Observation of Excited $\Omega_c$ Charmed Baryons in $e^+e^-$ Collisions

Using the entire Belle data sample of 980 ${\rm fb}^{-1}$ of $e^+e^-$ collisions, we present the results of a study of excited $\Omega_c$ charmed baryons in the decay mode $\Xi_c^+K^-$. We show confirmation of four of the five narrow states reported by the LHCb Collaboration: the $\Omega_c(3000)$ , $\Omega_c(3050)$, $\Omega_c(3066)$, and $\Omega_c(3090)$.

Using the entire Belle data sample of 980 fb −1 of e + e − collisions, we present the results of a study of excited Ωc charmed baryons in the decay mode Ξ + c K − . We show confirmation of four of the five narrow states reported by the LHCb Collaboration: the Ωc(3000) , Ωc(3050), Ωc(3066), and Ωc(3090).
PACS numbers: 14.20.Lq The Ω 0 c [1] charmed baryon is a combination of css quarks. Charmed baryons can be treated as a heavy (c) quark and a light (in this case ss) diquark [2][3][4]. The ground state of Ω 0 c can be considered as a spin-1 diquark in combination with the charm quark, as symmetry rules do not allow a spin-0 diquark. Thus, the ground-state Ω c , although weakly decaying, has a quark structure analagous to the Σ c and Ξ ′ c rather than Λ c and Ξ c baryons. Until recently, the only excited state of the Ω 0 c observed was the J = 3 2 + state known as the Ω * 0 c [5,6], which decays electromagnetically into the ground state. All excitations have restricted decay possibilities, because the decay Ω * 0 c → Ω 0 c π 0 would violate isospin conservation. However, provided there is sufficient mass, strong decays into Ξ cK , Ξ ′ cK , and Ξ * cK are possible. Recently, the LHCb collaboration announced the discovery of five narrow resonances in the final state Ξ + c K − [7]. In addition they showed a wide enhancement at the higher mass of 3.188 GeV/c 2 , which may comprise more than one state. Here we present the results of an analysis of the same final state using data from the Belle experiment, and confirm many of the LHCb discoveries.
This analysis uses a data sample of e + e − annihilations recorded by the Belle detector [8] operating at the KEKB asymmetric-energy e + e − collider [9]. It corresponds to an integrated luminosity of 980 fb −1 . The majority of these data were taken with the accelerator energy tuned for production of the Υ(4S) resonance, as this is optimum for investigation of B decays. However, the excited charmed baryons in this analysis are produced in continuum charm production and are of higher momentum than those that are decay products of B mesons, so the data set used in this analysis also includes the Belle data taken at beam energies corresponding to the other Υ resonances and the nearby continuum (e + e − → qq, where q ∈ {u, d, s, c}).
The Belle detector is 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, and the K 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 detail elsewhere [8]. Two inner detector configurations were used. The first comprised a 2.0 cm radius beampipe and a 3-layer silicon vertex detector, and the second a 1.5 cm radius beampipe and a 4-layer silicon detector and a small-cell inner drift chamber.
In 2016, Belle published [10] the results of an analysis of excited Ξ c states decaying into Ξ +/0 c and a photon and/or pions. To do this, seven different Ξ + c decay modes (Ξ − π + π + , ΛK − π + π + , Ξ 0 π + , Ξ 0 π + π − π + , Σ + K − π + , ΛK 0 S π + , and Σ 0 K 0 s π + ) were reconstructed. The analysis presented here uses the identical reconstruction chains and the same selection criteria to reconstruct these same ground state Ξ + c baryons. The Ξ + c candidates are made by kinematically fitting the decay daughters to a common decay vertex. The position of the interaction point (IP) is not included in this vertex, as the small decay length associated with the Ξ + c decays, though very short, is not completely negligible. The χ 2 of this vertex is required to be consistent with all the daughters having a common parent. Those combinations with a measured mass within 2 standard deviations of the nominal mass of the Ξ + c [11] are then constrained to that mass and retained for further analysis. The resolution of the Ξ + c signals depends on the decay mode and has a range of 3.2-15.0 MeV/c 2 . In Fig.1, we show the yield and signal-tonoise ratio of the reconstructed Ξ + c candidates by plotting the "pull-mass", i.e., the difference in the reconstructed mass of the candidate and the nominal mass of the Ξ + c divided by the resolution, for all the modes together. The candidates in this distribution have a requirement on the scaled momentum, where p * is the momentum of the combination in the e + e − center-of-mass frame, s is the total center-of-mass energy squared, M is the invariant mass of the combination, and c is the speed of light. This requirement is not applied as part of the final analysis as we prefer to place an x p cut requirement only on the Ξ + c K − combinations; however, it serves to display the approximate signal-to-noise ratio of our reconstructed Ξ + c baryons.
Candidates/0.02 To investigate resonances decaying into Ξ + c K − , Ξ + c candidates obtained as described above are combined with an appropriately charged kaon candidate not contributing to the reconstructed Ξ + c . The kaons used to make these combinations are identified using the same criteria as in the Ξ + c resonstruction. That is, they are selected using the likelihood information from the tracking (SVD, CDC) and charged-hadron identification (CDC, ACC, TOF) systems into a combined likelihood, L(K : h) = L K /(L K + L h ) where h is a proton or a pion, with requirements of L(K : p) > 0.6 and L(K : π) > 0.6. These requirements are approximately 93% efficient.
To optimize the mass resolution, a vertex constraint of the particles is made with the IP included. All decay modes of the Ξ + c are considered together. We then place a requirement of x p > 0.75 on the Ξ + c K − combination. This requirement is typical for studies of orbitally excited charmed baryons as they are known to be produced with much higher average momenta than the combinatorial background. Figure 2(a) shows the invariant mass distribution of the Ξ + c K − combinations in the mass range of interest, which starts at the kinematic threshold. A fit is made to this spectrum, comprising six signal functions and a background threshold function of the form A √ ∆M + B∆M , where ∆M is the mass difference from threshold, and A and B are free parameters. Each of the signal functions is a Voigtian function (a Breit-Wigner function convolved with a Gaussian resolution). The masses and intrinsic widths of all six are fixed to the values found by LHCb [7]. The resolutions are obtained from Monte Carlo simulation, and vary from 0.72 MeV/c 2 for the lowest-mass peak to 1.96 MeV/c 2 for the high-mass wide resonance. We use an unbinned likelihoood fit. Figure 2(b) shows the same distribution for wrong-sign, i.e. Ξ + c K + combinations. The background function, with floating values of A and B, fits well to this distribution. Figure 2(c) shows the same distribution using Ξ + c candidates with reconstructed masses between three and five standard deviations from the canonical mass. Again, this sideband distribution shows no significant peaks, and the background function, with floating values of A and B, fits the distribution well. Table I shows the yield for each of the five narrow resonances and the wide enhancement reported by LHCb. The significance of each signal is calculated by excluding that one peak from the fit, finding the change in the log-likelihood (∆[log(L)]), and expressing the significance in terms of standard deviation using the formula n σ = 2∆[log(L)]. Systematic uncertainties are included by calculating the signficances using a series of different fits and choosing the lowest resultant significance value. The differences in the fits considered are the use of different masses and widths within the uncertainties of the LHCb result, allowing the presence or not of an extra C∆M 2 term in the threshold function, changing the functions fitting the peaks from Voigtian functions to s-wave relativistic Breit-Wigner functions convolved with the resolution functions, and lastly adding or not extra functions representing possible feed-down from Ω c (3066), Ω c (3080) and Ω c (3119) decays to Ξ ′+ c K − as seen by LHCb, with shapes found by Monte Carlo simulation, and floating yields.
It is clear that these data unambiguously confirm the existence of the Ω c (3066) and Ω c (3090). Signals of reasonable significance are seen for the Ω c (3000) and the Ω c (3050), but no signal is apparent for the Ω c (3119). We note that, for the four narrow signals seen, we find the ratio of yields with respect to LHCb to be ≈ 0.036. If this were also to hold for the Ω c (3119), we would expect an Ω c (3119) signal yield of ≈ 17, whereas we find 3.6 ± 6.9. Thus our non-observation of this particle is not in disagreement with LHCb. There is an excess in the Belle data around 3.188 GeV/c 2 , which may (as was the case in the LHCb data) be due to one or more particles.
We can measure the masses of the five confirmed signals, by fitting the same distribution without constraining the masses. In all cases, the masses we find are consistent with the LHCb values, as shown in Table I. The systematic uncertainty in the reconstruction of these masses is smaller than the statistical uncertainties. The uncertainty due to the knowledge of the momentum scale is less than 0.05 MeV/c 2 , which is small compared with the other uncertainties. The systematic uncertainties in Table I are dominated by the variations of the measured masses when fitting with different values of the intrinsic widths as defined by the uncertainties in the LHCb measurements, and the use of different -yet reasonablebackground functions in the fit as was done when calculating the significances of the signals. In addition to the uncertainties shown in Table I, there is an important systematic uncertainty of (+0.3, −0.4) MeV/c 2 common to the Belle and LHCb mass measurements, due to the mass measurement of the ground state Ξ + c [11]. Five states, each with one unit of orbital angular momentum between the diquark and the charm quark, are naturally predicted by the heavy-quark-light-diquark model of baryons [2]. Since the LHCb observation, there have been several theoretical interpretations of the five narrow states found [12][13][14][15][16], either in terms of these five states or by other configurations of the quarks. The wide state at higher mass appears to fit the pattern of wide states at around 500 MeV/c 2 above the groundstate charmed baryons (the Λ + c (2765) and Ξ +/0 c (2970)). A possible explanation is that they are the radial excitations of the ground state, with J P = 1 2 + .
To conclude, of the five narrow resonances observed in the Ξ + c K − mass spectrum by LHCb, we strongly confirm the Ω c (3066) and Ω c (3090) with very similar parameters and confirm two more -the Ω c (3000) and Ω c (3050)with less significance, but cannot confirm the Ω c (3119). In addition, we present indications that there is wide excess, consistent with that found by LHCb, at higher mass.
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 PNNL/EMSL computing group for valuable computing and SINET5 network support.
We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau