Flavour independent search for neutral Higgs bosons at LEP

A flavour independent search for the CP-even and CP-odd neutral Higgs bosons h and A is performed in 624 pb −1 of data collected with the L3 detector at LEP at centre-of-mass energies between 189 and 209 GeV. Higgs boson production through the e+e− → Zh and the e +e− → hA processes is considered and decays of the Higgs bosons into hadrons are studied. No significant signal is observed and 95% confidence level limits on the hZZ and hAZ couplings are derived as a function of the Higgs boson masses. Assuming the Standard Model cross section for the Higgs-strahlung process and a 100% branching fraction into hadrons, a 95% confidence level lower limit on the mass of the Higgs boson is set at 110.3 GeV.  2004 Published by Elsevier B.V. Open access under CC BY license. L3 Collaboration / Physics Letters B 583 (2004) 14–27 17


Introduction
One of the goals of the LEP program is the search for Higgs bosons, the particles postulated by the Standard Model of the electroweak interactions [1], and some of its extensions, to explain the mechanism [2] which gives the elementary particles their observed masses.
At the centre-of-mass energies, √ s, at which the LEP e + e − collider was operated, the Standard Model Higgs boson, H, is predicted to decay dominantly into b quarks. For a large part of the parameter space of the Minimal Supersymmetric Standard Model (MSSM) [3], decays of neutral Higgs bosons into b quarks are also predicted to be dominant. Experimental searches for the Higgs bosons predicted both in the Standard Model and in the MSSM exploit this feature through sophisticated flavour tagging techniques. No significant signal was found at LEP either for the Standard Model Higgs boson [4][5][6][7] or for neutral Higgs bosons of the MSSM [5,8,9].
In some extensions of the Standard Model, decays of the Higgs bosons into bb pairs are strongly suppressed to the benefit of other decay modes such as cc, gg or τ + τ − . For instance, this occurs for specific parameters of the two Higgs doublet model [10] or the MSSM [11], as well as for some composite models [12]. It is hence important to investigate such scenarios with dedicated experimental analyses in which the information about the flavour of the Higgs boson decay products is not used, reducing the model dependence of the conventional Higgs searches.
This Letter describes the search for hadronic decays of the light CP-even Higgs boson, h, and of the CPodd Higgs boson, A, using data collected by the L3 detector [13] at LEP. Production of a h boson in 1  association with a Z boson, Higgs-strahlung, and pairproduction of the h and A bosons, are considered: e + e − → hZ, e + e − → hA.
The tree level cross sections of these processes are related to the cross section of the Standard Model Higgs boson production through the Higgs-strahlung process, σ SM HZ , as [10]: whereλ is a p-wave suppression factor, which depends on √ s and on the Higgs boson masses, m h and m A . The hZZ and hAZ couplings relative to the HZZ coupling of the Standard Model are defined as ξ = g hZZ /g SM HZZ and η = g hAZ /g SM HZZ . In the following, these couplings are not fixed to any prediction but rather considered as free parameters, reducing the model dependence of the analysis.

Data and Monte Carlo samples
An integrated luminosity of 624 pb −1 of data, collected at √ s = 189-209 GeV, is analysed. The data are grouped into several subsamples according to their √ s value, as listed in Table 1.
The cross section of the Higgs-strahlung process in the Standard Model is calculated using the HZHA generator [14]. For efficiency studies, Monte Carlo samples are generated using PYTHIA [15] for the two production mechanisms and for each of the decay modes h → bb, cc and gg, A → bb, cc and gg. Several Higgs mass hypotheses are considered and 2000 events are generated in each case. For the e + e − → hZ process, m h ranges in steps of 10 GeV from 60 to 100 GeV, and in steps of 1 GeV from 100 to 120 GeV. For the e + e − → hA process, m h and m A range from 40 to 110 GeV in steps of 10 GeV.
For background studies, the following Monte Carlo programs are used: KK2f [16] for e + e − → qq(γ ) and e + e − → τ + τ − , PYTHIA for e + e − → ZZ and e + e − → Ze + e − and YFSWW [17] for e + e − → W + W − . EXCALIBUR [18] is used for four-fermion final states not covered by these generators. Hadron production in two-photon interactions is simulated with PYTHIA and PHOJET [19]. The number of simulated events for the most important background Two jets and missing energy bbgg, cccc bb + − , cc + − , gg + − Two jets and two leptons ccgg, gggg channels is more than 100 times the number of expected events. The L3 detector response is simulated using the GEANT program [20], which models the effects of energy loss, multiple scattering and showering in the detector. The GHEISHA program [21] is used to simulate hadronic interactions. Time dependent detector inefficiencies, monitored during data taking, are also taken into account.

Analysis procedures
Three different decay modes are considered for the h and A bosons: bb, cc and gg. Table 2 summarises the different signal signatures and the investigated topologies. Three topologies cover the possible final states of the e + e − → hZ process. They correspond to the decay of the Z boson into hadrons, neutrinos or charged leptons, associated to the hadrons from the h decay. They give rise to events with four hadronic jets, two hadronic jets and missing energy and two hadronic jets and two charged leptons, respectively. A single topology consisting of four hadronic jets, covers all final states of the e + e − → hA process.
Analyses in all channels proceed from a preselection of high multiplicity hadronic events which suppresses copious backgrounds from two-photon interactions, lepton-pair production and pair-production of gauge bosons which decay into leptons. A selection based on kinematic cuts, neural networks or likeli-hoods is then applied to further discriminate the signal from the background. Finally, discriminant variables which depend on the Higgs mass hypothesis are built to separate signal and background. Their distributions are studied to test the presence of a signal and to probe the ξ and η couplings as a function of m h and m A . Events are ordered as a function of the signal over background ratio and only events with this ratio greater than 0.05 are retained.

Search for e + e − → hZ
The three analyses used in the search for e + e − → hZ are similar to those used in the search for the Standard Model Higgs boson [4], with the exception that no b quark identification is used.

Four jets
If both the h and the Z bosons decay into hadrons, the signature is four hadronic jets. The invariant mass of two of them has to be compatible with the mass of the Z boson, m Z . The dominant background comes from hadronic decays of pair-produced gauge bosons and from the e + e − → qq(γ ) process.
After a preselection of high multiplicity events [4], events are resolved into four jets using the DURHAM algorithm [22] and a kinematic fit imposing fourmomentum conservation is performed. A likelihood, L hZ , is built [4] from the following variables: • the maximum energy difference between any two jets, • the minimum jet energy, • the parameter y 34 of the DURHAM algorithm for which the event is resolved from three into four jets, • the minimum opening angle between any two jets, • the event sphericity, • the absolute value of the cosine of the polar angle, Θ 2B , for the di-jet system most compatible with the production of a pair of gauge bosons, • the mass from a kinematic fit imposing fourmomentum conservation and equal di-jet masses, m 5C , • the maximal triple-jet boost, γ triple , defined as the maximum three-jet boost obtained from the four possibilities to construct a one-jet against three-jet configuration in a four-jet event. Fig. 1 shows the distributions of | cos Θ 2B |, m 5C , γ triple and L hZ for data collected at √ s > 203 GeV, the expected background and a signal with m h = 110 GeV. Events are retained for which the value of L hZ exceeds a threshold, around 0.6, optimised separately for each √ s and m h hypothesis. For each of the three possible jet pairings, the quantity [4], where Σ and ∆ are the di-jet mass sum and difference, while σ Σ and σ ∆ are the corresponding resolutions. The pairing which minimises χ 2 hZ is chosen and the corresponding value is used as the final discriminant variable. Fig. 2(a) presents the distributions of the signal over background ratio in the χ 2 hZ variable for selected data and Monte Carlo events. Table 3 lists the numbers of selected and expected events for different m h hypotheses.

Two jets and missing energy
The signature for h decays into hadrons and Z decays into neutrinos is a pair of high multiplicity jets, large missing energy and a missing mass, m mis , consistent with m Z . The dominant backgrounds are the e + e − → qq(γ ) process, W pair-production in which only one W decays into hadrons and Z pair-production with a Z decaying into hadrons and the other into neutrinos.
High multiplicity hadronic events are selected with a visible energy, E vis , such that 0.25 < E vis / √ s < 0.70. Events with isolated photons of energy greater than 20 GeV are rejected. The events are forced into two jets using the DURHAM algorithm and the dijet mass is required to be greater than 40 GeV to suppress background from two-photon interactions. Events from the e + e − → qq(γ ) process are suppressed by requiring m mis > 60 GeV. In addition, the polar angle, θ , of the missing momentum must satisfy | cos θ | < 0.9 and the energy deposited in the very forward calorimeters is required to be less than 20 GeV. Finally, the sine of the angle Ψ between the beam axis and the plane spanned by the directions of the two jets must be greater than 0.025. Fig. 3(a) and (b) presents the distributions of m mis and sin Ψ for data collected Table 3 Numbers of selected candidates, N D , expected background events, N B , and expected signal events, N S , for different m h hypotheses in the e + e − → hZ search. The selection efficiencies, ε, are also given. The numbers of signal events are quoted for the h decay mode corresponding to the lowest efficiency and are computed assuming ξ 2 × B(h → hadrons) = 1. Only events with a signal over background ratio greater than 0.05 are considered at √ s > 203 GeV, expected background and a signal with m h = 110 GeV, when all other cuts are applied.
A neural network [23] is built from the following variables: • E vis , • m mis , • sin Ψ , • the longitudinal missing momentum, • the transverse missing momentum, • the absolute value of the cosine of the angle between the two jets in the plane transverse to the beam direction, • the event thrust, • the sum of the jet opening angles after forcing the event into a three-jet configuration.
The distributions of the output of the neural network are presented in Fig. 3(c). Fig. 3(d) shows the distributions of the hadronic mass m qq , calculated with a fit which imposes m mis = m Z . These two variables are combined into a final discriminant, whose distributions are presented in Fig. 2(b) in terms of the signal over background ratio. Table 3 lists the numbers of selected events for different m h hypotheses.

Two jets and two leptons
Different signal topologies correspond to h decays into hadrons and Z decays into electrons and muons or into tau leptons. For decays into electrons and muons, the signature is a pair of well-isolated leptons with mass close to m Z and two hadronic jets. In the case of tau leptons, events with four jets are expected, where two of the jets are narrow, of low multiplicity, and of unit charge. The dominant background is due to Z-pair production followed by the hadronic decay of one Z and the decay into leptons of the other.
The event selection is identical to that used for the same final states of the Standard Model Higgs search [4]. After this selection, a kinematic fit is applied which imposes four-momentum conservation and constrains the di-lepton mass to m Z . The mass of the hadronic system after the fit is used as a discriminant to test different m h hypotheses. Its distributions in terms of the signal over background ratio are presented in Fig. 2(c). The yield of this selection is presented in Table 3.

Search for e + e − → hA
The pair-production of h and A bosons gives rise to high multiplicity events with four hadronic jets. The largest backgrounds are the pair-production of W and Z bosons which decay into hadrons and the e + e − → qq(γ ) process. High multiplicity events are selected, subjected to a kinematic fit which enforces four-momentum conservation and forced into four jets with the DURHAM algorithm. A neural network [24] is used to separate genuine four-jet events from events most likely due to fermion-pair production.
For each (m h , m A ) hypothesis, a likelihood, L hA , is built [8] to separate the signal from the background from W-and Z-pair production. It uses the following variables: • the maximum energy difference between any two jets, • the minimum jet energy, • the probabilities of kinematic fits which impose four-momentum conservation together with the hypotheses of W-or Z-pair production, • the cosine of the polar angle of the di-jet system which best fits the hA pair-production hypothesis, • the cosine of the polar angle, Θ W + , at which the positive charged 7 boson is produced for the di- jet system which best fits the W-pair production hypothesis, • y 34 , • the absolute value of the cosine of the polar angle, Θ T , of the thrust axis. Fig. 4 shows the distributions of the last three variables and of L hA for data, the expected background and the signal corresponding to the Higgs boson mass hypothesis (m h , m A ) = (60, 80) GeV. A cut on L hA is applied, which depends on √ s and on the (m h , m A ) hypothesis, typically around 0.2. The remaining events are tested for consistency with a given (m h , m A ) hypothesis by means of the variable χ 2 hA [8], defined analogously to χ 2 hZ . The pairing which minimises the value of χ 2 hA is chosen. For each event and each (m h , m A ) hypothesis, the value of the signal over background ratio of the variable χ 2 hA is calculated. The distributions of these ratios are presented in Fig. 5 for different mass hypotheses. Table 4 reports the numbers of observed events, expected background and expected signal events for several Higgs boson mass hypotheses, together with selection efficiencies. Table 3 shows the result of the combination of the different channels of the e + e − → hZ search. The observed number of events agrees with the Standard Model expectations. No significant excess is observed  either in the e + e − → hZ search or in the e + e − → hA search, which is summarised in Table 4. Limits on the ξ and η couplings are extracted as a function of m h and m A from the distributions of the signal over background ratios derived from the final discriminant variables. The log-likelihood ratio technique [7] is used for the combination of the different channels of the e + e − → hZ search and to derive all the limits. For each final state, among the three possible decays of the h and A bosons into bb, cc and gg, the case with the lowest efficiency is considered. Several sources of systematic uncertainties are investigated and their impact on the signal efficiency and the determination of the background level is assessed. The limited Monte Carlo statistics affects the signal by around 2% and the background by around 5%, depending on the final state. The selection criteria are varied within the resolution of the corresponding variables yielding an uncertainty from the selection procedure around 2% on the signal and from 3% to 6% on the background. Lepton identification criteria contribute to this source with an additional 1% for the signal and 2% for the background. The expected background level has an uncertainty up to 5%, depending on the final state, due to the uncertainty in the calculation of the cross sections of background processes.

Results
Particular care is payed to validate the accuracy of the simulation of gluon jets. A reference sample of three-jet events, from the e + e − → qqg(γ ) process, is selected and the jet with the smallest energy in the rest frame of the hadronic system is taken as the gluon jet. The distributions of the most important gluon Fig. 6. The 95% confidence level upper limit on ξ 2 × Br(h → hadrons) as a function of m h . The solid line indicates the observed limit and the dashed line stands for the median expected limit. The shaded areas show the 1σ and 2σ intervals centered on the median expected limit. The observed and expected limits on m h for ξ 2 × Br(h → hadrons) = 1 are also shown. jet characteristics such as jet broadening, boosted sphericity and charged track multiplicity are compared for data and Monte Carlo samples. The latter, for instance, is found to be on average overestimated by the simulations and is not considered as input to the likelihoods and the neural networks. From this comparison, an additional systematic uncertainty is assigned as 1.5% for the signal and 2% for the background.
The overall systematic uncertainties depend on the search channel and are estimated to range between 2% and 4% for the signal efficiencies and between 4% and 8% for the background levels. They are included in the derivation of the limits. For ξ 2 = 1 they lower the sensitivity to m h by about 0.8 GeV and for η 2 = 1 and m h = m A by about 0.7 GeV. Fig. 6 shows the 95% confidence level (CL) upper limit on ξ 2 × B(h → hadrons) as a function of m h . The expected limit and the 68.3% and 95.4% probability bands expected in the absence of a signal are also displayed and denoted as 1σ and 2σ , respectively. For ξ 2 × B(h → hadrons) = 1, i.e., for a cross section equivalent to the Standard Model one and a Higgs boson decaying into hadrons, a 95% CL lower limit of 110.3 GeV is set on m h . The expected limit is 108.7 GeV. Fig. 7 shows the 95% CL upper limit on η 2 × B(hA → hadrons) as a function of m h + m A for several values of |m h − m A |. The expected limits and the 1σ and 2σ probability bands in absence of a signal are also shown. The observed limits for η = 1 are between 120 and 140 GeV, as expected. An excess of 2.9σ is observed around 135 GeV for the m h = m A hypothesis. A similar behaviour is also observed in the search for charged Higgs bosons [26]. This excess is mainly due to data at low values of √ s. At higher energies and for larger integrated luminosities it does not scale with the cross section expected for a e + e − → hA signal. It is hence ascribed to a statistical fluctuation.
In conclusion, a flavour independent search for h and A bosons produced through Higgs-strahlung or in pairs and decaying into hadrons, shows no evidence of a signal and further constrains the scenario of Higgs bosons light enough to have been produced at LEP.