Observation of an excited $\Omega^-$ baryon

Using data recorded with the Belle detector, we observe a new excited hyperon, an $\Omega^{*-}$ candidate decaying into $\Xi^0K^-$ and $\Xi^-K^0_S$ with a mass of $2012.4\pm0.7\ {\rm (stat)\pm\ 0.6\ (\rm syst)}\ {\rm MeV}/c^2$ and a width of $\Gamma=6.4^{+2.5}_{-2.0}\ {\rm(stat)}\pm1.6\ {\rm(syst)}\ {\rm MeV}$. The $\Omega^{*-}$ is seen primarily in $\Upsilon(1S), \Upsilon(2S)$, and $\Upsilon(3S)$ decays.

PACS numbers: 14.20.Jn, 13.30.Eg The Ω − comprises three strange quarks. Its excited states have proved difficult to find; the Particle Data Group (PDG) [1] lists only one of them, the Ω(2250), in its summary tables and it has a mass almost 600 MeV/c 2 higher than that of the ground state. In addition, the particle listings detail two other states for which the evidence of existence is considered to be "only fair", and they are at even higher masses. The gap in the spectrum is surprising as there are negative-parity orbital excitations of many other baryons approximately 300 MeV/c 2 above their respective ground states. A particular feature of Ω − baryons are their zero isospin which means that Ω * − → Ω − π 0 decays are highly suppressed and this restricts the possible decays of excited states, with the largest expected decay mode for low-lying states being to ΞK. Such decays are analogous to the Ω 0 c → Ξ + c K − decays recently discovered by the LHCb Collaboration [2] and confirmed soon after by Belle [3].
In this Letter, we present the results of a search for Ω * − using a data sample of e + e − annihilations recorded by the Belle detector [4] operating at the KEKB asymmetricenergy e + e − collider [5]. The analysis concentrates on data taken with the accelerator energy tuned for the production of the Υ(1S), Υ(2S), and Υ(3S) resonances, with integrated luminosities of 5.7 fb −1 , 24.9 fb −1 , and 2.9 fb −1 , respectively. The decays of these narrow resonances proceed via gluons, and it has long been known that they contain an enhanced baryon fraction compared with continuum e + e − → qq events [6][7][8].
The Belle detector was a large solid-angle spectrometer comprising six sub-detectors: the silicon vertex detector (SVD), the 50-layer central drift chamber (CDC), the aerogel cherenkov counter (ACC), the time-of-flight scintillation counter (TOF), the electromagnetic calorimeter (ECL, divided into the barrel ECL in the central region, and the forward and backward endcaps at smaller angles with respect to the beam axis), and the K 0 L and muon detector. A superconducting solenoid produces a 1.5 T magnetic field throughout the first five of these sub-detectors. The detector is described in more detail in Ref. [4]. Two inner detector configurations were used. The first comprised a 2.0 cm radius beampipe and a 3layer SVD, and the second a 1.5 cm radius beampipe and a 4-layer SVD and a small-cell inner CDC. Charged particles, π ± , K − , and p, are selected using the information from the tracking (SVD, CDC) and charged-hadron identification (CDC, ACC, TOF) systems combined into a likelihood, L(h1 : h2) = L h1 /(L h1 + L h2 ) where h 1 and h 2 are p, K, and π as appropriate. Kaon candidates are defined as those with L(K : π) > 0.9 and L(K : p) > 0.9, which is approximately 83% efficient. For protons the requirements are L(p : π) > 0.2 and L(p : K) > 0.2, while for charged pions L(π : p) > 0.2 and L(π : K) > 0.2; these requirements are approximately 99% efficient.
The π 0 candidates are reconstructed from two neutral clusters detected in the ECL, each consistent with being due to a photon and having an energy greater than 30 MeV in the laboratory frame (for those in the endcap calorimeter, the energy threshold is increased to 50 MeV).
Candidate Λ (K 0 S ) decays are made from pπ − (π + π − ) pairs with a production vertex significantly separated from the average interaction point (IP) and a reconstructed invariant mass within 3.5 (5.0) MeV/c 2 of the peak values.
Each Ξ − candidate is reconstructed by combining a Λ candidates with a π − candidate. The vertex formed from these two is required to be at least 0.35 cm from the IP, to be a shorter distance from the IP than the Λ decay vertex, and to signify a positive Ξ − flight distance. The Ξ 0 → Λπ 0 reconstruction is complicated by the fact that the π 0 has negligible vertex position information. Combinations of Λ and π 0 candidates are made, and then assuming the IP to be production point of the Ξ 0 , the sum of the Λ and π 0 momenta is taken as the momentum vector of the Ξ 0 candidate. The intersection of this trajectory with the reconstructed Λ trajectory is then found and this position is taken as the decay location of the Ξ 0 hyperon. The π 0 is then re-made from the two photons, using this location as its point of origin. The reconstructed invariant mass of the π 0 candidate must be within 10.8 MeV/c 2 of the nominal mass (approximately 94% efficient). To reduce the large combinatorial background the momentum of the π 0 candidate is required to be greater than 200 MeV/c. Combinations are retained if they have a decay location of the Ξ 0 indicating a positive Ξ 0 path length of greater than 2 cm but less than the distance between the Λ decay vertex and the IP. The refitting of the π 0 at the reconstructed Ξ 0 decay vertex improves the Ξ 0 mass resolution by around 15%.
The resultant invariant mass plots for the Ξ 0 and Ξ − candidates are shown in Fig. 1. The red vertical arrows indicate the limits of the reconstucted invariant masses of the candidates retained for further analysis, which are ±5.0 MeV/c 2 and ±3.5 MeV/c 2 around the central values of the Ξ 0 and Ξ − mass peaks, respectively, which are each approximately 95% efficient. For the Ξ 0 the value of the mass peak is 1.3155 GeV/c 2 and is higher than the PDG [1] value of 1.31486 ± 0.00020 GeV/c 2 . This difference is later used in the estimate of the systematic uncertainty of the Ω * − resonance mass measurement. The Ξ 0 and Ξ − candidates are kinematically constrained to their nominal masses [1], and then combined with K − and K 0 S candidates, respectively. The two particle combinations are kinematically constrained to come from a common vertex at the IP, and the χ 2 of this is required to be consistent with the daughters being produced by a common parent. For the Ξ 0 K − case, if there is more than one candidate with the same Λ and K − but a different π 0 , the one with the higher π 0 momentum is kept and others discarded to avoid double counting. This occurs around 3% of the time. Figure 2 shows the Ξ 0 K − and Ξ − K 0 S invariant mass distributions. Excesses are present in both distributions at around 2.01 GeV/c 2 . It should be noted that real Ξ 0 K − combinations have three units of strangeness, and are therefore highly suppressed. In contrast, Ξ − K 0 S combinations may have one unit of strangeness and thus have a larger combinatorial background.
A simultaneous fit applied to the two distributions is shown in Fig. 2 and uses fitting functions where the signal functions are Voigtian functions (Breit-Wigners convolved with a Gaussian resolution functions) and the background functions second-order Chebyshev polynomials. The masses and intrinsic widths of the two Voigtian functions are kept the same. The resolution functions are obtained from Monte Carlo (MC) events, generated using EvtGen [10] with the Belle detector response simulated using the GEANT3 [11] framework, and parameterized as Gaussian distributions with widths of 2.27 MeV/c 2 for Ξ 0 K − and 1.77 MeV/c 2 for Ξ − K 0 S . The fit is made to the binned invariant mass distributions with a large number of small bins, using the maximum-likelihood method. A convenient test of the goodness-of-fit is the χ 2 per degree of freedom (χ 2 /d.o.f.) for the distribution plotted in 2.5 MeV/c 2 bins. The signal yields, mass, instrinsic width, and χ 2 /d.o.f. resulting from this fit are listed in Table I. We calculate the statistical significance of the signal by excluding the peaks from the fit, finding the change in the log-likelihood (∆[ln(L)]) and converting this to a pvalue taking into account the change in d.o.f. This is then converted to an effective number of standard deviations, n σ , and for this simultaneous fit we find n σ = 8.3. Table I also lists results obtained from fitting to each of the two distrubutions separately. The signals in the Ξ 0 K − and Ξ − K 0 S mass distributions have significances of n σ = 6.9 and n σ = 4.4, respectively, and have statistically compatible masses and widths.
We have performed a series of checks to confirm the stability of the signal peak. Reasonable changes to the selection criteria of the daughter particles produce changes in the signal yield consistent with statistics. It would be surprising if an Ω * − were not also produced in continuum e + e − → qq events. In Fig. 3 we present mass distributions as in Fig. 2 but for the remainder of the Belle data, which comprises a total of 946 fb −1 taken mostly at the Υ(4S) energy but also in the continuum below and above this energy as well as at the Υ(5S). For the fits shown in Fig. 3 we use second-order Chebyshev background functions together with signal functions with mass and width fixed to the values found in the Υ(1S, 2S, 3S) data. Both   Table I. Taking into account the detection efficiency of the two modes, we use the results of the simultaneous fit to calculate the branching fraction ratio R = B(Ω * − →Ξ 0 K − ) B(Ω * − →Ξ −K 0 ) = 1.2 ± 0.3, where statistical uncertainties dominate. Due to isospin symmetry this ratio would be expected to be 1, but the isospin mass-splitting of the Ξ and K doublets will lead to an increase in this ratio of up to approximately 15% depending on the spin associated with decay. Thus the obtained value of R is consistent with the expectation.
The significance of the observation is largely unaffected by systematic uncertainties associated with the limited knowledge of the resolution and momentum scale of the detector. However, the use of different background functions can change the significance values. If we replace the background functions by third-order Chebyshev polynomials, the significance of the signal in the simulataneous fit is reduced to n σ = 7.2. We take this value as the signal sigificance including systematic uncertainties.
The dominant systematic uncertainty of the mass measurement is that due to the masses of the Ξ 0 and Ξ − hyperons, which enter almost directly into the calculation of the Ω * − mass. Conservatively, we take the difference between the reconstructed Ξ 0 mass and the PDG value, 0.6 MeV/c 2 . The Belle charged-particle momentum scale is very well understood, and the uncertainty in the Ω * − mass measurement due to this is much smaller than 0.6 MeV/c 2 . Similarly, changing the fit function to a relativistic Breit-Wigner has negligible effect on the mass value.
MC simulation is known to reproduce the resolution of mass peaks within 10% over a large number of different systems. The resultant systematic uncertainty in Γ from this source is (±0.37 MeV). Changing the background shapes to third-order Chebyshev polynomials changes the measured value of Γ by 1.6 MeV and this is the dominant contributor to the systematic uncertainty of the width.
The quark model [12][13][14][15], Skyrme model [16], and lattice gauge theory [17] predict a J P = 1 2 − and J P = 3 2 − pair of excited Ω − states with masses in the 2000 MeV/c 2 region. There are large discrepencies in the mass predictions, but our value is in general closer to the those for the J P = 3 2 − state. We also note that an Ω * − with J P = 3 2 − is restricted to decay to ΞK via a d-wave, whereas a state with J P = 1 2 − could decay via an s-wave. Thus the rather narrow width observed implies that the 3 2 − identification is the more likely.
We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, the National Institute of Informatics, and the Pacific Northwest National Laboratory (PNNL) Environmental Molecular Sciences Laboratory (EMSL) computing group for valuable computing and Science In-