Observation of the bottomonium ground state, , at BaBar
We present the first observation of the bottomonium ground state in the photon energy spectrum using a sample of million of events recorded at the energy with the BaBar detector at the PEP-II factory at SLAC. A peak at MeV observed with a significance of 10 standard deviations in the photon energy spectrum is interpretated as being due to the radiative transition . This photon energy corresponds to an mass of MeV/. The hyperfine - mass splitting is MeV/. The branching fraction for this radiative decay is obtained as .
Bottomonium spectroscopy started thirty years ago with the discovery of the resonances ref:Ydiscovery (). The spin-singlet states and have yet to be observed. In particular, the ground state of the bottomonium spectrum, , was still missing. The mass difference between the and the , the hyperfine splitting, is very important in understanding the role of spin-spin interaction in heavy quark bound systems and in testing calculations and predictions from various models such as Quark Models, pNRCQCD and Lattice QCD QWG-YR (). Predictions for the hyperfine splitting vary from 36 to 100 MeV/ ref:GodfreyRosner ().
We report on the observation of the bottomonium ground state from the radiative transition ref:ourPRL (). Theoritical predictions for the branching fraction of the decay vary from 1 to 20ref:GodfreyRosner (). The CLEO III experiment has published a 90 confidence level upper limit for the branching fraction ref:cleo ().
The data used in this study was recorded with the BaBar detector ref:babar () at the PEP-II asymmetric-energy storage rings. It consists of 28.0 fb of integrated luminosity collected at a CM energy of 10.355 GeV, corresponding to the mass of the resonance. Samples of 2.4 fb and 43.9 fb recorded 30 MeV below the and 40 MeV below the resonances were used for background studies. The trajectories of charged particles are reconstructed using a combination of five layers of double-sided silicon strip detectors and a 40-layer drift chamber, all operated inside the 1.5-T magnetic field of a superconducting solenoid. Photons are detected using a CsI(Tl) electromagnetic calorimeter (EMC), which is also inside the coil. The energy resolution for photons varies from 2.9% (at 600 MeV) to 2.5% (at 1400 MeV).
Ii Backgrounds and Signal Selection
The signal for is extracted from a binned maximum likelihood fit to the inclusive photon energy spectrum in the center of mass (CM) frame. The monochromatic photon from the decay will appear as a bump in the photon energy () distribution. For an mass of 9.4 GeV, and the energy, the photon energy shall peak at 911 MeV. We are therefore looking for an enhancement in the distribution near 900 MeV.
ii.1 Background contributions to the distribution
There are two main background contributions to the photon energy distribution The first contribution produces a smooth non-peaking background. It comes from continuum events ( where ) and bottomonium decays. The second contribution produces peaks in the spectrum, close to the expected signal position. It comes from two processes:
The exclusive decay . The second radiative transitions produce a broad peak centered at 760 MeV. As there are three transitions, we would expect to observe three peaks. However, due to the detector energy resolution and to the Doppler broadening, that arises from the motion of the states in the CM frame, the three peaks merge into a single broad bump.
The radiative production of the through initial state radiation (ISR): . This process produces a peak centered at 856 MeV.
In order to extract the signal, it is crucial to understand both the lineshapes and the yields of the two peaking background components.
ii.2 Signal Selection
The selection criteria have been optimized by maximazing the figure of merit , where and represent the expected yield for signal and background respectively. The signal sample is obtained from a detailed Monte Carlo (MC) simulation. There is no reliable event generator to model the various bottomonium decays. A small fraction () of the data sample (in the region GeV) was used to model the background. In order to avoid any bias, this small data set was not used for the extraction of the signal in the final fit.
As the is expected to decay mainly through two gluons, one can expect a large track multiplicity in the final state. Events are selected by requiring at least four tracks in the event and that the ratio of the second to zeroth Fox-Wolfram moments ref:fox () be less than 0.98.
Photons are first required to be isolated from all charged tracks, and their shapes are required to be consistent with an electromagnetic shower: the lateral moments ref:LAT () are required to be less than 0.55. In order to reduce the contribution from ISR events , candidate photons are required to be detected in the central region of the calorimeter , where is the angle between the photon and the beam axis in the laboratory frame.
We apply a cut on the angle between the direction of the photon momemtum and the thrust axis ref:brandt (). The thrust axis is computed with all charged tracks and neutral calorimeter clusters in the event, excluding the photon candidate. Given that the is a spin-zero resonance, the angle distribution for the signal should be flat. However, for continuum events the distribution should be peaking at the forward and backward directions. We require .
Finally we apply a veto to reduce photons coming from decays. These photons represents the main source of background. A photon candidate combined with any photons in the event is required not to have an invariant mass within 15 MeV of the nominal mass. The energy of the second photon in the candidate is required to be larger than 50 MeV.
These selection criteria lead to an efficiency of and on signal and background respectively.
The optimization procedure was checked on data using the broad peak from the second radiative transition of the process. It yielded to a very similar cut optimization.
Iii Fitting Procedure
The signal is extracted, after all selection cuts are applied, using a binned maximum likelihood fit to the inclusive photon energy spectrum in the CM frame in the range GeV.
There are four components to the fit:
iii.2 Probability density functions
The non-peaking backround has been parametrized by the following probability density function: .
As explained above, due to detector energy resolution and Doppler broadening, the three peaks from the transitions are merged. The three peaks have been modeled using a Gaussian modified with a power-law tail on the low side (Crystall Ball (CB) function ref:CB ()). The relatives rates and peak positions between the three peaks have been fixed from the PDG values ref:PDG (). For each lineshape, the parameters of the power-law tail have been fixed to a commom value. The PDF parameters have been determined from fitting non-peaking background subtracted the distribution where the signal region (840 to 960 MeV) has been excluded (see Figure 2). For the final fit, all the component parameters were fixed to the values obtained from this fit, except the yield.
The PDF for the (i.e. ISR peak) peaking background component was modeled with a CB function. All the CB parameters were obtained from MC. Given the detector energy resolution, the ISR and signal peaks are likely to overlap. Depending on the mass of the , the overlap could be large. In the final fit, it was therefore decided to fix the yield of the ISR peak. The rate of the ISR peak was estimated using data taken 40 MeV below the resonance ( Off-Peak data). The top plot of Figure 1 shows the distribution for the Off-Peak data after all cuts are applied. The bottom plot shows the same distribution after subtracting the non-peaking background. A clear ISR peak is seen. A fit with a CB functions yields to events. The yield is extrapolated to the energy using the relative cross-sections, integrated luminosities and signal reconstruction efficiencies. The estimated yield is then events. The error includes systematic uncertainties. This is consistent with but more precise than the yield estimated with data taken below the resonance.
The PDF is modeled with a non-relativistic Breit-Wigner funtion (for the natural shape of the ) convolved with a CB function which models the energy resolution. The CB paramaters were fixed from MC. MC experiments have shown that the width of the had to be fixed in the final fit. It is not known, but theoritical prediction vary from 4 to 20 MeV ref:widththeory (). We used a value of 10 MeV for the nominal fit.
iii.3 Fit to the full data sample
The final fit to the distribution was performed with the PDFs described above. The free paramaters were the process yield, the non-peaking background parameters and the signal yield. Figure 3(a) shows the distribution and the fit result. In addition to the non-peaking background, only the broad peak is visible. Figure 3(b) shows the non-peaking background subtracted plot in the signal region. The , , and signal peaks are clearly visible. Figure 3(c) shows the background subtracted distribution overlaid with the fit result for the PDF.
The fitted signal yield is events, where the first error is statistical and the second systematic. The systematic error has been obtained from varying the width (from 5 to 20 MeV), the yield within 1 of the nominal value, and the PDF parameters within 1 .
The signal significance is estimated using the ratio log, where and are the likelihood values obtained from the nominal fit and from a fit with the PDF removed, respectively. The significance the signal has been conservativaly estimated with the following method: a fit to the data has been performed with all parameters entering the systematic errors moved by 1 standard deviation in the direction of smallest significance. This method yields to a 10 standard deviations significance.
The fitted signal position is MeV. A photon energy calibration shift of MeV is then applied. It is obtained by comparing the fitted position of the peak to the PDG value. Applying the energy calibration shift, we obtain for the peak position of the signal: MeV.
This yields to the mass: MeV/. Using the PDG value of MeV/ for the mass, we determine the - mass splitting to be MeV/.
Using the signal reconstruction efficieny and the number of events, we estimate the branching fraction to be , where the first uncertainty is statistical and the second systematic. The main systematic uncertainty is from the efficiency. We have compared the reconstruction efficiency of the peak between data and MC, giving a error.
In conlusion, we have made the first observation of the bottomonium ground state, the . The new state has been observed in the radiative decay of the . The is the most likely interpretation of the signal, although other hypothesis are not excluded. The mass of the is MeV/, which corresponds to a mass splitting between the and the of MeV/. The estimated branching fraction of the decay is found to be .
Acknowledgements.The author is representing the BaBar Collaboration. We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BaBar. We thank Bob McElrath and Michael Peskin for helpful discussions. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MES (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.
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