Search for a Low-Mass Scalar Higgs Boson Decaying to a Tau Pair in Single-Photon Decays of Upsilon(1S)

We search for a low-mass scalar CP-odd Higgs boson, A0, produced in the radiative decay of the Upsilon resonance and decaying into a tau+tau- pair: Upsilon(1S)->gamma A0. The production of Upsilon(1S) mesons is tagged by Upsilon(2S)->pi+pi-Upsilon(1S) transitions, using a sample of (98.3+/-0.9) million Upsilon(2S) mesons collected by the BaBar detector. We find no evidence for a Higgs boson in the mass range 3.5 GeV<= m(A0)<=9.2 GeV, and combine these results with our previous search for the tau decays of the light Higgs in radiative Upsilon(3S) decays, setting limits on the coupling of A0 to the b/bbar quarks in the range 0.09-1.9. Our measurements improve the constraints on the parameters of the Next-to-Minimal-Supersymmetric Standard Model and similar theories with low-mass scalar degrees of freedom.

We search for a low-mass scalar CP-odd Higgs boson, A 0 , produced in the radiative decay of the Upsilon resonance and decaying into a τ + τ − pair: Υ (1S) → γA 0 . The production of Υ (1S) mesons is tagged by Υ (2S) → π + π − Υ (1S) transitions, using a sample of (98.3 ± 0.9) × 10 6 Υ (2S) mesons collected by the BABAR detector. We find no evidence for a Higgs boson in the mass range 3.5 GeV ≤ m A 0 ≤ 9.2 GeV, and combine these results with our previous search for the tau decays of the light Higgs in radiative Υ (3S) decays, setting limits on the coupling of A 0 to the bb quarks in the range 0.09 − 1.9. Our measurements improve the constraints on the parameters of the Nextto-Minimal-Supersymmetric Standard Model and similar theories with low-mass scalar degrees of freedom. The Higgs boson is a scalar elementary particle predicted by the Higgs mechanism [1] which attempts to explain the origin of mass of the elementary particles within the Standard Model (SM) [2]. Present experimental evidence suggests a Higgs-like state with the mass of ≈ 126 GeV [3]. However, low-mass Higgs states with masses of O(10 GeV) appear in several extensions to the SM [4], such as the Next-to-Minimal Supersymmetric Standard Model (NMSSM) [5]. The NMSSM adds a singlet superfield to the Minimal Supersymmetric Standard Model, solving the so-called naturalness problem. The NMSSM contains two charged Higgs bosons, three neutral CP -even bosons, and two CP -odd bosons. The lightest CP -odd state, A 0 , could have a mass below the bb production threshold, avoiding detection at LEP [4]. Such a particle could be produced in radiative Υ → γA 0 decays [6] with a branching fraction as large as 10 −4 for the narrow states Υ (nS) (where n ≤ 3), depending on the A 0 mass and couplings [5], making it accessible at B-Factories. Thus, constraining the low-mass NMSSM Higgs sector is important for understanding the recent LHC discovery [7].
The Υ (1S) resonance is produced from the Υ (2S) resonance with the emission of two charged pions. The reaction chain is e + e − → Υ (2S) → π + π − Υ (1S), Υ (1S) → γA 0 , A 0 → τ + τ − . We identify the Υ (1S) by the dipion transition; the production and decay of the Higgs candidates are identified by the photon and the two charged tracks from one-prong decays of the two tau leptons.
This analysis is based on a sample of (98.3 ± 0.9) × 10 6 Υ (2S) decays collected at the Υ (2S) resonance with the BABAR detector [13] at the PEP-II asymmetric-energy e + e − collider at the SLAC National Accelerator Laboratory. This sample corresponds to an integrated luminosity of 14 fb −1 . We also use a sample of 28 fb −1 taken at the Υ (3S) resonance for studies of the QED (continuum) backgrounds and the optimization of the selection of the Υ (2S) dipion transition candidates. Υ (3S) decays are rejected by the analysis selection criteria due to their different kinematics distributions compared with the Υ (2S) decays, and therefore the Υ (3S) events form a pure high-statistics continuum QED sample. An additional dataset of 1.4 fb −1 taken at a center-of-mass (CM) energy 30 MeV below the Υ (2S) mass is used for studies of systematic effects. We use Monte Carlo (MC) simulated samples of signal and Υ (1S) background events [14,15] to tune the selection of the Higgs events. The tau-lepton branching fractions are fixed to the values of Ref. [16]. The BABAR detector, including the Instrumented Flux Return, the electromagnetic calorimeter, and the tracking and particle identification (PID) systems, is described in detail elsewhere [13,17].
A signal candidate consists of a photon plus four charged tracks: π + π − from the Υ (2S) → π + π − Υ (1S) transition, and the one-prong decays of the two tau leptons. The event may contain as many as 19 additional photons with laboratory energy greater than 30 MeV, mostly from beam-induced backgrounds, but no additional charged tracks. Additional signal candidates may be formed using these extra photons, but a single final candidate per event is selected, as described below.
We select events where at least one tau lepton decays leptonically, resulting in five different combinations of tau lepton daughters: ee, eµ, eπ, µµ, µπ. Events in which both tau leptons decay hadronically suffer from significantly larger and poorly modeled backgrounds than the leptonic channels, and are therefore excluded. The tau lepton daughters are identified using multivariate discriminants based on the information from all subdetectors. Typical PID efficiencies are 98% (e), 90% (µ), and 97% (π), while the typical pion misidentification rates are less than 0.5% (e) and 5% (µ). Requirements on the electromagnetic shower shapes of the primary photon candidates are also imposed to improve the signal purity, and events with π 0 candidates, formed from pairs of photons with invariant mass satisfying 100 < m γγ < 160 MeV and laboratory energy above 200 MeV, are discarded.
In order to achieve a balanced selection efficiency that does not depend strongly on the reconstructed Higgs mass m A 0 (or photon energy), we optimize the selection in two Higgs mass intervals: 3.6 ≤ m A 0 ≤ 8.0 GeV (L range) and 8.0 < m A 0 ≤ 9.2 GeV (H range). The choice of the mass ranges is motivated by the rapidly varying signal-to-background ratio at low photon energies (which correspond to higher m A 0 for the signal), and differences in kinematics for each photon energy range. The masses of the Υ (1S) and A 0 candidates are calculated from two primary kinematic variables: Here m recoil is the recoil mass of the dipion system (which peaks at the value of the Υ (1S) mass for signal), m 2 X is the mass recoiling against the signal photon in the Υ (1S) frame (which peaks near the square of the expected Higgs mass, m 2 A 0 , and is linear in the photon energy), and P denotes the four-momentum.
In order to reject backgrounds, we train two multilayer perceptron neural networks (NN) [18]: a pion discriminant (N π ), which describes the kinematics of the process Υ (2S) → π + π − Υ (1S), and a tau discriminant (N τ ) describing the transition Υ (1S) → γA 0 , A 0 → τ + τ − . Each NN uses kinematic variables only weakly correlated to m 2 X or m recoil . The two discriminants are uncorrelated. The pion discriminant N π combines nine kinematic variables specific to the dipion system [10,19]. The discriminant N τ is a combination of 14 variables: the missing energy and the cosine of the polar angle of the missing momentum in the event; the extra calorimeter energy in the lab frame and the energy of the second most energetic photon in the CM frame; the net transverse momentum of the reconstructed signal candidate particles; the acoplanarity of the photon relative to the plane formed by the two tau decay prongs; the momentum and polar angle in the CM frame of the most energetic tau decay prong; the invariant mass, vertex probability, and the distance between the vertex and the e + e − interaction region of the two tau decay prongs; the angle between the signal photon and the most energetic tau decay prong in the event. The discriminants are trained using signal MC events Υ (1S) → γA 0 in the range 4.0 ≤ m A 0 ≤ 9.2 GeV. The background samples for training are taken from the continuum sample for the pion discriminant and from the simulated generic Υ (1S) decays for the tau discriminant.
Each NN outputs a value N close to +1 for signal and to −1 for background. Based on the NN outputs, the selection criteria for N π and N τ are chosen to optimize ε/(1.5+ √ B) [20], where ε is the signal efficiency, and B is the expected background yield. We accept signal candidates if N τ is above a threshold value chosen individually for each final state and mass range. The thresholds for N π are the same for all final states, but different for the two mass ranges. The typical signal efficiency and back-ground rejection estimated from the corresponding MC samples are listed in Table I. Due to reconstruction ambiguities, in particular extra photon candidates in the event and a large µ-asπ misidentification rate, a fraction of signal and background events have more than a single reconstructed candidate. The multiplicity of candidates per event is on average 1.8 for the simulated signal samples, 1.6 for the generic Υ (2S) decays, 1.3 for the continuum sample, and 1.5 for the data. We select a single candidate based on (1) the highest value of N π , then, if multiple candidates still remain, (2) the highest value of N τ , and finally, (3) the tau decay final state with the highest signal/background ratio.
We further suppress the continuum background by applying a cut on the mass recoiling against the dipion system m recoil : where m recoil is the expected location of the Υ (1S) peak, determined by the mass difference between the Υ (2S) and Υ (1S) mesons [21]. The final signal selection efficiency varies between 1% and 4.5% (Fig. 1), and is lowest at the highest masses (lowest photon energy). We extract the yield of signal events as a function of m A 0 in the interval 3.6 ≤ m A 0 ≤ 9.2 GeV by performing a series of maximum likelihood fits in steps of m A 0 . We perform one-dimensional unbinned extended maximum likelihood (ML) fits to the distribution of m 2 X in the intervals 12 ≤ m 2 X ≤ 72 GeV 2 (L range) and 49 ≤ m 2 X ≤ 89 GeV 2 (H range).The fit intervals overlap to provide sufficient sidebands for all values of m A 0 . The likelihood contains contributions from signal, which is expected to peak near the Higgs mass squared, and from the smooth background function, arising from continuum and radiative leptonic Υ (1S) backgrounds. We search for the A 0 in varying mass steps that correspond to approximately half of the expected resolution on m A 0 , as described below. A total of 201 mass points are sampled.
We use signal MC samples Υ (2S) → π + π − Υ (1S), Υ (1S) → γA 0 generated at nine (seven) different values of m A 0 in the L (H) mass range to determine the signal probability density functions (PDFs) in m 2 X and selection efficiencies. We interpolate these distributions and efficiencies between fixed m A 0 points, correcting for known small differences between data and MC simulations. The signal PDFs only include events in which the simulated signal photon, π + π − tracks, and the tracks from the decay of the tau leptons are correctly reconstructed. The signal efficiency, however, includes contributions from events in which one of the final-state particles may be misreconstructed. The signal PDF is modeled as a Crystal Ball function [22]. We parameterize the background PDFs as where z ≡ m 2 X , C n (z) is an nth-order Chebyshev polynomial (with different parameters for each mass range), α and β are threshold parameters, and z min = 12.5 GeV 2 and z max = 88.9 GeV 2 are determined by the kinematic end points of the photon energy spectrum in the luminosity-weighted mixture of simulated generic Υ (1S) decays and continuum sample. A common background PDF describes all five decay channels adequately well. Parameters of the Chebyshev polynomials C n (z) and the threshold parameters α and β are determined from a fit to the data distribution of m 2 X with the signal yield fixed to zero. This accounts for uncertainties in the modeling of the radiative Υ (1S) decays and additional backgrounds that may not be well described by the continuum sample, such as two-photon events with low photon energy (high m 2 X ). For each m A 0 hypothesis, we determine two parameters: the background yield N bkg and the signal yield N sig . In the H range, we also allow the two coefficients of C 2 (z) and the parameter β to vary in the fit. The fit is performed simultaneously over the distributions in each τ + τ − decay channel, taking advantage of the difference in the signal-to-background ratios over the decay channels. The fraction of events in each channel is fixed from MC samples for signal, and from the luminosityweighted mixture of simulated generic Υ (1S) decays and continuum sample for the background.
Each fixed nuisance parameter in the fit is varied according to its uncertainty; correlations between parameters are taken into account. The systematic uncertainties for this measurement can be divided into two categories: • Additive errors: uncertainties on the event yield, which do not scale with the number of reconstructed signal events. These include uncertainties of the parameters fixed in the fit (PDF shape parameters for signal and backgrounds) and a small bias in the ML fit. These uncertainties reduce the significance of any observed signal [23].
• Multiplicative errors: uncertainties that scale with the number of reconstructed signal events. These include uncertainties on the reconstruction efficiency, the ML fit bias which scales with the true number of signal events, the uncertainty in the number of produced Υ (2S) mesons, and the uncertainty in the branching fraction of Υ (2S) → π + π − Υ (1S).
We compute the average bias of the ML fit for a set of generated N sig values using a large ensemble of simulated pseudo-experiments. In each pseudo-experiment, the signal events are fully simulated, and the background events are sampled from their PDFs. We determine the fit bias that is independent of N sig and is part of the additive uncertainties, as well as the bias which scales linearly with N sig , and can be thought of as a "fit inefficiency", i.e. a relative correction to the signal reconstruction efficiency. The bias arises from imperfections in modeling of the signal PDFs, from events in which signal candidates are misreconstructed, and from low-statistics properties of the ML estimators. We see that a correction of 3.1 ± 1.1% (L range) and 7.6 ± 1.4% (H range) has to be applied. The additive parts of the fit bias are small.
• Photon selection efficiency. A correction of 0.967 ± 0.017 is determined from a high-statistics e + e − → γγ sample in which one of the photons converts in the inner detector material to produce a detectable e + e − pair [10].
• Neural Network selection efficiency. We evaluate the systematic uncertainty due to possible data/MC differences in the distributions of the NN discriminant N τ using an inclusive background sample. We select signal-like events that pass the requirement N τ > 0 and compute the ratio of partial selection efficiencies for the actual N τ thresholds for the data and the background. These ratios are 1.038 ± 0.013 (L range) and 0.991 ± 0.014 (H range).
The total correction to the efficiency is a product of all corrections discussed above: We compute the statistical significance of a particular fit centered at m A 0 as S = 2 log(L max /L 0 ), where L max is the maximum likelihood value for a fit with a free signal yield, and L 0 is the value of the likelihood for N sig = 0. Including additive systematic uncertainties, the most significant upward fluctuations occur at m A 0 = 6.36 GeV with S = 2.7σ (Fig. 2a) and m A 0 = 8.93 GeV with S = 3.0σ (Fig. 2b). Fluctuations of +3σ or higher occur in 7.5% of pseudo-experiments that simulate a scan of 201 mass points with an average correlation of 94.5% between adjacent points, as observed in our dataset. Therefore, we conclude that no significant A 0 signal is found.
Since we do not observe a significant excess of events above the background, we set 90% confidence level (C.L.) Bayesian upper limits on the product B(Υ (1S) → γA 0 )× B(A 0 → τ + τ − ), computed with a uniform prior for N sig > 0. The limits are shown in Fig. 3. Systematic uncertainties on N sig and ε data are included assuming their likelihood profiles are Gaussian [23].
We combine our results with the previous limits on the branching ratios B(Υ (3S) → γA 0 ) × B(A 0 → τ + τ − ) [9] to set a limit on the Yukawa coupling g 2 b of the b-quark to the A 0 . The branching fractions B(Υ (nS) → γA 0 ) are related to g b through [6,24,25]: where l ≡ e or µ, α is the fine structure constant computed at the scale m Υ (nS) , G F is the Fermi constant, and F QCD includes the m A 0 -dependent QCD and relativistic corrections to B(Υ (nS) → γA 0 ) [25] and the leptonic width of Υ (nS) [26]. To first order in α S , the corrections range from 0 to 30% [25] and may have large uncertainties [27].
We combine our data on Υ (1S) → γA 0 with the BABAR results of Ref. [9] using the full likelihood functions for g 2 b at each m A 0 point from this analysis, and a Gaussian approximation for the g 2 b likelihood from Ref. [9]. The combined upper limits on the product g 2 b × B(A 0 → τ + τ − ) b × B(A 0 → τ + τ − ). Shown are combined BABAR results (red solid line), results from this analysis only (dashed green line), the previous BABAR measurement [9] (dotted blue line), and results from the CLEO experiment [12] (dot-dashed black line). The shaded vertical bar shows the region around χ b (2P ) mass excluded from Ref. [9].
In summary, we find no evidence for the radiative decays Υ (1S) → γA 0 in which A 0 decays into a pair of tau leptons, and we set 90% C.L. upper limits on the product of branching fractions B(Υ (1S) → γA 0 ) × B(A 0 →