Search for exclusive Higgs and Z boson decays to ϕγ and ργ with the ATLAS detector

A search for the exclusive decays of the Higgs and Z bosons to a ϕ or ρ meson and a photon is performed with a pp collision data sample corresponding to an integrated luminosity of up to 35.6 fb−1 collected at s=13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=13 $$\end{document} TeV with the ATLAS detector at the CERN Large Hadron Collider. These decays have been suggested as a probe of the Higgs boson couplings to light quarks. No significant excess of events is observed above the background, as expected from the Standard Model. Upper limits at 95% confidence level were obtained on the branching fractions of the Higgs boson decays to ϕγ and ργ of 4.8 × 10−4 and 8.8 × 10−4, respectively. The corresponding 95% confidence level upper limits for the Z boson decays are 0.9 × 10−6 and 25 × 10−6 for ϕγ and ργ, respectively.


Introduction
Following the observation [1,2] of a Higgs boson, , with a mass of approximately 125 GeV [3] by the ATLAS and CMS collaborations at the Large Hadron Collider (LHC), the properties of its interactions with the electroweak gauge bosons have been measured extensively [4][5][6].The coupling of the Higgs boson to leptons has been established through the observation of the  →  +  − channel [4, 7, 8], while in the quark sector indirect evidence is available for the coupling of the Higgs boson to the top-quark [4] and evidence for the Higgs boson decays into  b has been recently presented [9,10].Despite this progress, the Higgs boson interaction with the fermions of the first and second generations is still to be confirmed experimentally.In the Standard Model (SM), Higgs boson interactions to fermions are implemented through Yukawa couplings, while a wealth of beyond-the-SM theories predict substantial modifications.Such scenarios include the Minimal Flavour Violation framework [11], the Froggatt-Nielsen mechanism [12], the Higgsdependent Yukawa couplings model [13], the Randall-Sundrum family of models [14], and the possibility of the Higgs boson being a composite pseudo-Goldstone boson [15].An overview of relevant models of new physics is provided in Ref. [16].
Currently, the light (, , ) quark couplings to the Higgs boson are loosely constrained by existing data on the total Higgs boson width, while the large multijet background at the LHC inhibits the study of such couplings with inclusive  →  q decays.Rare exclusive decays of the Higgs boson into a light meson, , and a photon, , have been suggested as a probe of the couplings of the Higgs boson to light quarks and would allow a search for potential deviations from the SM prediction [23,25,26].Specifically, the observation of the Higgs boson decay to a  or (770) (denoted as  in the following) meson and a photon would provide sensitivity to its couplings to the strange-quark, and the up-and down-quarks, respectively.The expected SM branching fractions are B ( → ) = (2.31 ± 0.11) × 10 −6 and B ( → ) = (1.68 ± 0.08) × 10 −5 [23].The decay amplitude receives two main contributions that interfere destructively.The first is referred to as "direct" and proceeds through the  →  q coupling, where subsequently a photon is emitted before the  q hadronises exclusively to .The second is referred to as "indirect" and proceeds via the  →  coupling followed by the fragmentation  * → .In the SM, owing to the smallness of the light-quark Yukawa couplings, the latter amplitude dominates, despite being loop induced.As a result, the expected branching fraction predominantly arises from the "indirect" process, while the Higgs boson couplings to the light quarks are probed by searching for modifications of this branching fraction due to changes in the "direct" amplitude.This paper describes a search for Higgs boson decays into the exclusive final states  and .The decay  →  +  − is used to reconstruct the  meson, and the decay  →  +  − is used to reconstruct the  meson.The branching fractions of the respective meson decays are well known and are accounted for when calculating the expected signal yields.The presented search uses approximately 13 times more integrated luminosity than the first search for  →  decays [27], which led to a 95% CL upper limit of B ( → ) < 1.4 × 10 −3 , assuming SM production rates of the Higgs boson.Currently, no other experimental information about the  →  decay mode exists.
The searches for the analogous decays of the  boson into a meson and a photon are also presented in this paper.These have been theoretically studied [28,29] as a unique precision test of the SM and the factorisation approach in quantum chromodynamics (QCD), in an environment where the power corrections in terms of the QCD energy scale over the vector boson's mass are small [29].The large  boson production cross section at the LHC means that rare  boson decays can be probed at branching fractions much smaller than for Higgs boson decays into the same final states.The SM branching fraction predictions for the decays considered in this paper are B ( → ) = (1.04 ± 0.12) × 10 −8 [28,29] and B ( → ) = (4.19± 0.47) × 10 −8 [29].The first search for  →  decays by the ATLAS Collaboration was presented in Ref. [27] and a 95% CL upper limit of B ( → ) < 8.3 × 10 −6 was obtained.So far no direct experimental information about the decay  →  exists.

ATLAS detector
ATLAS [30] is a multi-purpose particle physics detector with a forward-backward symmetric cylindrical geometry and near 4 coverage in solid angle. 1 It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer.
The inner tracking detector (ID) covers the pseudorapidity range || < 2.5, and is surrounded by a thin superconducting solenoid providing a 2 T magnetic field.At small radii, a high-granularity silicon pixel detector covers the vertex region and typically provides three measurements per track.A new innermost pixel-detector layer, the insertable B-layer, was added before 13 TeV data-taking began in 2015 and provides an additional measurement at a radius of about 33 mm around a new and thinner beam pipe [31].The pixel detectors are followed by a silicon microstrip tracker, which typically provides four space-point measurements per track.The silicon detectors are complemented by a gas-filled straw-tube transition radiation tracker, which enables radially extended track reconstruction up to || = 2.0, with typically 35 measurements per track.
The calorimeter system covers the pseudorapidity range || < 4.9.A high-granularity lead/liquid-argon (LAr) sampling electromagnetic calorimeter covers the region || < 3.2, with an additional thin LAr presampler covering || < 1.8 to correct for energy losses upstream.The electromagnetic calorimeter is divided into a barrel section covering || < 1.475 and two endcap sections covering 1.375 < || < 3.2.For || < 2.5 it is divided into three layers in depth, which are finely segmented in  and .A steel/scintillatortile calorimeter provides hadronic calorimetry in the range || < 1.7.LAr technology, with copper as absorber, is used for the hadronic calorimeters in the endcap region, 1.5 < || < 3.2.The solid-angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules in 3.1 < || < 4.9, optimised for electromagnetic and hadronic measurements, respectively. 1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the -axis along the beam pipe.The -axis points from the IP to the centre of the LHC ring, and the -axis points upward.Cylindrical coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.The pseudorapidity is defined in terms of the polar angle  as  = − ln tan(/2).
The muon spectrometer surrounds the calorimeters and comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field provided by three air-core superconducting toroids.
A two-level trigger and data acquisition system is used to provide an online selection and record events for offline analysis [32].The level-1 trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to 100 kHz or less from the maximum LHC collision rate of 40 MHz.It is followed by a software-based high-level trigger which filters events using the full detector information and records events for detailed offline analysis at an average rate of 1 kHz.

Data and Monte Carlo simulation
The search is performed with a sample of   collision data recorded at a centre-of-mass energy √  = 13 TeV.Events are retained for further analysis only if they were collected under stable LHC beam conditions and the detector was operating normally.This results in an integrated luminosity of 35.6 and 32.3 fb −1 for the  and  final states, respectively.The integrated luminosity of the data sample has an uncertainty of 3.4% derived using the method described in Ref. [33].
The  and  data samples used in this analysis were each collected with a specifically designed trigger.Both triggers require an isolated photon with a transverse momentum,  T , greater than 35 GeV and an isolated pair of ID tracks, one of which must have a  T greater than 15 GeV, associated with a topological cluster of calorimeter cells [34] with a transverse energy greater than 25 GeV.The photon part of the trigger follows the same process as the inclusive photon trigger requiring an electromagnetic cluster in the calorimeter consistent with a photon and is described with more detail in Ref. [32], while requirements on the ID tracks are applied in the high-level trigger through an appropriately modified version of the -lepton trigger algorithms which are described in more detail in Ref. [35].The trigger for the  final state was introduced in September 2015.This trigger requires that the invariant mass of the pair of tracks, under the charged-kaon hypothesis, is in the range 987-1060 MeV, consistent with the  meson mass.The trigger efficiency for both the Higgs and  boson signals is approximately 83% with respect to the offline selection, as described in Section 4. The corresponding trigger for the  final state was introduced in May 2016.This trigger requires the invariant mass of the pair of tracks, under the charged-pion hypothesis, to be in the range 475-1075 MeV to include the bulk of the broad  meson mass distribution.The trigger efficiency for the Higgs boson signal is approximately 78% and for the  boson signal is approximately 72% with respect to the offline selection.
Higgs boson production through the gluon-gluon fusion () and vector-boson fusion (VBF) processes was modelled up to next-to-leading order (NLO) in  S using the Powheg-Box v2 Monte Carlo (MC) event generator [36][37][38][39][40] with CT10 parton distribution functions [41].Powheg-Box was interfaced with the Pythia 8.186 MC event generator [42,43] to model the parton shower, hadronisation and underlying event.The corresponding parameter values were set according to the AZNLO tune [44].Additional contributions from the associated production of a Higgs boson and a  or  boson (denoted by   and  , respectively) are modelled by the Pythia 8.186 MC event generator with NNPDF23LO parton distribution functions [45] and the A14 tune for hadronisation and the underlying event [46].The production rates and kinematic distributions for the SM Higgs boson with   = 125 GeV are assumed throughout.These were obtained from Ref. [16] and are summarised below.The  production rate is normalised such that it reproduces the total cross section predicted by a next-to-next-to-next-to-leadingorder QCD calculation with NLO electroweak corrections applied [47][48][49][50].The VBF production rate is normalised to an approximate NNLO QCD cross section with NLO electroweak corrections applied [51][52][53].The   and   production rates are normalised to cross sections calculated at next-to-next-toleading order (NNLO) in QCD with NLO electroweak corrections [54,55] including the NLO QCD corrections [56] for  →  .The expected signal yield is corrected to include the 2% contribution from the production of a Higgs boson in association with a  t or a  b pair.
The Powheg-Box v2 MC event generator with CT10 parton distribution functions was also used to model inclusive  boson production.Pythia 8.186 with CTEQ6L1 parton distribution functions [57] and the AZNLO parameter tune was used to simulate parton showering and hadronisation.The prediction is normalised to the total cross section obtained from the measurement in Ref. [58], which has an uncertainty of 2.9%.The Higgs and  boson decays were simulated as a cascade of two-body decays, respecting angular momentum conservation.The meson line shapes were simulated by Pythia.The branching fraction for the decay  →  +  − is (48.9 ± 0.5)% whereas the decay  →  +  − has a branching fraction close to 100% [59].The simulated events were passed through the detailed Geant 4 simulation of the ATLAS detector [60,61] and processed with the same software used to reconstruct the data.Simulated pile-up events (additional   collisions in the same or nearby bunch crossings) are also included and the distribution of these is matched to the conditions observed in the data.
4 Event selection for  →  +  −  and  →  +  −  final states The  and  exclusive final states are very similar.Both final states consist of a pair of oppositely charged reconstructed ID tracks.The difference is that for the former the mass of the pair, under the charged-kaon hypothesis for the two tracks, is consistent with the  meson mass, while for the later, under the charged-pion hypothesis for the tracks, it is consistent with the  meson mass.Events with a   interaction vertex reconstructed from at least two ID tracks with  T > 400 MeV are considered in the analysis.Within an event, the primary vertex is defined as the reconstructed vertex with the largest  2 T of associated ID tracks.
Photons are reconstructed from clusters of energy in the electromagnetic calorimeter.Clusters without matching ID tracks are classified as unconverted photon candidates while clusters matched to ID tracks consistent with the hypothesis of a photon conversion into  +  − are classified as converted photon candidates [62].Reconstructed photon candidates are required to have   T > 35 GeV, |  | < 2.37, excluding the barrel/endcap calorimeter transition region 1.37 < |  | < 1.52, and to satisfy "tight" photon identification criteria [62].An isolation requirement is imposed to further suppress contamination from jets.The sum of the transverse momenta of all tracks within Δ = √︁ (Δ) 2 + (Δ) 2 = 0.2 of the photon direction, excluding those associated with the reconstructed photon, is required to be less than 5% of   T .Moreover, the sum of the transverse momenta of all calorimeter energy deposits within Δ = 0.4 of the photon direction, excluding those associated with the reconstructed photon, is required to be less than 2.45 GeV + 0.022 ×   T .To mitigate the effects of multiple   interactions in the same or neighbouring bunch crossings, only ID tracks which originate from the primary vertex are considered in the photon track-based isolation.For the calorimeter-based isolation the effects of the underlying event and multiple   interactions are also accounted for on an event by event basis using an average underlying event energy density determined from data, as described in Ref. [62].
Charged particles satisfying the requirements detailed below are assumed to be a  ± meson in the  analysis and a  ± meson in the  analysis.No further particle identification requirements are applied.In the following, when referring to charged particles collectively the term "charged-hadron candidates" is used, while when referring to the charged particles relevant to the  and the  analyses the terms "kaon candidates" and "pion candidates" are used, respectively, along with the corresponding masses.A pair of oppositely-charged charged-hadron candidates is referred to collectively as .
Charged-hadron candidates are reconstructed from ID tracks which are required to have || < 2.5,  T > 15 GeV and to satisfy basic quality criteria, including a requirement on the number of hits in the silicon detectors [63].The  →  +  − and  →  +  − decays are reconstructed from pairs of oppositely charged-hadron candidates; the candidate with the higher  T , referred to as the leading charged-hadron candidate, is required to have  T > 20 GeV.
Pairs of charged-hadron candidates are selected based on their invariant masses.Those with an invariant mass, under the charged-kaon hypothesis,   +  − between 1012 MeV and 1028 MeV are selected as  →  +  − candidates.Pairs with an invariant mass, under the charged-pion hypothesis,   +  − between 635 MeV and 915 MeV are selected as  →  +  − candidates.The candidates where   +  − is consistent with the  meson mass are rejected from the  analysis.This requirement rejects a negligible fraction of the signal in the  analysis.Selected  candidates are required to satisfy an isolation requirement: the sum of the  T of the reconstructed ID tracks from the primary vertex within Δ = 0.2 of the leading charged hadron candidate (excluding the charged-hadron candidates defining the pair) is required to be less than 10% of the  T of the  candidate.
The  candidates are combined with the photon candidates, to form  candidates.When multiple combinations are possible, a situation that arises only in a few percent of the events, the combination of the highest- T photon and the  candidate with an invariant mass closest to the respective meson mass is selected.The event is retained for further analysis if the requirement Δ(, ) > /2 is satisfied.The transverse momentum of the  candidates is required to be greater than a threshold that varies as a function of the invariant mass of the three-body system,    .Thresholds of 40 GeV and 47.2 GeV are imposed on   T for the regions    < 91 GeV and    ≥ 140 GeV, respectively.The threshold is varied from 40 GeV to 47.2 GeV as a linear function of    in the region 91 ≤    < 140 GeV.This approach ensures good sensitivity for both the Higgs and  boson searches, while keeping a single kinematic selection.
For the (→  +  − )  final state, the total signal efficiencies (kinematic acceptance, trigger and reconstruction efficiencies) are 17% and 10% for the Higgs and  boson decays, respectively.The corresponding efficiencies for the  final state are 8% and 2.4%.The difference in efficiency between the Higgs and  boson decays arises primarily from the softer  T distributions of the photon and charged-hadron candidates associated with the  →   production, as can be seen for the  case by comparing Figures 1(a) and 1(b).The overall lower efficiency in the  final state is a result of the lower efficiency of the   requirement due to the large -meson natural width and the different kinematics of the  decay products, as presented in Figures 1(c) and 1(d).Meson helicity effects have a relatively small impact for the  →  +  − decays, where the kaons carry very little momentum in the  rest frame.Specifically, the expected Higgs () boson signal yield in the signal region is 2.4% larger (9% larger) than in the hypothetical scenario where the meson is unpolarised.For the  →  +  − decays the yields are increased by 12% (increased by 7%).
The average    resolution is 1.8% for both the Higgs and  boson decays.The Higgs boson signal    distribution is modelled with a sum of two Gaussian probability density functions (pdf) with a common mean value, while the  boson signal    distribution is modelled with a double Voigtian pdf (a convolution of relativistic Breit-Wigner and Gaussian pdfs) corrected with a mass-dependent efficiency factor.Figure 1: Generator-level transverse momentum ( T ) distributions of the photon and of the charged-hadrons, ordered in  T , for (a)  → , (b)  → , (c)  →  and (d)  →  simulated signal events, respectively.The hatched histograms denote the full event selection while the dashed histograms show the events at generator level that fall within the analysis geometric acceptance (both charged-hadrons are required to have || < 2.5 while the photon is required to have || < 2.37, excluding the region 1.37 < || < 1.52).The dashed histograms are normalised to unity, and the relative difference between the two sets of distributions corresponds to the effects of reconstruction, trigger, and event selection efficiencies.The leading charged-hadron candidate ℎ = ,  is denoted by  ℎ1 T and the sub-leading candidate by  ℎ2 T .
The   +  − distribution for the selected  candidates, with no   +  − requirement applied, is shown in Figure 2(a) exhibiting a visible peak at the  meson mass.The  peak is fitted with a Voigtian pdf, while the background is modelled with a function typically used to describe kinematic thresholds [64].The experimental resolution in   +  − is approximately 4 MeV, comparable to the 4.3 MeV [59] width of the  meson.In Figure 2(b), the corresponding distribution for the selected  candidates is shown, where the  meson can also be observed.The  peak is fitted with a single Breit-Wigner pdf, modified by a mass-dependent width to match the distribution obtained from Pythia [42].The background is fitted with the sum of a combinatoric background, estimated from events containing a same-sign di-track pair, and other backgrounds determined in the fit using a linear combination of Chebychev polynomials up to the second order.Figure 2 only qualitatively illustrates the meson selection in the studied final state, and is not used any further in this analysis. [GeV]

Background
For both the  and  final states, the main sources of background in the searches are events involving inclusive photon + jet or multijet processes where an  candidate is reconstructed from ID tracks originating from a jet.
From the selection criteria discussed earlier, the shape of this background exhibits a turn-on structure in the    distribution around 100 GeV, in the region of the  boson signal, and a smoothly falling background in the region of the Higgs boson signal.Given the complex shape of this background, these processes are modelled in an inclusive fashion with a non-parametric data-driven approach using templates to describe the relevant distributions.The background normalisation and shape are simultaneously extracted from a fit to the data.A similar procedure was used in the earlier search for Higgs and  boson decays into  [27] and the search for Higgs and  boson decays into /  and Υ()  described in Ref. [21].

Background modelling
The background modelling procedure for each final state exploits a sample of approximately 54 000  +  −  and 220 000  +  −  candidate events in data.These events pass all the kinematic selection requirements described previously, except that the photon and  candidates are not required to satisfy the nominal isolation requirements, and a looser   T > 35 GeV requirement is imposed.This selection defines the background-dominated "generation region" (GR).From these events, pdfs are constructed to describe the distributions of the relevant kinematic and isolation variables and their most important correlations.In this way, in the absence of appropriate simulations, pseudocandidate events are generated, from which the background shape in the discriminating variable is derived.This ensemble of pseudocandidate events is produced by randomly sampling the distributions of the relevant kinematic and isolation variables, which are estimated from the data in the GR.Each pseudocandidate event is described by  and  four-momentum vectors and the associated  and photon isolation variables.The  four-momentum vector is constructed from sampled   ,   ,   and   T values.For the  four-momentum vector, the   and   are determined from the sampled Δ(, ) and Δ(, ) values whereas   T is sampled directly.The most important correlations among these kinematic and isolation variables in background events are retained in the generation of the pseudocandidates through the following sampling scheme, where the steps are performed sequentially: i) Values for   ,   ,   and   T are drawn randomly and independently according to the corresponding pdfs.
ii) The distribution of   T values is parameterised in bins of   T , and values are drawn from the corresponding bins given the previously generated value of   T .The  isolation variable is parameterised in bins of   T (   T ) for the  () model and sampled accordingly.The difference between the two approaches for the  and  accounts for the difference in the observed correlations arising in the different datasets.
iii) The distributions of the values for Δ(, ), photon calorimeter isolation, normalised to   T , and their correlations are parameterised in a two-dimensional distribution.For the  analysis, several distributions are produced corresponding to the   T bins used earlier to describe the   T and  isolation variables, whereas for the  final state the two-dimensional distribution is produced inclusively for all   T values.iv) The photon track isolation, normalised to   T , and the Δ(, ) variables are sampled from pdfs generated in bins of relative photon calorimeter isolation and Δ(, ), respectively, using the values drawn in step iii).
The nominal selection requirements are imposed on the ensemble, and the surviving pseudocandidates are used to construct templates for the    distribution, which are then smoothed using Gaussian kernel density estimation [65].It was verified through signal injection tests that the shape of the background model is not affected by potential signal contamination.

Background validation
To validate the background model, the    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.Three validation regions are defined, each based on the GR selection and adding one of the following: the   T requirement (VR1), the photon isolation requirements (VR2), or the meson isolation requirement (VR3).The    distributions in these validation regions are shown in Figure 3.The background model is found to describe the data in all regions within uncertainties (see Section 6).Potential background contributions from  → ℓℓ decays and inclusive Higgs decays were studied and found to be negligible for the selection requirements and dataset used in this analysis.
A further validation of the background modelling is performed using events within a sideband of the  mass distribution.For the  analysis the sideband region is defined by 1.035 GeV <   +  − < 1.051 GeV.For the  analysis the sideband region is defined by 950 MeV <   +  − < 1050 MeV.All other selection requirements and modelling procedures are identical to those used in the signal region.Figures 4(a) and 4(b) show the    distributions for the sideband region.The background model is found to describe the data within the systematic uncertainties described in Section 6.

Systematic uncertainties
Trigger and identification efficiencies for photons are determined from samples enriched with  →  +  − events in data [32,62].The systematic uncertainty in the expected signal yield associated with the trigger efficiency is estimated to be 2.0%.The photon identification and isolation uncertainties, for both the converted and unconverted photons, are estimated to be 2.4% and 2.6% for the Higgs and  boson signals, respectively.An uncertainty of 6.0% per  candidate is assigned to the track reconstruction efficiency and accounts for effects associated with the modelling of ID material and track reconstruction algorithms if a nearby charged particle is present.This uncertainty is derived conservatively by assuming a 3% uncertainty in the reconstruction efficiency of each track [66], and further assuming the uncertainty to be fully correlated between the two tracks of the  candidate.
The systematic uncertainties in the Higgs production cross section are obtained from Ref. [16] as described in Section 3. The  boson production cross-section uncertainty is taken from the measurement in Ref. [58].
The photon energy scale uncertainty, determined from  →  +  − events and validated using  → ℓℓ events [67], is applied to the simulated signal samples as a function of   and   T .The impact of the photon energy scale uncertainty on the Higgs and  boson mass distributions does not exceed 0.2%.The uncertainty associated with the photon energy resolution is found to have a negligible impact.Similarly, the systematic uncertainty associated with the ID track momentum measurement is found to be negligible.The systematic uncertainties in the expected signal yields are summarised in Table 1.
The shape of the background model is allowed to vary around the nominal shape, and the parameters controlling these systematic variations are treated as nuisance parameters in the maximum-likelihood fit used to extract the signal and background yields.Three such shape variations are implemented through varying   T , linear distortions of the shape of the Δ(, ), and a global tilt of the three-body mass.The first two variations alter the kinematics of the pseudocandidates that are propagated to the three-body mass.

Results
The data are compared to background and signal predictions using an unbinned maximum-likelihood fit to the    distribution.The parameters of interest are the Higgs and  boson signal normalisations.Systematic uncertainties are modelled using additional nuisance parameters in the fit; in particular the background normalisation is a free parameter in the model.The fit uses the selected events with    < 300 GeV.The expected and observed numbers of background events within the    ranges relevant to the Higgs and  boson signals are shown in Table 2.The observed yields are consistent with the number of events expected from the background-only prediction within the systematic and statistical uncertainties.
The results of the background-only fits for the  and  analyses are shown in Figures 5(a) and 5(b), respectively.Upper limits are set on the branching fractions for the Higgs and  boson decays into   using the CL s modified frequentist formalism [68] with the profile-likelihood-ratio test statistic [69].For the upper limits on the branching fractions, the SM production cross section is assumed for the Higgs boson [16], while the ATLAS measurement of the inclusive  boson cross section is used for the  boson signal [58], as discussed in Section 3. The results are summarised in Table 3.The observed 95% CL upper limits on the branching fractions for  →  and  →   decays are 208 and 87 times the expected SM branching fractions, respectively.The corresponding values for the  decays are 52 and 597 times the expected SM branching fractions, respectively.Upper limits at 95% CL on the production cross section times branching The systematic uncertainties described in Section 6 result in a 14% deterioration of the post-fit expected 95% CL upper limit on the branching fraction in the  →  and  →  analyses, compared to the result including only statistical uncertainties.For the  analysis the systematic uncertainties result in a 2.3% increase in the post-fit expected upper limit for the Higgs boson decay, while for the  boson decay the upper limit deteriorates by 29%.

8 Summary
A search for the decays of Higgs and  bosons into  and  has been performed with √  = 13 TeV   collision data samples collected with the ATLAS detector at the LHC corresponding to integrated luminosities of up to 35.6 fb −1 .The  and  mesons are reconstructed via their dominant decays into the  +  − and  +  − final states, respectively.The background model is derived using a fully data driven approach and validated in a number of control regions including sidebands in the  +  − and  +  − mass distributions.

Figure 2 :
Figure 2: The (a)   +  − and (b)   +  − distributions for  and  candidates, respectively.The candidates fulfil the complete event selection (see text), apart from requirements on   +  − or   +  − .These requirements are marked on the figures with dashed lines topped with arrows indicating the included area.The signal and background models are discussed in the text.

Figure 3 :
Figure 3: The distribution of   +  −  top (  +  −  bottom) in data compared to the prediction of the background model for the VR1, VR2 and VR3 validation regions.The background model is normalised to the observed number of events within the region shown.The uncertainty band corresponds to the uncertainty envelope derived from variations in the background modelling procedure.The ratio of the data to the background model is shown below the distributions.

Figure 4 :
Figure 4: The distribution of    for the (a)  and (b)  selections in the sideband control region.The background model is normalised to the observed number of events within the region shown.The uncertainty band corresponds to the uncertainty envelope derived from variations in the background modelling procedure.The ratio of the data to the background model is shown below the distributions.

Figure 5 :
Figure 5: The (a)   +  −  and (b)   +  −  distributions of the selected  and  candidates, respectively, along with the results of the maximum-likelihood fits with a background-only model.The Higgs and  boson contributions for the branching fraction values corresponding to the observed 95% CL upper limits are also shown.Below the figures the ratio of the data to the background-only fit is shown.

Table 1 :
Summary of the relative systematic uncertainties in the expected signal yields.The magnitude of the effects are the same for both the  and  selections.

Table 2 :
The number of observed events and the mean expected background, estimated from the maximum-likelihood fit and shown with the associated total uncertainty, for the    ranges of interest.The expected Higgs and  boson signal yields, along with the total systematic uncertainty, for  and , estimated using simulations, are also shown in parentheses.

Table 3 :
Expected and observed branching fraction upper limits at 95% CL for the  and  analyses.The ±1 intervals of the expected limits are also given.
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