Observation of new $\Omega_c^{0}$ states decaying to the $\Xi_c^+K^-$ final state

Two new excited states, $\Omega_c(3185)^0$ and $\Omega_c(3327)^0$, are observed in the $\Xi_c^{+}K^{-}$ invariant-mass spectrum using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9\,{\rm fb}^{-1}$. Five previously observed excited $\Omega_c^0$ states are confirmed, namely $\Omega_c(3000)^0$, $\Omega_c(3050)^0$, $\Omega_c(3065)^0$, $\Omega_c(3090)^0$, and $\Omega_c(3119)^0$. The masses and widths of these seven states are measured with the highest precision to date.

Singly charmed baryons consist of one charm quark and two lighter quarks.Due to the large mass difference between the charm quark and the lighter quarks, the singly charmed baryon mass spectrum can be described systematically in heavy quark effective theory (HQET) [1].Many excited states are expected because of the complex interplay of the three-quark system, which makes them an ideal testing ground for theories of the strong force.Studies of charmed baryon spectroscopy have the potential to reveal important insights into the fundamental nature of hadronic matter.
In 2017, the LHCb collaboration reported the observation of five new narrow Ω 0 invariant-mass sideband region, defined as [2400,2440] MeV and [2500,2540] MeV.The working points are chosen such that the BDT classifier efficiency on the signal is 75%; no fine-tuned optimization is performed to avoid favoring any particular excited state.
To improve the mass resolution, the variable m(Ξ + c K − ) is defined as the difference between the invariant mass of the Ω c (X) 0 and Ξ + c candidates, to which the known Ξ + c mass [37] is added.The Ξ + c K − invariant-mass distribution is shown in Fig. 1, where seven peaking structures are seen.Five of them have been observed in the previous analysis [2], while the Ω c (3185) 0 and Ω c (3327) 0 states are observed for the first time.There are no similar structures in the wrong-sign sample (Ξ + c K + ) or in the spectrum of Ξ + c sideband candidates combined with a kaon.
To determine the masses and widths of these Ω c (X) 0 states, an extended maximum likelihood fit with bin widths of 1 MeV is performed to the Ξ + c K − invariant-mass distributions, simultaneously to data sets 1 and 2. The Ω c (X) 0 contributions are described by S-wave relativistic Breit-Wigner functions convolved with a Gaussian resolution function whose width is determined from simulated signal samples.The combinatorial background is parameterized by an empirical function, where ∆m is the difference between the invariant mass of the Ξ + c K − candidate and the Ξ + c K − mass threshold, and a, b 1 and b 2 are free parameters.In addition, three feed-down components from partially reconstructed decays of the Ω c (3065) 0 , Ω c (3090) 0 , and Ω c (3119) 0 resonances are included.These contributions are from Ω c (X) 0 → Ξ ′+ c (→ Ξ + c γ)K − decays, where the photon is not reconstructed.Their shapes are determined from simulated samples and are fixed, while their yields are free to vary in the fit.The fit results are shown in Fig. 1 and summarized in Table 1.In addition to the five narrow states at lower invariant mass that were previously observed, two new states with masses of about 3185 MeV and 3327 MeV, denoted Ω c (3185) 0 and Ω c (3327) 0 are observed with high significance.
The enhancement around the Ξ + c K − mass threshold is described by the partially reconstructed decays of Ω c (X) 0 → Ξ ′+ c (→ Ξ + c γ)K − , as was done in the previous analysis [2].In the exclusive analysis using the feed-down components are excluded by requiring an appropriate signal mass window of the Ω − b baryon, while the threshold enhancement is still present.This enhancement was modeled as an S-wave Breit-Wigner distribution, but the available data in Ref. [4] are not sufficient to declare an observation.To check if this resonance structure is present in this analysis, the enhancement is fitted using two alternative models: a Breit-Wigner component with and without the feed down coming from the Ω c (3065) 0 contribution.The yield of the Ω c (3065) 0 feed down is constrained to be 10% of the Ω c (3065) 0 signal yield for the former.This constraint is equivalent to fixing the ratio B(Ω c (3065 1, which is chosen due to the small phase space of the Ω c (3065) 0 → Ξ ′+ c K − decay.The yields of the other feed-down contributions are free to float.Unfortunately, the shape of the Ω c (3065) 0 feed down and the additional Breit-Wigner structure are too similar to be separated in this analysis.The relative contributions from these two components cannot be determined from data, and hence this is accounted for as a systematic uncertainty.The existence of another hidden state cannot be excluded.
The mass difference between the Ω c (3185) 0 and Ω c (3327) 0 baryons is approximately the mass of the pion.It is possible that partially reconstructed candidates from the Ω c (3327) 0 decay fall into the Ω c (3185) 0 region, such as Ω c (3327 with the π 0 or γ not reconstructed.The m(Ξ + c K − ) line shapes of such contributions are obtained using the fast simulation toolkit Rapid-Sim [40].The feed-down contributions have been studied under different spin structure hypotheses, and differences from phase-space simulation were found to be negligible.The fit favors the presence of the Ω c (3327) 0 feed down with the π 0 missing.The Ω c (3327) 0 feed down strongly affects the measured mass and width of the Ω c (3185) 0 baryon, and is assigned as a systematic uncertainty.None of the models for the Ω c (3185) 0 region can be ruled out.In addition, the effects of the three-body decay Ω c (3327) 0 → Ξ + c K − π 0 are checked with a uniform phase-space model, and found to be insignificant on any of the states when assuming the ratio B(Ω c (3327 The effects of the Ξ c (3055 and Ξ c (2923/2939/2965) 0 → Ξ + c π − decays, for which the pion is misidentified as a kaon and the π 0 /γ from the Ξ c (2645) + /Ξ ′+ c decays is missing, are studied and found to be negligible.The contribution from Ω c (3327) 0 → Ξ + c K * − is kinematically suppressed.Several checks are performed to confirm the existence of the observed states and the stability of the fitted parameters.Each data set is divided into subsamples according to data-taking conditions, charge combination (Ξ + c K − or Ξ − c K + ), or different intervals of p T (K − ) and p T (Ξ + c ).In all tests, the results are consistent with the default fit.A two-peak structure also describes the data well in the mass region around 3185 MeV, hence the presence of two states in this region cannot be excluded.The bias from the fit model itself is estimated using pseudoexperiments.For each parameter, the mean differences between the fitted values and the input ones are included as systematic uncertainties.
The uncertainty related to the signal model is estimated by fitting the data with variations in the spin hypotheses and the Blatt-Weisskopf factor [41].The systematic uncertainty from the combinatorial background model is estimated by using a fourth-order Chebyshev polynomial as an alternative function.In addition, a systematic uncertainty is assigned based on the spread of results obtained by performing the fit with different bin widths.Source Some sources of systematic uncertainty only contribute to the mass measurement, including the momentum calibration for charged particles, which has a relative accuracy of 0.03% [42,43], and the energy loss due to the imperfect modeling of the detector material, which results in a 0.04 MeV uncertainty.The differences between simulation and data mainly affect the measurement of the natural width of each state.It is calculated by varying the width of the resolution function by 10% [44].Other assumptions for the Ω c (3185) 0 structure, such as the two-peak structure, additional feed-down components or a combination of the two-peak structure and one more feed-down assumption cannot be excluded, and are included in the systematic uncertainties.
The systematic uncertainties are summarized in Table 2.After considering the systematic uncertainty, the significances of the Ω c (3185) 0 and Ω c (3327) 0 states are larger than 12 σ and 10 σ, respectively.The significance for each state is determined from Wilk's theorem using the difference in log-likelihood with and without that signal component.The results of the measured mass and natural width of all seven states , shown in Table 3, are the most precise to date, and supersede those in Ref. [2].The correlations between these results and those in Ref. [4] are negligible, except for the systematic uncertainty due to the momentum calibration and energy loss, which are fully correlated.The natural widths of the Ω c (3050) 0 and Ω c (3119) 0 baryons are very close to zero; therefore upper limits on them are set at Bayesian 95% confidence level, assuming Gaussian behavior for both statistical and systematic uncertainties.
In conclusion, the Ξ + c K − invariant-mass spectrum is investigated using pp collision data collected by the LHCb experiment.With a total integrated luminosity of 9 fb −1 , we were able to select a high-purity sample of Ξ + c candidates and observe seven excited states, including two that had never been seen before: the Ω c (3185) 0 and Ω c (3327) 0 states, and also the Ω c (3119) 0 state that is not seen in the exclusive analysis using the The Ω c (3185) 0 and Ω c (3327) 0 states have masses close to the threshold of the ΞD and ΞD * final states.Referring to the lattice QCD result of Ref. [22], the Ω c (3185) 0 mass is in the predicted range for P-wave states, and the Ω c (3327) 0 mass is in the range for many possible states.While the quantum numbers of these states remain to be determined, their observations provide new information on the complex hadron spectroscopy in order to develop a deeper understanding of the strong interaction and its underlying principles.

Figure 1 :
Figure 1: Invariant-mass distribution of the Ω c (X) 0 candidates in (a) data set 1 and (b) data set 2, with the fit results overlaid.A bin width of 5 MeV is used for plotting.The previously observed excited Ω 0 c states are shown in blue dashed lines.The Ω c (3185) 0 state is shown in the brown area, and the Ω c (3327) 0 state is shown in the red area.Three feed-down components are shown as the yellow areas, while the green long-dashed line corresponds to the combinatorial background.

Table 1 :
Fit results of the mass, width, and yield for each state, and for each data set.Uncertainties are statistical only.

Table 2 :
Systematic uncertainties on the measured masses and natural widths.

Table 3 :
Measured mass and natural width for each of the seven Ω c (X) 0 states.The first uncertainty is statistical and the second is systematic, the third (mass only) arises from the uncertainty of the known Ξ + c mass.