Studies of Ξ c baryons at LHCb

The LHCb detector at the Large Hadron Collider is one of the best instruments for charmed baryon spectroscopy available today. Due to its unique design and characteristics as well as stable operation of the LHC, the detector enables measurements of rare and suppressed decays with high accuracy. The report is devoted to the recent observations of the suppressed decays of the baryons Ξc+ and Ξc0 and search for CP violation in Ξc+ baryon decays that were performed by the LHCb collaboration.


Introduction
Modern studies in baryon physics are aided by various features of high precision experimental setups. Despite the fact that studies using e + e − collisions are the more clean research method, experiments on hadron colliders often provide more data. Moreover, a Lorentz boost provides an opportunity to measure lifetimes of weakly decaying particles, as well as to separate promptproduction and production in decay chains of heavier hadrons. Among the existing detectors on hadron colliders, the LHCb experiment [1] excels due to its excellent particle identification and vertex reconstruction capabilities. This opens up great possibilities for studying rare and suppressed decays, as well as performing baryon spectroscopy in general.
The LHCb detector is located at Large Hadron Collider in CERN. It is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for studies of particles containing b or c quarks. The performance values of LHCb are presented in the table 1. The LHCb experiment collected a data sample corresponding to 9.1 fb −1 of integrated luminosity in two data taking periods, named Run I (2010-12) and Run II . This review is devoted to LHCb results for charmed baryons containing both strange and charm quarks (Ξ + c , Ξ 0 c and their excited states).

2.
Observation of the doubly Cabibbo-suppressed decay Ξ + c → pϕ Rates of the different decay processes of charm baryons are governed by the elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Among the CKM matrix elements that appear in the corresponding amplitude of the quark transition, V us and V cd have smaller magnitudes than V ud and V cs . This provides a corresponding classification of decays: Cabibbo-favoured (CF), which don't contain u → s or c → d transitions; singly Cabibbo-suppressed (SCS), containing one of them; and doubly Cabibbo-suppressed (DCS), containing both.
The DCS decays are interesting because they can provide information about a role of nonspectator quark and the hierarchy of the lifetimes of charmed baryons [2]. Prior to 2019 only one DCS decay channel had been observed for the charm baryons [3,4]. Recently, the LHCb experiment discovered a DCS decay of the Ξ + c baryon into the pϕ decay channel [5]. The measurement is based on data sample of pp collisions collected in 2012 with the LHCb detector at the centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2 fb −1 . The leading order quark diagram for the Ξ + c → pϕ decay is shown in figure 1.
The branching fraction for the observed Ξ + c → pϕ DCS decay has been measured with respect to the Ξ + c → pK − π + decay channel: The pK + K − final state in a mass region of interest is selected using kinematical and particle identification requirements. The Ξ + c baryon manifests in the M pK + K − spectrum as a peak on top of a smooth background distribution for the candidates with M K + K − around ϕ meson peak (see figure 2(a)). The corresponding spectrum for M K + K − is shown on figure 2(b). The fraction of ϕ component is calculated using maximum likelihood fit of the background subtracted M K + K − spectrum. An sP lot unfolding technique is used for this purpose [6]. The fit model contains ϕ signal, parameterized with a relativistic Breit-Wigner distribution convolved with a detector resolution function and non-ϕ contribution described by a Flatte parameterization of a f 0 (980) lineshape.
The ratio of the branching fractions R ρϕ is measured to be (19.8±0.7±0.9±0.2) 10 −3 , where the first uncertainty is statistical, the second is systematic and the third due to the knowledge of the ϕ → K + K − branching fraction.

Observation of new Ξ 0
c baryons decaying to Λ + c K − The LHCb experiment is excellent for baryon spectroscopy studies. An example is the simultaneous discovery of the five new narrow excited states of the Ω 0 c baryon in the Ξ 0 c K − final state [7]. A similar analysis has recently been performed using the the Λ + c K − final state [8] in a mass region close to the Ξ c (2930) 0 baryon announced by Belle experiment [9] and Ξ c (2970) 0 reported by BaBar collaboration [10].
The analysis is performed using a data sample of pp collisions collected by the LHCb detector at the centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 5.6 fb −1 . Three peaking contribution as well as couple of additional structures on top of a smooth background distribution are visible in the mass spectrum covering 300 MeV/c 2 range above the Λ + c K − threshold (see figure 3).  A maximum likelihood fit of the mass distribution has been performed to extract masses and widths of the narrow structures, which were parameterized by an S-wave relativistic Breit-Wigner distribution convolved with the detector resolution function. Lineshapes of partially reconstructed contributions were determined from simulations. The mass resolution was estimated from simulations also, and varies from 1.7 to 2.2 MeV/c 2 in the mass range of interest. Measured parameters of resonances are presented in table 2, where the first uncertainties are statistical, second systematic and the third corresponds to the present knowledge of the Λ + c mass. Ξ c (2923) 0 142.91 ± 0.25 ± 0.20 2923.04 ± 0.25 ± 0.20 ± 0.14 7.1 ± 0.8 ± 1.8 Ξ c (2939) 0 158.45 ± 0.21 ± 0.17 2938.55 ± 0.21 ± 0.17 ± 0.14 10.2 ± 0.8 ± 1.1 Ξ c (2965) 0 184.75 ± 0.26 ± 0.14 2964.88 ± 0.26 ± 0.14 ± 0.14 14.1 ± 0.9 ± 1.3 The Ξ c (2930) 0 state observed by Belle might be interpreted as an overlap of the states Ξ c (2923) 0 and Ξ c (2939) 0 . Parameters of the observed Ξ c (2965) 0 resonance are significantly different with respect to the parameters of the previously reported Ξ c (2970) 0 state. A future investigation using additional final states will probably help to distinguish whether the Ξ c (2965) 0 and Ξ c (2970) 0 states are different baryons.  A signal interpreted as Ξ 0 c → Λ + c π − decay was observed by the Belle collaboration [11]. However, no branching fraction measurement was done for this decay channel. Recently, the LHCb collaboration provided the first measurement of the branching fraction for this decay [12].

First branching fraction measurement for the suppressed decay
A measurement this branching ratio is hampered by the lack of accurately measured Ξ 0 c branching fractions to be used for normalization. The LHCb collaboration measured two ratios where N (Q) indicates the efficiency corrected number of signal events for baryon Q, f Q indicates the fraction of particle production with respect to total c-or b-quark production. Both ratios are measured from signals of promptly produced charm baryons. Corresponding mass spectrum for Ξ 0 c is presented in the figure 5.  differences between the two Dalitz plots was performed using a binned significance method and an unbinned k-nearest neighbour method. Both methods give results that are consistent with CP symmetry in these decays.

Conclusions
Four analyses, which are presented in this review, clearly demonstrate that the LHCb detector is an excellent and stable tool for precise measurements in the charm physics sector. The experimental mass resolution for charmed baryons is on a few MeV/c 2 level, which is undoubtedly nice for new baryon states studies. The ability of precise particle identification and huge sample sizes allow to measure a branching fractions for rare decays and suppressed decays with good accuracy. Due to this high performance we can confidently expect more interesting results from LHCb in the future.