Search for Dimuon Decays of a Light Scalar Boson in Radiative Transitions Upsilon ->gamma A0

We search for evidence of a light scalar boson in the radiative decays of the Upsilon(2S) and Upsilon(3S) resonances: Upsilon(2S,3S)->gamma A0, A0 ->mu^+ mu^-. Such a particle appears in extensions of the Standard Model, where a light CP-odd Higgs boson naturally couples strongly to b-quarks. We find no evidence for such processes in the mass range 0.212<= m(A0)<= 9.3 GeV in the samples of 99*10^6 Upsilon(2S) and 122*10^6 Upsilon(3S) decays collected by the BABAR detector at the PEP-II B-factory and set stringent upper limits on the effective coupling of the b quark to the A0. We also limit the dimuon branching fraction of the eta_b meson: BR(eta_b->mu^+mu^-)<0.9% at 90% confidence level.

where a light CP-odd Higgs boson naturally couples strongly to b quarks. We find no evidence for such processes in the mass range 0:212 m A 0 9:3 GeV in the samples of 99 Â 10 6 Çð2SÞ and 122 Â 10 6 Çð3SÞ decays collected by the BABAR detector at the SLAC PEP-II B factory and set stringent upper limits on the effective coupling of the b quark to the A 0 . We also limit the dimuon branching fraction of the b meson: Bð b ! " þ " À Þ < 0:9% at 90% confidence level. DOI The concept of mass is one of the most intuitive ideas in physics since it is present in everyday human experience. Yet the fundamental nature of mass remains one of the great mysteries of science. The Higgs mechanism is a theoretically appealing way to account for the different masses of elementary particles [1]. It implies the existence of at least one new scalar particle, the Higgs boson, which is the only standard model (SM) [2] particle yet to be observed. The SM Higgs boson mass is constrained to be of Oð100-200 GeVÞ by direct searches [3] and by precision electroweak measurements [4].
A number of theoretical models extend the Higgs sector to include additional Higgs fields, some of them naturally light [5]. Similar light scalar states, e.g., axions, appear in models motivated by astrophysical observations and are typically assumed to have Higgs-like couplings [6]. Direct searches typically constrain the mass of such a light particle A 0 to be below 2m b [7], making it accessible to radiative decays of Ç resonances [8]. Model predictions for the branching fraction (BF) of Ç ! A 0 decays range from 10 À6 [6,9] to as high as 10 À4 [9]. Empirical motivation for a low-mass Higgs search comes from the HyperCP experiment [10], which observed three anomalous events in the AE þ ! p" þ " À final state. These events have been interpreted as production of a scalar boson with the mass of 214.3 MeV decaying into a pair of muons [11,12]. The large data sets available at BABAR allow us to place stringent constraints on such models.
If a light scalar A 0 exists, the pattern of its decays depends on its mass. Assuming no invisible (neutralino) decays [13], for low masses m A 0 < 2m ( the BF B "" BðA 0 ! " þ " À Þ should be sizable. Significantly above the ( threshold, A 0 ! ( þ ( À would dominate [14,15], and hadronic decays might also be significant. This Letter describes a search for a resonance in the dimuon invariant mass distribution for the fully reconstructed final state Çð2S; 3SÞ ! A 0 , A 0 ! " þ " À . We assume that the decay width of the A 0 resonance is negligibly small compared with the experimental resolution, as expected [6,16] for m A 0 sufficiently far from the mass of the b [17]. We further assume that the resonance is a scalar (or pseudoscalar) particle. While the significance of any observation would not depend on this assumption, the signal efficiency and, therefore, the BFs are computed for a spin-0 particle. In addition, following the recent discovery of the b meson [17], we look for the leptonic decay of the b through Çð2S; 3SÞ ! b , b ! " þ " À . We use Àð b Þ ¼ 10 AE 5 MeV, the range expected in most theoretical models and consistent with the BABAR results [17]. We search for two-body transitions Çð2S; 3SÞ ! A 0 , followed by decay A 0 ! " þ " À in samples of ð98:6 AE 0:9Þ Â 10 6 Çð2SÞ and ð121:8 AE 1:2Þ Â 10 6 Çð3SÞ decays collected with the BABAR detector at the PEP-II asymmetric-energy e þ e À collider at the SLAC National Accelerator Laboratory. We use a sample of 79 fb À1 accumulated on the Çð4SÞ resonance [Çð4SÞ sample] for studies of the continuum backgrounds. Since the Çð4SÞ is 3 orders of magnitude broader than the Çð2SÞ and Çð3SÞ, the BF BðÇð4SÞ ! A 0 Þ is expected to be negligible. For characterization of the background events and selection optimization, we also use a sample of 1:4 fb À1 (2:4 fb À1 ) collected 30 MeV below the Çð2SÞ [Çð3SÞ] resonance (offresonance samples). The BABAR detector is described in detail elsewhere [18,19].
We select events with exactly two oppositely charged tracks and a single energetic photon with a center-of-mass (c.m.) energy E Ã ! 0:2 GeV, while allowing additional photons with c.m. energies below 0.2 GeV to be present in the event. We assign a muon mass hypothesis to the two tracks (henceforth referred to as muon candidates) and require that at least one is positively identified as a muon [19]. We require that the muon candidates form a geometric vertex with 1 2 vtx < 20 for 1 degree of freedom and displaced transversely by at most 2 cm [20] from the nominal location of the e þ e À interaction region. We perform a kinematic fit to the Ç candidate formed from the two muon candidates and the energetic photon. The c.m. energy of the Ç candidate is constrained, within the beam energy spread, to the total beam energy ffiffi ffi s p , and the decay vertex of the Ç is constrained to the beam interaction region. We select events with À0:2 < ffiffi ffi s p À mðÇÞ < 0:6 GeV and place a requirement on the kinematic fit 1 2 Ç < 30 (for 6 degrees of freedom). We further require that the momenta of the dimuon candidate A 0 and the photon are back-to-back in the c.m. frame to within 0.07 rad and that the cosine of the angle between the muon direction and A 0 direction in the center of mass of the A 0 is less than 0.92. The selection criteria are chosen to maximize "= ffiffiffi ffi B p , where " is the average selection efficiency for a broad m A 0 range and B is the background yield in the off-resonance sample.
The criteria above select 387 546 Çð2SÞ and 724 551 Çð3SÞ events [mass spectra for Çð2SÞ and Çð3SÞ data sets are shown in Fig. 1 in [21]]. The backgrounds are dominated by two types of QED processes: ''continuum'' week ending 21 AUGUST 2009 081803-4 e þ e À ! " þ " À and the initial-state radiation (ISR) production of & 0 , 0, J=c , c ð2SÞ, and Çð1SÞ vector mesons. In order to suppress contributions from the ISR-produced & 0 ! % þ % À final state in which a pion is misidentified as a muon (probability $3%=pion), we require that both tracks are positively identified as muons when we search for A 0 candidates in the range 0:5 m A 0 < 1:05 GeV. Finally, when selecting candidate events in the b region with dimuon invariant mass m "" $ 9:39 GeV in the Çð2SÞ [Çð3SÞ] data set, we suppress the decay chain Çð2SÞ Çð1SÞ] by requiring that no secondary photon 2 above a c.m. energy of E Ã 2 ¼ 0:1 GeV (0.08 GeV) is present in the event.
We use signal Monte Carlo (MC) samples [22,23] Çð2SÞ ! A 0 and Çð3SÞ ! A 0 generated at 20 values of m A 0 over a broad range 0:212 m A 0 9:5 GeV to measure the selection efficiency for the signal events. The efficiency varies between 24% and 55%, depending on m A 0 .
We extract the yield of signal events as a function of m A 0 in the interval 0:212 m A 0 9:3 GeV by performing a series of unbinned extended maximum likelihood fits to the distribution of the reduced mass m R ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi m 2 "" À 4m 2 " q . The likelihood function contains contributions from the signal, continuum background, and, where appropriate, peaking backgrounds, as described below. For 0:212 m A 0 < 0:5 GeV, we fit over a fixed interval 0:01 < m R < 0:55 GeV; near the J=c resonance, we fit over the interval 2:7 < m R < 3:5 GeV; and near the c ð2SÞ resonance, we fit over the range 3:35 < m R < 4:1 GeV. Elsewhere, we use sliding intervals " À 0:2 < m R < " þ 0:1 GeV, where " is the mean of the signal distribution of m R . We search for A 0 in fine mass steps Ám A 0 ¼ 2-5 MeV. We sample a total of 1951 m A 0 values. For each m A 0 value, we determine the BF products B nS BðÇðnSÞ ! A 0 Þ Â B "" , where n ¼ 2; 3. Both the fitting procedure and the event selection were developed and tested using MC and Çð4SÞ samples prior to their application to the Çð2SÞ and Çð3SÞ data sets.
The signal probability density function (PDF) is described by a sum of two Crystal Ball functions [24] with tail parameters on either side of the maximum. The signal PDFs are centered around the expected values of m R and have a typical resolution of 2-10 MeV, which increases monotonically with m A 0 . We determine the PDF as a function of m A 0 using the signal MC samples, and we interpolate PDF parameters and signal efficiency values linearly between the simulated points. We determine the uncertainty in the PDF parameters by comparing the distributions of the simulated and reconstructed e þ e À ! ISR J=c , J=c ! " þ " À events. We describe the continuum background below m R < 0:23 GeV with a threshold function f bkg ðm R Þ / tanhð P 3 '¼1 p ' m ' R Þ. The parameters p ' are fixed to the values determined from the fits to the e þ e À ! " þ " À MC sample [25] and agree, within statistics, with those determined by fitting the Çð2SÞ, Çð3SÞ, and Çð4SÞ samples with the signal contribution set to zero. Elsewhere the background is well described in each limited m R range by a first-order (m R < 9:3 GeV) or a second-order (m R > 9:3 GeV) polynomial with coefficients determined by the fit.
Events due to known resonances 0, J=c , c ð2SÞ, and Çð1SÞ are present in our sample in specific m R intervals and constitute peaking backgrounds. We include these contributions in the fit where appropriate and describe the shape of the resonances using the same functional form as for the signal, a sum of two Crystal Ball functions, with parameters determined from fits to the combined Çð2SÞ and Çð3SÞ data set. The contribution to the event yield from 0 ! K þ K À , in which one of the kaons is misidentified as a muon, is fixed to 111 AE 24 [Çð2SÞ] and 198 AE 42 [Çð3SÞ]. We determine this contribution from the event yield of e þ e À ! 0, 0 ! K þ K À in a sample where both kaons are positively identified, corrected for the measured misidentification rate of kaons as muons. We do not search for A 0 candidates in the immediate vicinity of J=c and c ð2SÞ, excluding regions of AE40 MeV around J=c (% AE5') and AE25 MeV (% AE 3') around c ð2SÞ.
We compare the overall selection efficiency between the data and the MC simulation by measuring the absolute cross section d'=dm R for the radiative QED process e þ e À ! " þ " À over the broad kinematic range 0 < m R 9:6 GeV, using the off-resonance sample. We use the ratio of measured to expected [25] cross sections to correct the signal selection efficiency as a function of m A 0 . This correction ranges between 4% and 10%, with a systematic uncertainty of 5%. This uncertainty accounts for effects of selection, reconstruction (for both charged tracks and the photon), and trigger efficiencies.
We determine the uncertainty in the signal and peaking background PDFs by comparing the distributions of %4000 data and MC e þ e À ! ISR J=c , J=c ! " þ " À events. We correct for the observed difference in the width of the m R distribution (5.3 MeV in MC simulations versus 6.6 MeV in the data) and use half of the correction to estimate the systematic uncertainty on the signal yield. This is the dominant systematic uncertainty on the signal yield for m A 0 > 0:4 GeV. We estimate that the uncertainties in the tail parameters of the Crystal Ball PDF contribute less than 1% to the uncertainty in signal yield based on the observed variations in the J=c yield. The systematic uncertainties due to the fixed continuum background PDF for m R < 0:23 and the fixed contribution from e þ e À ! 0 do not exceed ' bkg ðB nS Þ ¼ 0:2 Â 10 À6 . These are the largest systematic contributions for 0:212 m A 0 < 0:4 GeV.
We test for possible bias in the fitted value of the signal yield with a large ensemble of pseudoexperiments. The bias is consistent with zero for all values of m A 0 , and we assign a BF uncertainty of ' bias ðB nS Þ ¼ 0:05 Â 10 À6 at all values of m A 0 to cover the statistical variations in the results of the test.
To estimate the significance of any positive fluctuation, we compute the likelihood ratio variable Sðm A 0 Þ ¼ sgnðN sig Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 logðL max =L 0 Þ p , where L max is the maximum likelihood value for a fit with a free signal yield centered at m A 0 , N sig is that fitted signal yield, and L 0 is the value of the likelihood for the signal yield fixed at zero. Under the null hypothesis S is expected to be normal-distributed with " ¼ 0 and ' ¼ 1 (Fig. 1) Since we do not observe a significant excess of events above the background in the range 0:212 < m A 0 9:3 GeV, we set upper limits on B 2S and B 3S . We add statistical and systematic uncertainties in quadrature. The 90% confidence level (C.L.) Bayesian upper limits, computed with a uniform prior and assuming a Gaussian likelihood function, are shown in Fig. 2 as a function of mass m A 0 . The limits vary from 0:26 Â 10 À6 to 8:3 Â 10 À6 (B 2S ) and from 0:27 Â 10 À6 to 5:5 Â 10 À6 (B 3S ).
The BFs BðÇðnSÞ ! A 0 Þ are related to the effective coupling f Ç of the bound b quark to the A 0 through [8,12,26] BðÇðnSÞ where l e or " and is the fine structure constant. The effective coupling f Ç includes the Yukawa coupling of the b quark and the m A 0 -dependent QCD and relativistic corrections to B nS [26] and the leptonic width of ÇðnSÞ [27].
To first order in S , the corrections range from 0 to 30% [26] but have comparable uncertainties [28]. The ratio of corrections for Çð2SÞ and Çð3SÞ is within 4% of unity [26] in the relevant range of m A 0 . We do not attempt to factorize these contributions but instead compute the experimentally accessible quantity f 2 Ç B "" and average Çð2SÞ and Çð3SÞ results, taking into account both correlated and uncorrelated uncertainties. The combined upper limits are shown as a function of m A 0 in Fig. 2(c) (plots with expanded mass scales in three ranges of m A 0 are available in Figs. 2-4 in [21]) and span the range ð0:44-44Þ Â 10 À6 , at 90% C.L.
q is shown in Fig. 1(c), where w nS is the statistical weight of the ÇðnSÞ data set in the average. The largest fluctuation is hSi ¼ 3:3. Our set of 1951 overlapping fit regions corresponds to % 1500 independent measurements [29]. We determine the probability to observe a fluctuation of hSi ¼ 3:3 or larger in such a sample to be at least 45%.
A fit to the b region ( Fig. 6 in [21]) includes background contributions from the ISR process e þ e À ! ISR Çð1SÞ and from the cascade decays ÇðnSÞ ! 2 1 bJ , 1 bJ ! 1 Çð1SÞ with Çð1SÞ ! " þ " À . We measure the rate of the ISR events in the Çð4SÞ data set, scale it to the Çð2SÞ and Çð3SÞ data, and fix this contribution in the fit. The rate of the cascade decays, the number of signal events, and the continuum background are free in the fits to   1 (color online). Distribution of the log-likelihood variable S with both statistical and systematic uncertainties included for a (a) Çð2SÞ fit, (b) Çð3SÞ fit, and (c) combination of Çð2SÞ and Çð3SÞ data. There are no points outside of the displayed region of S. The solid curve is the standard normal distribution.