][34][35][36][37], gives rise to a rich and interesting phenomenology, including the presence of additional Higgs bosons, some of which could have masses below 125 GeV.Such models provide good motivation for extending searches for Higgs bosons to masses as far below m H = 110 GeV as possible, where H refers to an additional Higgs boson which is "SM-like", meaning that the relative contributions of the production processes are similar to those of the SM.
The H → γγ decay channel provides a clean final-state topology that allows the mass of a Higgs boson in the search range to be reconstructed with high precision.The primary production mechanism for Higgs bosons in proton-proton (pp) collisions at the CERN LHC is gluon fusion (ggH), with additional smaller contributions from vector boson fusion (VBF) and production in association with a W or Z boson (VH), or with a tt pair (ttH).The dominant sources of background are irreducible direct diphoton production, and the reducible pp → γ + jet and pp→ jet + jet processes, where the jets are misidentified as isolated photons.An additional source of reducible background relevant for the search range below m H = 110 GeV is Drell-Yan dielectron production, where both electrons are misidentified as isolated photons.
The CERN LEP collaborations [38], in the context of the search for the SM Higgs boson, explored the mass range below 110 GeV extensively in the VH production mode, in the bb and τ + τ − channels.Several of the BSM models mentioned above predict reduced decay rates in these channels with respect to SM predictions and enhanced decay rates in the diphoton channel.A previous search in the diphoton decay channel by ATLAS [39] at a center-of-mass energy of 8 TeV, in the mass range of 65 < m γγ < 110 GeV, found no excess with respect to expectations.
This letter presents the result of a search in the diphoton channel for an additional Higgs boson with an invariant mass lower than 110 GeV, whose natural width is small compared to the detector resolution.The search is performed on a data set collected in 2012 and 2016 with the CMS detector at the LHC, corresponding to, respectively, integrated luminosities of 19.7 fb −1 at a center-of-mass energy of 8 TeV, referred to as the "8 TeV data", and 35.9 fb −1 at 13 TeV, the "13 TeV data".
The analysis is based on a search for a localized excess in the diphoton invariant mass spectrum over a smoothly falling background from prompt diphoton production and from events with at least one jet misidentified as a photon, in addition to the Drell-Yan contribution.It uses an extended version of the method developed by the CMS Collaboration for the observation and the measurement of the properties of the 125 GeV boson [40,41].The invariant mass range explored in the 8 (13) TeV data is 80 (70) < m γγ < 110 GeV.The principal challenges associated with a search in the diphoton decay channel in this mass range are the ability to trigger on events while maintaining acceptable rates, and the background from Z bosons decaying to electron pairs that are misidentified as photon pairs.To achieve the best possible sensitivity, the events are separated into classes.Multivariate analysis (MVA) techniques are used both for photon identification and event classification, and the signal is extracted from the background using a fit to the diphoton mass spectrum in all event classes.

The CMS detector
A detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [42].The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors.Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.The ECAL, surrounding the tracker volume, consists of 75 848 lead tungstate crystals, which provide coverage in |η| < 1.48 in a barrel region (EB) and 1.48 < |η| < 3.0 in two endcap regions (EE).Preshower detectors consisting of two planes of silicon sensors interleaved with a total of 3X 0 of lead are located in front of each EE detector.In the EB, an energy resolution of about 1% is achieved for unconverted or late-converting photons that have energies in the range of tens of GeV.For the remaining barrel photons, a resolution of about 1.3% is achieved up to |η| = 1, rising to about 2.5% at |η| = 1.4.In the EE, an energy resolution for unconverted or late-converting photons of about 2.5% is achieved, while for the remaining endcap photons it is between 3 and 4% [43].

Trigger and simulation
Events of interest are selected using a two-tiered trigger system [44].The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 µs.The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to less than 1 kHz before data storage.For this analysis, diphoton HLT paths with asymmetric transverse momentum (p T ) thresholds are used.In the case of the 8 TeV data, the same paths are used as in [40].The paths that select almost all of the events impose thresholds of 26 and 18 GeV on the p T of the individual photon trigger objects, and minimum requirements on the invariant mass of diphoton trigger objects of either 60 or 70 GeV depending on the datataking period.For the 13 TeV data, two dedicated HLT paths are used, both with photon p T thresholds of 30 and 18 GeV.One path has nearly identical requirements to those used in [41], except that only events with both photon candidates in the EB are selected.This path requires each of the photon candidates to satisfy criteria on the ratio of its energy in the HCAL and in the ECAL (H/E), and on either shower shape or on its isolation energy.The other path selects events with photon candidates from any part of the ECAL, but they must satisfy more stringent shower shape requirements as well as the requirements on both isolation energy and H/E.In addition, both paths impose a veto on the presence of hits compatible with the photon direction in the silicon pixel detector, and require that the invariant mass of the two photon candidates be greater than 55 GeV.These requirements limit the search range to m γγ > 70 (80) GeV for the 13 (8) TeV data, in order to avoid the portion of the offline diphoton spectrum that is distorted due to turn-on effects from the HLT criteria.For both data sets, the trigger efficiency is measured from Z → e + e − events using the tag-and-probe technique [45], except for the pixel hit veto requirement relevant for the triggering of the 13 TeV data, where the efficiency is measured using diphoton events in data that have passed the trigger used in [41], which does not require a pixel veto.
Monte Carlo (MC) simulations are used to produce SM Higgs boson events from all four production processes (ggH, VBF, VH, and ttH), with invariant masses ranging from 70 to 110 GeV.These events are the input to the signal modeling procedure, representing a new resonance decaying to two photons.In the case of the 8 TeV data, for the ggH and VBF processes, these events are generated at next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD) using POWHEG 1.0 [46][47][48][49][50], while the events from the associated production processes are generated at leading order (LO) with PYTHIA 6.426 [51].For the 13 TeV data, events are generated at NLO using MADGRAPH5 aMC@NLO 2.2.2 [52] with FxFx merging [53], for all four production processes.Events generated at LO (NLO) for the analysis of the 8 TeV data use the CTEQ6L [54] (CTEQ6M [55]) set of parton distribution functions (PDFs), while those intended for the analysis of the 13 TeV data use the NNPDF3.0[56] PDF set.The parton-level samples are interfaced to PYTHIA 6.426 for the 8 TeV data, and to PYTHIA 8.205 [57] for the 13 TeV data for parton showering and hadronization, with the Z2 * [58,59] and CUETP8M1 [59] tune parameter sets used, respectively, for the underlying event activity.The cross sections and branching fractions (B) recommended by the LHC Higgs cross section working group for center-of-mass energies of 8 and 13 TeV [60] are assumed.After the generation step, the events are processed by the full CMS detector simulation with GEANT4 [61].Multiple pp interactions in each bunch crossing in each recorded event (pileup) are simulated.These events are then weighted to reproduce the distribution of the number of interactions observed in data in 2012 (2016) for the 8 (13) TeV data, the average values of which were 21 and 23 interactions, respectively.The trigger efficiencies measured using the method described above are applied to the simulated SM Higgs boson events as a correction, and the associated statistical and systematic uncertainties are propagated to the expected signal yields.
Events corresponding to the SM background processes mentioned in Section 1 are simulated using various generators.The diphoton background is modeled with the SHERPA 1.4.2(2.2.0) [62] generator for the analysis of the 8 (13) TeV data; it includes the Born processes with up to 2 (3) additional jets, as well as the box processes at LO. Multijet and γ + jet backgrounds are modeled with PYTHIA 6.426 (8.205) in the case of the 8 (13) TeV data, with a filter [40,41] applied at generator level in order to enhance the production of jets with a large fraction of electromagnetic energy.Drell-Yan events are simulated at LO with MADGRAPH5 1.3.30[52] and at NLO with POWHEG 1.0 [63] in the case of the 8 TeV data, and entirely at NLO with MADGRAPH5 aMC@NLO 2.2.2 for the 13 TeV data.All background events are generated using the same PDF sets and simulated under the same conditions as the SM Higgs boson events described above.The background events are used in the calculation of energy scale and smearing corrections, preselection and photon identification efficiencies, training of the multivariate boosted decision trees (BDTs) used in the analysis, estimations of systematic uncertainties, and for validation.In particular, the Drell-Yan events are used to obtain initial values for some of the parameters used to model the shape of the small background contribution from dielectron decays of the Z boson, which can be misidentified as photon pairs.As in [40] and [41], the background estimation is extracted from data.

Photon reconstruction, event selection and classification
The same diphoton vertex identification is used as in [40] ( [41]) for the 8 (13) TeV data.For both data sets, a BDT is used to select a diphoton vertex from the set of all reconstructed primary vertices, incorporating as input variables the sum of the squared transverse momenta of the charged particle tracks associated with the vertex, and two variables that quantify the vector and scalar balance of p T between the diphoton system and the charged particle tracks associated with the vertex.Furthermore, if either photon is associated with any charged particle tracks that have been identified as resulting from conversion, the pull between the longitudinal positions of the primary vertex obtained from the conversion tracks alone and from all associated tracks is added to the BDT input variable set, and, in the case of the 13 TeV data, the number of conversions.
The same photon reconstruction is used as in [40] ( [41]) for the 8 (13) TeV data.For the 8 TeV data, photon candidates are reconstructed from energy deposits in the ECAL grouped into extended clusters or groups of clusters known as "superclusters".In the EB, superclusters are formed from five-crystal-wide strips in η, centered on the locally most energetic crystal, and have a variable extension in φ.In the EE detectors, where the crystals are arranged according to an x-y rather than an η-φ geometry, matrices of 5×5 crystals, which may partially overlap and are centered on a locally most energetic crystal, are summed if they lie within a narrow φ road.For the 13 TeV data, photon candidates are reconstructed as part of the global event reconstruction, as described in [64].First, cluster "seeds" are identified as local energy maxima above a given threshold.Second, clusters are grown from the seeds by aggregating crystals with at least one side in common with a clustered crystal and with an energy in excess of a given threshold.This threshold represents approximately two standard deviations of the electronic noise in the ECAL, and amounts to 80 MeV in the EB and, depending on |η|, up to 300 MeV in the EE detectors.The energy of each crystal can be shared among adjacent clusters assuming a Gaussian transverse profile of the electromagnetic shower.Finally, clusters are merged into superclusters.
For both data sets, the energy of photons is computed from the sum of the energy of the clustered crystals, calibrated and corrected for changes in the response over time [65].The preshower energy is added to that of the superclusters in the region covered by this detector.To optimize the resolution, the photon energy is corrected for the containment of the electromagnetic shower in the superclusters and the energy losses from converted photons [43].The correction is computed with a multivariate regression technique that estimates simultaneously the energy of the photon and its uncertainty.This regression is trained on simulated photons using as the target the ratio of the true photon energy and the sum of the energy of the clustered crystals.The inputs are shower shapes and position variables-both sensitive to shower containment and possible unclustered energy-preshower information, and global event observables sensitive to pileup.
Photon candidates are subject to a preselection that imposes requirements on p T , hadronic leakage, and shower shape, and that uses an electron veto to reject photon candidates geometrically matched to a hit in the pixel detector.The preselection is designed to be slightly more stringent than the trigger requirements.A BDT combining lateral shower shape variables, isolation variables, the median energy density, the pseudorapidity, and the raw energy is used to separate prompt photons from nonprompt photons resulting from neutral meson decays [40,41].
The analysis uses all events that contain a diphoton pair where each of the photons in the pair satisfy a requirement on the ratio of its p T value to the invariant mass of the diphoton system, m γγ .Specifically, in the case of the 8 (13) TeV data, the requirements are p γ1 T /m γγ > 28.0/80.0= 0.35 (30.6/65.0= 0.47) and p γ2 T /m γγ > 20.0/80.0 = 0.25 (18.2/65.0= 0.28).Here, γ1 (γ2) refers to the photon candidate with the highest (next-highest) p T value.The use of p T thresholds scaled by m γγ [40,41] is intended to prevent a distortion of the low end of the diphoton mass spectrum that results if a fixed threshold is used; in particular, the minimum p T values in the above fractions, 28 (30.6)GeV and 20 (18.2) GeV for the 8 (13) TeV data, are chosen to be slightly higher than those of the HLT paths, i.e., 26 (30) GeV and 18 GeV for the 8 (13) TeV data, to further guard against distortion of the spectrum.Each photon candidate must in addition satisfy the preselection requirements as well as a requirement on the minimum value of the photon identification BDT output.As in [40,41], the efficiency of all preselection criteria, except for the electron veto requirement, is measured with a tag-and-probe technique using Z → e + e − events.The fraction of photons that satisfy the electron veto requirement is measured with Z → µ + µ − γ events, in which the photon is produced by final-state radiation providing a sample of prompt photons with purity higher than 99%.The ratios of the efficiencies in data and simulation are used to correct the signal efficiency in simulated signal samples and the associated statistical and systematic uncertainties are propagated to the expected signal yields.Finally, the diphoton system invariant mass must lie within the range 65 (75) < m γγ < 120 GeV in the case of the 13 (8) TeV data.
A multivariate event classifier [40,41] is used to discriminate between diphoton events from Higgs boson decays and those from the diphoton continuum, to further reduce background from events containing jets misidentified as isolated photons, and to assign a high score to events with good diphoton mass resolution.It incorporates the kinematic properties of the diphoton system (excluding m γγ ), a per-event estimate of the diphoton mass resolution, and the photon identification BDT output values.The events are separated into classes based on the classifier score, with a minimum score below which they are rejected.The number of classes and their boundaries are determined so as to maximize the expected signal significance.Four (three) classes are used for the 8 (13) TeV data; they are referred to as 0, 1, 2, and 3 (0, 1, and 2), where class 0 contains the events with greatest expected sensitivity.The fraction of events containing more than one diphoton candidate is of order 10 −4 .In these cases, the candidate assigned to the highest sensitivity class is selected; should this class still contain multiple diphoton candidates, the candidate with the highest value of p γ1 T + p γ2 T is then selected.

Signal parametrization
In order to perform a statistical interpretation of the data, it is necessary to have a description of the signal that includes the overall product of the efficiency and acceptance, as well as the shape of the diphoton mass distribution in each of the event classes.We use the same procedure as that described in [40,41], exploiting simulated Z → e + e − events where the electron showers have been reconstructed as photons.The photon energy resolution predicted by the simulation is modified by a Gaussian smearing determined from the comparison between the Z → e + e − line-shape in data and simulation.The amount of smearing is extracted differentially in bins of |η| and the R 9 shower shape variable [43], defined as the energy sum of 3×3 crystals centered on the most energetic crystal in the ECAL cluster divided by the energy of the cluster.Following application of the smearing and the trigger and preselection efficiency corrections described in Sections 3.1 and 3.2, respectively, the simulated signal events are used to construct a parameterized model that is defined continuously for any value of Higgs boson mass between 80 (70) and 110 GeV, for the 8 (13) TeV data.
Since the distribution of m γγ changes considerably depending on whether the vertex associated with the candidate diphoton is correctly identified, separate fits are made to the distributions for the correct and incorrect primary vertex selections when constructing the signal model.Events are considered to have the correct primary vertex if the vertex associated with the candidate diphoton is within 1 cm of the true vertex.For these events the signal shape is dominated by ECAL response and reconstruction, and is modeled empirically by a sum of between three and six (three and four) Gaussian functions in the case of the 8 (13) TeV data, depending on the event class.The signal shape for events with an incorrect primary vertex selection is smeared significantly by the variation in the z-coordinate position of the selected primary vertex with respect to the true Higgs boson production vertex.The signal shape for these events is modeled by a sum of between one and four (two and three) Gaussian functions in the case of the 8 ( 13) TeV data, depending on the event class.In both cases, the means, widths, and relative fractions of the Gaussian functions are determined by the fits.
The full signal model for all values of m H is obtained by linear interpolation of each of the fitted parameters.The final parameterized shapes for the combination of all production mechanisms, for all event classes, weighted by their SM cross sections are shown in Fig. 1

Background estimation
In this analysis, as in [11,40,41], the background is modeled by fitting analytic functions to the observed diphoton mass distributions, in each of the event classes.The fits are performed over the range 75 (65) < m γγ < 120 GeV for the 8 (13) TeV data.In the case of the 8 TeV data, a single fit function is chosen for each class after a study of the potential bias in the estimated back-ground, which is required to be negligible, following the method used in [11].For the 13 TeV data, as in [40,41], the model is determined from data with the discrete profiling method [66], which treats the choice of the background function as a discrete parameter in the likelihood fit to the data and estimates the systematic uncertainty associated with the choice of a particular function.
Since the search mass range of this analysis includes the Z boson peak region, a significant potential background source is Drell-Yan dielectron production, where both electrons have been misidentified as isolated photons.Therefore, an explicit component intended to describe the background from the Drell-Yan process in which the two electrons survive all the photon candidate selection requirements as stated in Section 3.2, is added to the smoothly falling polynomial distribution used to model the background in [11,40,41].This additional component, referred to as "doubly misidentified" events, is modeled with a double-sided Crystal Ball (DCB) function, which is a modification of the Crystal Ball function [67] with an exponential tail on both sides.The DCB function is characterized by seven parameters: the number of events for normalization, the Gaussian mean and standard deviation, and the four additional shape parameters α L , n L , α R , and n R , where α L,R and n L,R refer, respectively, to the slope and normalization of the left-hand (L) and right-hand (R) exponential tails.The values of the DCB shape parameters are determined by fitting the diphoton invariant mass distribution in a sample of simulated Drell-Yan doubly misidentified events for each event class.Because of the small size of the simulated event sample, we fix two of the six DCB shape parameters, α L and α R , to make the fit more stable.The fixed values are different in each event class and are obtained using the normalized χ 2 value for the 8 TeV data, and the minimal maximum pull value for the 13 TeV data, as a figure of merit.In each class the value of the mean, which coincides with the peak position, lies somewhat below the nominal Z boson mass value.This is due to the fact that the electrons surviving the photon selection requirements (in particular the electron veto) have in general been poorly reconstructed, for example having undergone wide-angle bremsstrahlung of high-energy photons; furthermore, the electron energies have been corrected with factors developed for photons.
For both the choice of the single fit function in the case of the 8 TeV data, and the application of the discrete profiling method in the case of the 13 TeV data, members of several families of analytic functions, including exponential, power law, Bernstein, and Laurent series are considered, each summed with a DCB function.The maximum order term in each series is determined using an F-test [68].In the analysis of the 13 TeV data, the minimum order of the series is determined as well, using a goodness-of-fit test.
In the analysis of the 8 TeV data these functions, called "truth models", are used to generate MC pseudo-data sets that are fitted with candidate functions from the same families of an order within the range determined by the above tests.The bias for a given candidate function to fit a given truth model is defined as the average pull of the fitted signal strength modifier over the set of relevant generated pseudo-data sets, and is required to be less than 0.14 to be considered negligible.This amount of bias necessitates an increase in the uncertainty in the frequentist coverage of the signal strength of less than 1%, which is deemed acceptable.The final background function is chosen from the candidate functions that fit all truth models in a given event class with negligible bias.
In the discrete profiling method used for the analysis of the 13 TeV data, when fitting these functions to the background m γγ distribution, the value of twice the negative logarithm of the likelihood (2NLL) is minimized.A penalty is added to the 2NLL value to take into account the number of floating parameters, including the fraction of background events attributed to the component arising from the doubly misidentified events (DCB fraction), in each candidate function.
In both methods, the normalization of the Drell-Yan background is determined in the fit.The shape parameters are constrained to the constant values that are obtained by fitting the doubly misidentified Drell-Yan events, as described above.
For the analysis of the 8 TeV data, the sum of a fifth-order Bernstein polynomial and the DCB function is chosen as the final background model for event classes 1, 2, and 3.For class 0, a fourth-order Bernstein polynomial is used.For the 13 TeV data, a third-order exponential series plus the DCB function is chosen for classes 0 and 2, and a first-order power-law series plus the DCB function for class 1.The DCB fractions for these chosen models in the subset of the diphoton mass range extending from 85 to 95 GeV, the most relevant for dielectron background from the Drell-Yan process, are, for the 8 (13) TeV data, 2.9, 6.1, 2.9, and 5.6 (4.8, 3.1, and 3.2)%, respectively, for event classes 0, 1, 2, and 3 (0, 1, and 2).
Binned likelihood fits of the chosen background models to the observed diphoton mass distribution, assuming no signal, are shown for all the event classes in Fig. 2 (3) for the 8 (13) TeV data.The one-and two-standard deviation (σ) bands include only the uncertainty in the background model normalization associated with the statistical uncertainties of the fits, and are thus shown for illustration purposes only.They are obtained using an extended likelihood fit parametrized in terms of the background yield in a window that is the size of the bin widths in Figs. 2 and 3.

Systematic uncertainties
Many of the systematic uncertainties relevant to the analyses performed in [11,40,41] also apply to this analysis and are described briefly below.Additional uncertainties specific to this analysis are described in more detail.

Uncertainties evaluated at the per-photon level
The systematic uncertainties in the shape of the photon identification BDT distribution and in the per-photon energy resolution described in [40,41] are applied in this analysis.These uncertainties propagate to the multivariate event classifier value, giving rise to the migration of events from one class to another, and to variations in the per-event efficiency in each class and for each production process.The uncertainties are evaluated using a signal sample with m H = 105 (90) GeV for the analysis of the 8 (13) TeV data.For the 8 TeV data, the largest variation in efficiency due to the photon identification BDT distribution shape is 5.9%, for the VBF process in event class 3.For the 13 TeV data the largest variation is 14.6% for the VBF process in event class 2, with other processes in class 2 having variations of less than 11%, and variations in the other classes being below 5%.The largest variation in the efficiency due to the per-photon energy resolution applicable to the 8 TeV data is 13.7% for the ggH process in class 0; otherwise the variations are below 9%.For the 13 TeV data, the largest variation is 7% for the VBF process in class 2; otherwise the variations are below 5%.
For the 8 (13) TeV data, uncertainties in the trigger efficiencies give rise to efficiency variations of 1 (less than 1)%, and in the scale factors of the preselection, of less than 1.5 (5.5)%.In the case of the 13 TeV data, the uncertainties in the scale factors of the electron veto and of the minimum value of the photon identification BDT are considered as supplemental sources of efficiency variations, which amount to less than 2% for each.The uncertainties in the measurement and in the correction of the photon energy scale in data, and in the correction of the energy resolution in simulation, arising from the methodology exploiting Z → e + e − events as described in Section 4 and [40,41], are calculated in the same bins as the corrections themselves.Uncertainties arising from modeling of the material budget and of nonuniformity of light collection (the fraction of crystal scintillation light detected as a function of its longitudinal depth when emitted), nonlinearity in the photon energy scale between data and simulation, imperfect electromagnetic shower simulation, and vertex finding [40,41], are propagated to the parametric signal model, where they result in uncertainties in the diphoton efficiency, mass scale, and resolution.

Uncertainties evaluated at the per-event level
The per-event systematic uncertainty in the total integrated luminosity, estimated from data [69,70], contributes an uncertainty of 2.6 (2.5)% in the signal yield for the 8 (13) TeV data.
The systematic uncertainties from the theoretical predictions considered in this analysis are of two types.Firstly, the uncertainties in the signal acceptance due to changes in particle p T and η values, arising from variations in the PDF and renormalization and factorization scales, are calculated [40,41] using a signal sample with m H = 105 (90) GeV for the analysis of the 8 (13) TeV data.The CT10 [55] PDF set (NNPDF3.0 [56] PDF set using the MC2HESSIAN procedure [71]) is used to estimate the PDF variations in the case of the 8 (13) TeV data.In the case of the 13 TeV data, the effects due to variations of the strong coupling strength, α S , are also considered, following the PDF4LHC prescription [60,72].The uncertainty of greatest magnitude due to PDF variations, in the 8 TeV data, is 2% for the VBF production process in event class 0; otherwise the uncertainties are below 1% and, in many cases, well below 1%.In the 13 TeV data, the uncertainties are equal to or less than 0.4%.The largest uncertainty due to scale variations, in the 8 TeV data, is 7.5% for the ggH production process in event class 0; otherwise the uncertainties are below 1%.In the 13 TeV data, the largest uncertainties also occur for the ggH process, with the maximum of 3.8% again occurring in event class 0. The uncertainties due to variations in α S , considered for the 13 TeV data, are typically below 0.5%, with the largest uncertainty of 0.7% occurring for the VBF process in event class 2.
Secondly, the uncertainties in the production cross sections for an SM-like Higgs boson, at center-of-mass energies of 8 and 13 TeV, are accounted for following the recommendations of the LHC Higgs cross section working group [60].These uncertainties are due to PDF, α S , and scale variations.They are used in the calculation of the expected and observed limits on the product of the production cross section and branching fraction into two photons relative to the expected value for an SM-like Higgs boson, and in the calculations of the expected and observed local p-values.The uncertainty in the branching fraction into two photons is neglected.
An additional source of per-event systematic uncertainty specific to this analysis is the modeling of the Z boson resonance component of the background.As explained previously, the parameters of the DCB function used to model the Z boson resonance are obtained from doubly misidentified events, which are simulated Drell-Yan events with all selection requirements applied including the electron veto requirement.These parameters could be different for data and simulation.To estimate these differences, we study simulated events from the Drell-Yan, diphoton, γ + jet, and QCD physics processes where one photon candidate survives all selection requirements including the electron veto, and the other survives all selection requirements but fails the electron veto ("singly misidentified" events).We fit the invariant diphoton mass of these events in data, in simulation including the sum of all background processes, and in simulated Drell-Yan events alone, with a DCB plus an exponential component that describes the additional continuum background inherent in singly misidentified events.We consider the pairwise differences among the DCB mean and standard deviation parameters extracted from these three types of fits for each event class.The differences are considered statistically significant if greater than the quadratic sum of the statistical uncertainties from the fit.These differences will contribute to the total systematic uncertainty in the DCB parameter values.The nominal parameter values are obtained from doubly misidentified events so the differences contributing to the parameter uncertainties that are estimated from singly misidentified events are doubled, to reflect the more conservative case where the parameters of the two photon candidates in a doubly misidentified event are completely correlated.
The total systematic uncertainty in each event class for the mean and standard deviation parameters, is then the quadratic sum of: the statistical uncertainty from the fit to the doubly misidentified simulated Drell-Yan events; the doubled difference between the parameter values from data and from the sum of all simulated background processes; and the doubled difference between the parameter values from the sum of all simulated background processes and from simulated Drell-Yan events alone, determined from the singly misidentified events.As a conservative measure in the case of the 8 TeV data, the doubled differences in the parameter values for the event class where the values are maximal are used for all four classes.
Finally, the analysis takes into account the statistical uncertainties in the values of the DCB n L and n R parameters obtained from the fits to the doubly misidentified simulated Z → e + e − Table 1: The expected number of SM-like Higgs boson signal events (m H = 90 GeV) per event class and the corresponding percentage breakdown per production process, for the 8 and 13 TeV data.The values of σ eff and σ HM are also shown, along with the number of background events ("Bkg.")per GeV estimated from the background-only fit to the data, including the number from the Drell-Yan process ("DY Bkg."), in a σ eff window centered on m H = 90 GeV.

Event classes
Expected SM-like Higgs boson signal yield (m H = 90 GeV) Bkg.DY Bkg.Total ggH VBF WH ZH ttH

Results
Table 1 shows the expected number of signal events corresponding to the production of a hypothetical additional SM-like Higgs boson with m H = 90 GeV, from the analyses of the 8 and 13 TeV data.The total number is broken down into the contributions from all the production processes in each of the event classes, where the VH processes corresponding to W and Z are listed separately.Also shown are the σ eff and σ HM (defined as the FWHM divided by 2.35) values, as well as the number of background events per GeV estimated from the backgroundonly fit to the data, including the number from the Drell-Yan process, in the corresponding σ eff window centered on m H = 90 GeV, using the chosen background function.
A simultaneous binned maximum likelihood fit to the diphoton invariant mass distributions in all event classes, with a step size of 0.1 GeV, is performed over the range 75 (65) < m γγ < 120 GeV for the 8 (13) TeV data, using an asymptotic approach [73][74][75] with a test statistic based on the profile likelihood ratio [76].The expected and observed 95% confidence level (CL) upper limits on the product of the cross section and branching fraction into two photons for an additional SM-like Higgs boson, from the analysis of each of the 8 and 13 TeV data sets, are presented in Fig. 4 for the parametric signal model.No significant (>3σ) excess with respect to the expected number of background events is observed.For the 8 TeV data, the minimum (maximum) observed upper limit on the product of the production cross section and branching fraction is approximately 31 (129) fb, corresponding to a mass hypothesis of 102.8 (91.0)GeV.For the 13 TeV data, the minimum (maximum) observed upper limits are 26 (161) fb, corresponding to a mass hypothesis of 103.0 (89.8)GeV.
In addition, the expected and observed 95% CL upper limits for the ggH plus ttH processes and for the VBF plus VH processes are shown in Fig. 5 for each of the 8 and 13 TeV data sets.The two production processes, in each case, are combined assuming relative proportions as predicted by the SM.
The results from the 8 and 13 TeV data are combined statistically applying the same methods used to obtain the results from each individual data set, in the diphoton invariant mass range  The inner and outer bands indicate the regions containing the distribution of limits located within ±1 and 2σ, respectively, of the expectation under the background-only hypothesis.The corresponding theoretical prediction for the product of the cross section and branching fraction into two photons for an additional SM-like Higgs boson is shown as a solid line with a hatched band, indicating its uncertainty [60].common to the two data sets, 80 < m γγ < 110 GeV.All of the experimental systematic uncertainties as well as the theoretical uncertainties in the signal acceptance due to PDF variations are assumed to be uncorrelated between the two data sets.The theoretical uncertainties in the signal acceptance due to scale variations as well as in the production cross sections at the center-of-mass energies of 8 and 13 TeV for an additional SM-like Higgs boson are assumed to be fully correlated.Figure 6 shows the expected and observed 95% CL upper limits on the product of the cross section and branching fraction into two photons for an additional Higgs boson, relative to the SM-like value from the latest theoretical predictions from the LHC Higgs cross section working group [60].No significant excess with respect to the expected number of background events is observed.The minimum (maximum) observed upper limit on the product of the production cross section and branching fraction normalized to the SM-like value is 0.17 (1.13) corresponding to a mass hypothesis of 103.0 (90.0)GeV. Figure 7 shows the expected and observed local p-values as a function of the mass of an additional SM-like Higgs boson, calculated with respect to the background-only hypothesis, from the analyses of the 8 and 13 TeV data, and from their combination.The most significant expected sensitivity occurs at the highest explored mass hypothesis of 110 GeV with a local expected significance close to 3σ (>6σ) for the 8 (13) TeV data, while the worst expected significance occurs in the neighborhood of 90 GeV, where it is approximately 0.4σ (slightly above 2σ).For the combination, the most (least) significant expected sensitivity occurs at a mass hypothesis of 110 (90) GeV with a local expected significance of approximately 6.8σ (slightly above 2.0σ).In the case of the 8 TeV data, one excess with approximately 2.0σ local significance is observed for a mass hypothesis of 97.7 GeV.For the 13 TeV data, one excess with approximately 2.90σ local (1.47σglobal) significance is observed for a mass hypothesis of 95.3 GeV, where the global significance has been calculated using the method of [77]

Summary
A search for an additional, SM-like, low-mass Higgs boson decaying into two photons has been presented.It is based upon data samples corresponding to integrated luminosities of 19.7 and 35.9 fb −1 collected at center-of-mass energies of 8 TeV in 2012 and 13 TeV in 2016, respectively.The search is performed in a mass range between 70 and 110 GeV.The expected and observed 95% CL upper limits on the product of the production cross section and branching fraction into two photons for an additional SM-like Higgs boson as well as the expected and observed local  p-values are presented.No significant (>3σ) excess with respect to the expected number of background events is observed.The observed upper limit on the product of the production cross section and branching fraction for the 2012 (2016) data set ranges from 129 (161) fb to 31 (26) fb.The statistical combination of the results from the analyses of the two data sets in the common mass range between 80 and 110 GeV yields an upper limit on the product of the cross section and branching fraction, normalized to that for a standard model-like Higgs boson, ranging from 0.7 to 0.2, with two notable exceptions: one in the region around the Z boson peak, where the limit rises to 1.1, caused by the presence of Drell-Yan dielectron production where both electrons are misidentified as isolated photons, and a second due to an observed excess with respect to the standard model prediction, which is maximal for a mass hypothesis of 95.3 GeV with a local (global) significance of 2.8 (1.3) standard deviations.More data are required to ascertain the origin of this excess.This is the first search for new resonances in the diphoton final state in this mass range based on LHC data at a center-of-mass energy of 13 TeV.
for a Higgs boson mass of 90 GeV for the 8 and 13 TeV data.Also shown are the full width at half maximum (FWHM) value and the value of the effective standard deviation for signal (σ eff ), which is defined as half the width of the narrowest interval containing 68.3% of the invariant mass distribution.The product of efficiency and acceptance of the signal model ranges from 36.2 (22.7)% for m H = 80 (70) GeV to 40.4 (26.5)% for m H = 110 (110) GeV in the case of the 8 (13) TeV data.

Figure 1 :
Figure 1: Full parameterized signal shape, integrated over all event classes, in simulated signal events with m H = 90 GeV at √ s = 8 TeV (left) and 13 TeV (right).The open points are the weighted MC events and the blue lines the corresponding parametric models.Also shown are the σ eff values and the shaded region limited by ±σ eff , along with the FWHM values, indicated by the position of the arrows on each distribution.

Figure 2 :
Figure 2: Background model fits using the chosen "best-fit" parametrization to data in the four event classes at √ s = 8 TeV.The corresponding signal model for each class for m H = 90 GeV, multiplied by 10, is also shown.The one-and two-σ bands reflect the uncertainty in the background model normalization associated with the statistical uncertainties of the fits, and are shown for illustration purposes only.The difference between the data and the best-fit model is shown in the lower panels.

Figure 3 :
Figure 3: Background model fits using the chosen "best-fit" parametrization to data in the three event classes at √ s = 13 TeV.The corresponding signal model for each class for m H = 90 GeV, multiplied by 10, is also shown.The one-and two-σ bands reflect the uncertainty in the background model normalization associated with the statistical uncertainties of the fits, and are shown for illustration purposes only.The difference between the data and the best-fit model is shown in the lower panels.

Figure 4 :
Figure4: Expected and observed exclusion limits (95% CL, in the asymptotic approximation) on the product of the production cross section and branching fraction into two photons for an additional SM-like Higgs boson, from the analysis of the 8 (left) and 13 (right) TeV data.The inner and outer bands indicate the regions containing the distribution of limits located within ±1 and 2σ, respectively, of the expectation under the background-only hypothesis.The corresponding theoretical prediction for the product of the cross section and branching fraction into two photons for an additional SM-like Higgs boson is shown as a solid line with a hatched band, indicating its uncertainty[60].

Figure 5 :
Figure 5: Expected and observed exclusion limits (95% CL, in the asymptotic approximation) on the product of the production cross section and branching fraction into two photons for an additional SM-like Higgs boson, for the ggH plus ttH (left) and VBF plus VH (right) processes, from the analysis of the 8 (top) and 13 (bottom) TeV data.The inner and outer bands indicate the regions containing the distribution of limits located within ±1 and 2σ, respectively, of the expectation under the background-only hypothesis.local (1.3σglobal) significance is observed for a mass hypothesis of 95.3 GeV.

Figure 6 :
Figure 6: Expected and observed exclusion limits (95% CL, in the asymptotic approximation) on the product of the production cross section and branching fraction into two photons for an additional Higgs boson, relative to the expected SM-like value, from the analysis of the 8 and 13 TeV data.The inner and outer bands indicate the regions containing the distribution of limits located within ±1 and 2σ, respectively, of the expectation under the background-only hypothesis.