Observation of five new narrow $\Omega_c^0$ states decaying to $\Xi_c^+ K^-$

TL;DR

This paper reports the discovery of five new narrow excited $\\Omega_c^0$ states in the $\\Xi_c^+ K^-$ mass spectrum using LHCb data, providing new insights into charmed baryon spectroscopy.

Contribution

The paper presents the first observation and measurement of five new excited $\\Omega_c^0$ states, expanding the known spectrum of charmed baryons.

Findings

Five new narrow $\\Omega_c^0$ states observed.

Masses and widths of these states measured.

Enhanced understanding of baryon spectroscopy.

Abstract

The $\Xi_c^+ K^-$ mass spectrum is studied with a sample of $pp$ collision data corresponding to an integrated luminosity of 3.3 fb$^{-1}$, collected by the LHCb experiment. The $\Xi_c^+$ is reconstructed in the decay mode $p K^- \pi^+$. Five new, narrow excited $\Omega_c^0$ states are observed: the $\Omega_c(3000)^0$, $\Omega_c(3050)^0$, $\Omega_c(3066)^0$, $\Omega_c(3090)^0$, and $\Omega_c(3119)^0$. Measurements of their masses and widths are reported.

Tables

Table 1. Table 1: Results of the fit to m ​ ( Ξ c + ​ K − ) 𝑚 subscript superscript Ξ 𝑐 superscript 𝐾 m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}) for the mass, width, yield and significance for each resonance. The subscript “ fd fd {\rm fd} ” indicates the feed-down contributions described in the text. For each fitted parameter, the first uncertainty is statistical and the second systematic. The asymmetric uncertainty on the Ω c ​ ( X ) 0 subscript Ω 𝑐 superscript 𝑋 0 {\mathchar 28938\relax}_{c}(X)^{0} arising from the Ξ c + subscript superscript Ξ 𝑐 {\mathchar 28932\relax}^{+}_{c} mass is given separately. Upper limits are also given for the resonances Ω c ​ ( 3050 ) 0 subscript Ω 𝑐 superscript 3050 0 {\mathchar 28938\relax}_{c}(3050)^{0} and Ω c ​ ( 3119 ) 0 subscript Ω 𝑐 superscript 3119 0 {\mathchar 28938\relax}_{c}(3119)^{0} for which the width is not significant.

Resonance	Mass ($\mathrm{MeV}$)	$\Gamma$ ($\mathrm{MeV}$)	Yield	$N_{\sigma }$
${\Omega }_c{\left(3000\right)}^0$	$3000.4\pm 0.2\pm {0.1}_{-0.5}^{+0.3}$	$4.5\pm 0.6\pm 0.3$	$1300\pm 100\pm 80$	20.4
${\Omega }_c{\left(3050\right)}^0$	$3050.2\pm 0.1\pm {0.1}_{-0.5}^{+0.3}$	$0.8\pm 0.2\pm 0.1$	$970\pm 60\pm 20$	20.4
		CL
${\Omega }_c{\left(3066\right)}^0$	$3065.6\pm 0.1\pm {0.3}_{-0.5}^{+0.3}$	$3.5\pm 0.4\pm 0.2$	$1740\pm 100\pm 50$	23.9
${\Omega }_c{\left(3090\right)}^0$	$3090.2\pm 0.3\pm {0.5}_{-0.5}^{+0.3}$	$8.7\pm 1.0\pm 0.8$	$2000\pm 140\pm 130$	21.1
${\Omega }_c{\left(3119\right)}^0$	$3119.1\pm 0.3\pm {0.9}_{-0.5}^{+0.3}$	$1.1\pm 0.8\pm 0.4$	$480\pm 70\pm 30$	10.4
		CL
${\Omega }_c{\left(3188\right)}^0$	$3188\pm 5\pm 13$	$60\pm 15\pm 11$	$1670\pm 450\pm 360$
${\Omega }_c{\left(3066\right)}_{\mathrm{fd}}^0$			$700\pm 40\pm 140$
${\Omega }_c{\left(3090\right)}_{\mathrm{fd}}^0$			$220\pm 60\pm 90$
${\Omega }_c{\left(3119\right)}_{\mathrm{fd}}^0$			$190\pm 70\pm 20$

Equations

$$\mathcal{L}(\mathbf{x})=\sum _{i=1}^{11}[\ln \mathrm{PD}{\mathrm{F}}_{\mathrm{sig}}(x_i)-\ln \mathrm{PD}{\mathrm{F}}_{\mathrm{back}}(x_i)],$$

$$m({\text{mathchar}28932}_c^{+}{K}^{-})=m([p{K}^{-}{\pi }^{+}{]}_{{\text{mathchar}28932}_c^{+}}{K}^{-})-m([p{K}^{-}{\pi }^{+}{]}_{{\text{mathchar}28932}_c^{+}})+m_{{\text{mathchar}28932}_c^{+}},$$

$$B(m)=\left\{\begin{array}[]{l}P(m)e^{a_{1}m+a_{2}m^{2}}\ \ \ \ {\rm for}\ m<m_{0},\\ P(m)e^{b_{0}+b_{1}m+b_{2}m^{2}}\ {\rm for}\ m>m_{0},\end{array}\right.$$

$${\text{mathchar}28938}_c(X{)}^0\to K^{-}\text{mathchar}28932{}_c^{\prime +}\text{mbox}with\text{mathchar}28932{}_c^{\prime +}\to {\text{mathchar}28932}_c^{+}\gamma ,$$

Full text

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

​​​

CERN-EP-2017-037

LHCb-PAPER-2017-002

14 March 2017

Observation of five new narrow ${{\mathchar 28938\relax}^{0}_{c}}$ states decaying to ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$

The LHCb collaboration†††Authors are listed at the end of this paper.

The ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ mass spectrum is studied with a sample of $p$ $p$ collision data corresponding to an integrated luminosity of 3.3$\mbox{\,fb}^{-1}$, collected by the LHCb experiment. The ${{\mathchar 28932\relax}^{+}_{c}}$ is reconstructed in the decay mode ${p}{{K}^{-}}{{\pi}^{+}}$. Five new, narrow excited ${{\mathchar 28938\relax}^{0}_{c}}$ states are observed: the ${\mathchar 28938\relax}_{c}(3000)^{0}$, ${\mathchar 28938\relax}_{c}(3050)^{0}$, ${\mathchar 28938\relax}_{c}(3066)^{0}$, ${\mathchar 28938\relax}_{c}(3090)^{0}$, and ${\mathchar 28938\relax}_{c}(3119)^{0}$. Measurements of their masses and widths are reported.

Published in Phys. Rev. Lett. 118 (2017) 182001

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

The spectroscopy of singly charmed baryons ${c}{q}{q}^{\prime}$ is intricate. With three quarks and numerous degrees of freedom, many states are expected. At the same time, the large mass difference between the charm quark and the light quarks provides a natural way to understand the spectrum by using the symmetries provided by Heavy Quark Effective Theory (HQET) [1, 2]. In recent years, considerable improvements have been made in the predictions of the properties of these heavy baryons [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. In many of these models, the heavy quark interacts with a $({q}{q}^{\prime})$ diquark, which is treated as a single object. These models predict seven states in the mass range $2.9$–$3.2\mathrm{\,Ge\kern-1.00006ptV}$,111Natural units are used throughout the paper. some of them narrow. Other models make use of Lattice QCD calculations [15].

The spectroscopy of charmed baryons, particularly the ${\mathchar 28931\relax}^{+}_{c}$, ${\mathchar 28934\relax}_{c}$, and ${\mathchar 28932\relax}_{c}$ states, has also seen considerable experimental progress, with results obtained at the $B$ factories and is in the physics program of the LHCb experiment at CERN [16, 17]. Among the expected charmed baryon states, this work addresses the ${{\mathchar 28938\relax}^{0}_{c}}$ baryons, which have quark content $c$ $s$ $s$ and isospin zero. Their spectrum is largely unknown: only the ${{\mathchar 28938\relax}^{0}_{c}}$ and ${\mathchar 28938\relax}_{c}(2770)^{0}$, presumed to be the $J^{P}=1/2^{+}$ and $3/2^{+}$ ground states, have been observed [16, 18].

To improve the understanding of this little-explored sector of the charmed baryon spectrum, this Letter presents a search for new ${{\mathchar 28938\relax}^{0}_{c}}$ resonances that decay strongly to the final state ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$, where the ${{\mathchar 28932\relax}^{+}_{c}}$ is a weakly decaying charmed baryon with quark content $c$ $s$ $u$.222The inclusion of charge-conjugate processes is implied throughout, unless stated otherwise. The measurement is based on samples of $p$ $p$ collision data corresponding to integrated luminosities of $1.0$, $2.0$ and $0.3\mbox{\,fb}^{-1}$ at center-of-mass energies of 7, 8 and 13$\mathrm{\,Te\kern-1.00006ptV}$, respectively, recorded by the LHCb experiment. The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range $2<\eta<5$, designed for the study of particles containing $b$ or $c$ quarks, and is described in detail in Refs. [19, 20]. Hadron identification is provided by two ring-imaging Cherenkov detectors [21], a calorimeter system, and a muon detector. The online event selection is performed by a trigger, which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction [22]. Simulated events are produced with the software packages described in Refs. [23, 24, 25, 26, 27, *Allison:2006ve, 29].

The reconstruction begins with the ${\mathchar 28932\relax}^{+}_{c}$ baryon, via the decay ${{\mathchar 28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$. The ${\mathchar 28932\relax}^{+}_{c}$ candidates are formed from combinations of three tracks that originate from a common vertex. These are required to pass a cut-based preselection and then a multivariate selection based on likelihood ratios, described below. Candidates fulfilling these requirements are then combined with a fourth track to form ${{\mathchar 28938\relax}^{0}_{c}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ candidates to which additional selection requirements, also described below, are applied.

The ${\mathchar 28932\relax}^{+}_{c}$ preselection requires a positively identified proton and a large ${\mathchar 28932\relax}^{+}_{c}$ flight-distance significance (defined as the measured flight distance divided by its uncertainty) from a primary $p$ $p$ interaction vertex (PV). The ${\mathchar 28932\relax}^{+}_{c}$ candidates are also constrained to originate from the PV by requiring a small $\chi^{2}_{\mathrm{IP}}$ (defined as the difference between the vertex-fit $\chi^{2}$ of the PV reconstructed with and without the candidate in question). The resulting ${p}{{K}^{-}}{{\pi}^{+}}$ mass spectrum is fitted with a linear function to describe the background and the sum of two Gaussian functions with a common mean to describe the signal. The fit is used to define signal and sideband regions of the ${\mathchar 28932\relax}^{+}_{c}$ invariant mass spectrum: the signal region consists of the range within $\pm 2.0\,\sigma$ of the fitted mass, where $\sigma=6.8\mathrm{\,Me\kern-1.00006ptV}$ is the weighted average of the standard deviations of the Gaussian functions, and the sidebands cover the range $3.5$–$5.5\,\sigma$ on either side. The fit is also used to determine the ${\mathchar 28932\relax}^{+}_{c}$ purity after the preselection, defined as the signal yield in the signal region divided by the total yield in the same region. A purity of 41% is obtained, which is not sufficient for the spectroscopy study, but allows the extraction of background-subtracted probability density functions (PDFs) of the kinematic and geometric properties of the signal. These distributions are taken from data rather than simulation, given the limited understanding of heavy baryon production dynamics and the difficulty of modeling them correctly for different center-of-mass energies.

For each variable of interest the background PDF is obtained from the corresponding distribution in the mass sideband regions, and is also used for the background subtraction. The signal PDF is obtained from the normalized, background-subtracted distribution in the signal mass region. Variables found to have a good discrimination between signal and background are: the vertex fit $\chi^{2}$, the ${\mathchar 28932\relax}^{+}_{c}$ flight-distance significance and $\chi^{2}_{\mathrm{IP}}$, the particle identification probability for the proton and the kaon from the ${\mathchar 28932\relax}^{+}_{c}$ decay, the $\chi^{2}_{\mathrm{IP}}$ of the three individual tracks, the ${\mathchar 28932\relax}^{+}_{c}$ transverse momentum $p_{\mathrm{T}}$ with respect to the beam axis, the pseudorapidity $\eta$, and the angle between the ${\mathchar 28932\relax}^{+}_{c}$ momentum and the vector joining the PV and the ${\mathchar 28932\relax}^{+}_{c}$ decay vertex.

The PDFs of the 11 variables (${\bf x}$) above are used to form a likelihood ratio, whose logarithm is defined as

[TABLE]

where ${\rm PDF_{sig}}$ and ${\rm PDF_{back}}$ are the PDF distributions for signal and background, respectively. Correlations between the variables are neglected in the likelihood.

The likelihood ratios and their PDFs are defined separately for the three data sets at different center-of-mass energies due to their different trigger conditions. The selection requirements on the likelihood ratios are also chosen separately for the three samples, and lead to ${\mathchar 28932\relax}^{+}_{c}$ purities of approximately 83% in the inclusive ${\mathchar 28932\relax}^{+}_{c}$ sample.

Figure 1 shows the ${p}{{K}^{-}}{{\pi}^{+}}$ mass spectrum of ${\mathchar 28932\relax}^{+}_{c}$ candidates passing the likelihood ratio selection for all three data sets combined, along with the result of a fit with the functional form described above. The ${\mathchar 28932\relax}^{+}_{c}$ signal region contains $1.05\times 10^{6}$ events. Note that this inclusive ${\mathchar 28932\relax}^{+}_{c}$ sample contains not only those produced in the decays of charmed baryon resonances but also from other sources, including decays of $b$ hadrons and direct production at the PV.

Each ${\mathchar 28932\relax}^{+}_{c}$ candidate passing the likelihood ratio selection and lying within the ${\mathchar 28932\relax}^{+}_{c}$ signal mass region is then combined in turn with each ${K}^{-}$ candidate in the event. A vertex fit is used to reconstruct each ${\mathchar 28932\relax}^{+}_{c}$ ${K}^{-}$ combination, with the constraint that it originates from the PV. The ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ candidate must have a small vertex fit $\chi^{2}$, a high kaon identification probability, and transverse momentum \mbox{p_{\mathrm{T}}}({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})>4.5\mathrm{\,Ge\kern-1.00006ptV}.

The ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ invariant mass is computed as

[TABLE]

where $m_{{\mathchar 28932\relax}^{+}_{c}}=~{}2467.89^{+0.34}_{-0.50}~{}\mathrm{\,Me\kern-1.00006ptV}$ is the world-average ${\mathchar 28932\relax}^{+}_{c}$ mass [16] and $[{p}{{K}^{-}}{{\pi}^{+}}]_{{\mathchar 28932\relax}^{+}_{c}}$ is the reconstructed ${{\mathchar 28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ candidate.

In this analysis, the distribution of the invariant mass $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$ is studied from threshold up to 3450$\mathrm{\,Me\kern-1.00006ptV}$.

The ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ mass distribution for the combined data sets is shown in Fig. 2 where five narrow structures are observed. To investigate the origin of these structures, Fig. 2 also shows the distribution of $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$ in the ${\mathchar 28932\relax}^{+}_{c}$ sidebands as a shaded (red) histogram; no structure is seen in this background sample. In addition, wrong-sign ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{+}}$ combinations are processed in the same way as the right-sign combinations. The resulting wrong-sign ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{+}}$ mass spectrum is shown in Fig. 3, scaled by a factor of 0.95 so that the two spectra approximately match at large invariant mass, along with the right-sign $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$ spectrum for comparison. No structure is observed in the wrong-sign mass spectrum. The absence of corresponding features in the control samples is consistent with the five structures being resonant states, henceforth denoted ${\mathchar 28938\relax}_{c}(X)^{0}$ for mass $X$. It can also be seen that the two mass spectra in Fig. 3 exhibit different behavior close to the ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ threshold (2960–2970$\mathrm{\,Me\kern-1.00006ptV}$). The right-sign distribution has a much steeper rise compared to the wrong-sign spectrum, suggesting the presence of additional components in the ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ mass spectrum as discussed below.

Further tests are performed by studying combinations of one of the ${{\mathchar 28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$ decay products with the other kaon used to form the ${\mathchar 28938\relax}_{c}(X)^{0}$ candidate (i.e. ${p}{{K}^{-}}$, ${{K}^{-}}{{K}^{-}}$, ${{\pi}^{+}}{{K}^{-}}$). The resulting two-body invariant mass spectra do not show any structure except for a small ${\kern 1.99997pt\overline{\kern-1.99997ptK}{}}{}^{*0}$ signal in the ${{\pi}^{+}}{{K}^{-}}$ mass, also visible in the ${\mathchar 28932\relax}^{+}_{c}$ sidebands, which is attributed to background contributions. Another class of potential misreconstruction consists of ${{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$ combinations in which the ${{\pi}^{-}}$ is misidentified as a kaon. To test for this, the selected ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ sample is investigated with the pion mass assigned to the kaon candidate. No narrow peaks are observed in this pseudo-${{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$ spectrum, indicating that peaks in the ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ spectrum do not arise from misidentified ${{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$ resonances.

The wrong-sign ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{+}}$ sample is used to study the combinatorial background. The parameterization used is [30]

[TABLE]

where $P(m)$ is a two-body phase-space factor and $m_{0}$, $a_{i}$ and $b_{i}$ are free parameters. Both $B(m)$ and its first derivative must be continuous at $m=m_{0}$; these constraints reduce the number of free parameters to four. This model gives a good description of the wrong-sign mass spectrum up to a mass of 3450$\mathrm{\,Me\kern-1.00006ptV}$ with a $p$-value of 18% for a binned $\chi^{2}$ fit.

To study the reconstruction efficiency and the mass resolution of each of the structures, samples of simulated events are generated in which ${\mathchar 28938\relax}_{c}(X)^{0}$ resonances decay to ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$, with the masses and natural widths of the ${\mathchar 28938\relax}_{c}(X)^{0}$ chosen to approximately match those seen in data. The mass residuals, defined as the difference between the generated ${\mathchar 28938\relax}_{c}(X)^{0}$ mass and the reconstructed value of $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$, are well described by the sum of two Gaussian functions with a common mean. The parameters of these fits are used to determine the mass-dependent experimental resolution, which runs from 0.75$\mathrm{\,Me\kern-1.00006ptV}$ at 3000$\mathrm{\,Me\kern-1.00006ptV}$ to 1.74$\mathrm{\,Me\kern-1.00006ptV}$ at 3119$\mathrm{\,Me\kern-1.00006ptV}$, and is found to be well described by a linear function. The simulation samples are also used to obtain the reconstruction efficiency, which is consistent with being constant as a function of $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$.

Another possible decay mode for ${\mathchar 28938\relax}_{c}(X)^{0}$ resonances is

[TABLE]

or, in general, to a final state that includes ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ but also contains one or more additional particles that are not included in the reconstruction. For the case of a narrow ${\mathchar 28938\relax}_{c}(X)^{0}$ resonance decaying via $\mathchar 28932\relax_{c}^{\prime+}$, the resulting distribution in $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$ is a relatively narrow structure that is shifted down in mass (feed-down) that needs to be taken into account in the description of the data. Simulation studies of the decay chain shown in Eq. 4 have been performed with resonance masses of 3066, 3090, and 3119$\mathrm{\,Me\kern-1.00006ptV}$. It is found that the feed-down shapes deviate from Breit-Wigner distributions and are therefore parameterized by B-splines [31].

A binned $\chi^{2}$ fit to the $m({{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}})$ spectrum is performed in the range from threshold to 3450$\mathrm{\,Me\kern-1.00006ptV}$. In this fit, the background is modeled by Eq. 3, while the resonances are described by spin-zero relativistic Breit–Wigner functions convolved with the experimental resolution. In addition, three feed-down contributions arising from the partially reconstructed decays of ${\mathchar 28938\relax}_{c}(3066)^{0}$, ${\mathchar 28938\relax}_{c}(3090)^{0}$, and ${\mathchar 28938\relax}_{c}(3119)^{0}$ resonances are included with fixed shapes but free yields. It is found that the fit improves if an additional broad Breit–Wigner function is included in the 3188$\mathrm{\,Me\kern-1.00006ptV}$ mass region. This broad structure may be due to a single resonance, to the superposition of several resonances, to feed-down from higher states, or to some combination of the above. Under the simplest hypothesis, namely that it is due to a single state, its parameters are given in Table 1.

This configuration is denoted the reference fit, and is shown in Fig. 2. No significant structure is seen above 3300$\mathrm{\,Me\kern-1.00006ptV}$. Table 1 gives the fitted parameters and yields of the resonances, along with the yields for the feed-down contributions indicated with the subscript “fd”. The statistical significance of each resonance is computed as $N_{\sigma}=\sqrt{\Delta\chi^{2}}$, where $\Delta\chi^{2}$ is the increase in $\chi^{2}$ when the resonance is excluded in the fit. Very high significances are obtained for all the narrow resonances observed in the mass spectrum. The threshold enhancement below 2970$\mathrm{\,Me\kern-1.00006ptV}$ is fully explained by feed-down from the ${\mathchar 28938\relax}_{c}(3066)^{0}$ resonance.

Several additional checks are performed to verify the presence of the signals and the stability of the fitted parameters. The likelihood ratio requirements are varied, testing both looser and tighter selections. As another test, the data are divided into subsamples according to the data-taking conditions, and each subsample is analyzed and fitted separately. The charge combinations ${{\overline{\mathchar 28932\relax}}{}_{c}^{-}}{{K}^{+}}$ and ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ are also studied separately. In all cases the fitted resonance parameters are consistent among the subsamples and with the results from the reference fit.

Systematic uncertainties on the ${\mathchar 28938\relax}^{0}_{c}$ resonance parameters are evaluated as follows. The fit bias is evaluated by generating and fitting an ensemble of 500 random mass spectra that are generated according to the reference fit. For each parameter, the absolute value of the difference between the input value and the mean fitted value of the ensemble is taken as the systematic uncertainty.

The background model uncertainty is estimated by exchanging it for the alternative function $B^{\prime}(m)=(m-m_{\rm th})^{\alpha}e^{\beta+\gamma m+\delta m^{2}}$, where $m_{\rm th}$ is the threshold mass and $\alpha,\beta,\gamma$ and $\delta$ are free parameters. The uncertainty associated with the choice of the Breit–Wigner model is estimated by fitting the data with relativistic $L=1,2$ Breit–Wigner functions with varying Blatt–Weisskopf factors [32], and is found to be negligible.

Resonances can interfere if they are close in mass and have the same spin-parity. The effect is studied by introducing interference terms between each resonance and its neighboring resonances, one pair of resonances at a time. This is implemented with an amplitude of the form $A=|c_{i}{\rm BW}_{i}+c_{j}{\rm BW}_{j}e^{i\phi}|^{2}$ for the interference between resonances $i$ and $j$, where ${\rm BW}_{i}$ and ${\rm BW}_{j}$ are complex Breit–Wigner functions and $c_{i,j}$ and $\phi$ are free parameters. For the central three resonances where interference could occur with the state to the left or to the right, the absolute values of the deviations are added in quadrature. No evidence for interference effects is observed.

Recently, the Belle collaboration has reported a measurement of the $\mathchar 28932\relax_{c}^{\prime+}$ mass [33] that is significantly more precise than the previous value, and which differs from it by +2.8$\mathrm{\,Me\kern-1.00006ptV}$. The effect of this is tested by shifting the ${\mathchar 28938\relax}_{c}(3066)^{0}$, ${\mathchar 28938\relax}_{c}(3090)^{0}$, and ${\mathchar 28938\relax}_{c}(3119)^{0}$ feed-down shapes accordingly, and it is included as a systematic uncertainty.

The mass scale uncertainty is studied with a series of control samples and is found to be 0.03% of the mass difference from threshold $(m-m_{\rm th})$. A comparison between the fitted ${\mathchar 28932\relax}^{+}_{c}$ mass resolution in data and simulation shows a 1.7% discrepancy, which is assigned as a systematic uncertainty on the width of the resonances. The description of the broad, high-mass structure labeled ${\mathchar 28938\relax}_{c}(3188)^{0}$ is changed to the sum of four incoherent Breit–Wigner functions and the effect on the other five resonances is included in the list of the systematic uncertainties. The largest contribution is found to be from possible interference, while the feed-down shift has a sizeable effect only on the ${\mathchar 28938\relax}_{c}(3000)^{0}$ parameters. For the total systematic uncertainty the individual contributions are added in quadrature. Finally, an uncertainty arises from the uncertainty on the ${{\mathchar 28932\relax}^{+}_{c}}$ mass, whose world-average value is $m({{\mathchar 28932\relax}^{+}_{c}})=2467.89^{+0.34}_{-0.50}\mathrm{\,Me\kern-1.00006ptV}$ [16]. It is quoted separately from the other uncertainties on the resonance masses, and is the dominant uncertainty on several of them.

The ${\mathchar 28938\relax}_{c}(3050)^{0}$ and ${\mathchar 28938\relax}_{c}(3119)^{0}$ resonances have very narrow widths. For these states, Table 1 also includes Bayesian 95% confidence level (CL) upper limits [16] on the widths, evaluated from the statistical and systematic uncertainties assuming Gaussian PDFs.

The observation of these ${\mathchar 28938\relax}_{c}$ states in an inclusive process through a two-body decay does not allow the determination of their quantum numbers, and therefore no attempt is made to compare the measured masses with HQET expectations. More information can be obtained from the study of possible three-body decays or when reconstructing these states in decays of heavy baryons.

In conclusion, the ${{\mathchar 28932\relax}^{+}_{c}}{{K}^{-}}$ mass spectrum is investigated using a data set corresponding to an integrated luminosity of 3.3$\mbox{\,fb}^{-1}$ collected by the LHCb experiment. A large and high-purity sample of ${\mathchar 28932\relax}^{+}_{c}$ baryons is reconstructed in the Cabibbo-suppressed decay mode ${p}{{K}^{-}}{{\pi}^{+}}$. Five new, narrow excited ${{\mathchar 28938\relax}^{0}_{c}}$ states are observed: the ${\mathchar 28938\relax}_{c}(3000)^{0}$, ${\mathchar 28938\relax}_{c}(3050)^{0}$, ${\mathchar 28938\relax}_{c}(3066)^{0}$, ${\mathchar 28938\relax}_{c}(3090)^{0}$, and ${\mathchar 28938\relax}_{c}(3119)^{0}$, and measurements of their masses and widths are reported. The data indicate also the presence of a broad structure around 3188$\mathrm{\,Me\kern-1.00006ptV}$ that is fitted as a single resonance but could be produced in other ways, for example as a superposition of several states. In addition, the partially reconstructed decay ${\mathchar 28938\relax}_{c}(3066)^{0}\rightarrow\mathchar 28932\relax_{c}^{\prime+}{{K}^{-}}$ is observed via its feed-down in the threshold region. Similarly, indications are found of ${\mathchar 28938\relax}_{c}(3090)^{0}$ and ${\mathchar 28938\relax}_{c}(3119)^{0}$ decays to $\mathchar 28932\relax_{c}^{\prime+}{{K}^{-}}$.

Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities behind the multiple open source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust (United Kingdom).