Reconstruction of Λ hyperons
For reconstruction of Λ hyperons, the first step of the analysis is selection of pure samples of π+, π−, p and \(\bar{p}\). The charged tracks are selected on the basis of their kinematics—transverse momentum \({p}_{{\rm{T}}}=\sqrt{{p}_{{\rm{x}}}^{2}+{p}_{{\rm{y}}}^{2}}\) and pseudorapidity η ≡ −ln(tan(ϑ/2))—in which ϑ is the angle between the particle momentum and the positive direction of the proton beam (z axis), and their number of hit points inside the TPC (N hits,TPC , N max,TPC ). These charged tracks are then identified on the basis of their energy loss in the TPC gas by limiting the nσ variable, which quantifies the difference between the measured energy loss and the expected energy loss for the hypothesized particle type. The selected proton and pion candidates are then paired and the pair topology is constrained to identify Λ and \(\bar{\Lambda }\) hyperon candidates.
The full selections on Λ reconstruction are summarized in Extended Data Table 1. Six topological selection variables are defined as follows: DCA p , DCA π , distance of the closest approach of the proton or pion track to the primary vertex; DCA pair , distance of the closest approach of the proton and pion tracks; DCA Λ , distance of the closest approach of Λ candidate to the primary vertex; L dec , reconstructed decay length of the hyperon candidate; cosθ, cosine of the pointing angle θ, in which θ is measured between the reconstructed momentum and the vector connecting the primary vertex to the decay point.
Last, the \({K}_{{\rm{S}}}^{0}\) candidates are reconstructed using a similar topological method. For details, see refs. 40,58.
Λ pairs signal extraction
To extract the signal of Λ candidates, two sets of distributions are filled for each of the Λ hyperon pairs.
First, an invariant mass, M inv , distribution that includes an unlike-sign (US) pπ pair matched with a different US pπ pair from the same event is obtained. An example of this distribution for \(\Lambda \bar{\Lambda }\) pair candidates is shown in Extended Data Fig. 1. The US–US M inv distribution has three components: (1) the main peak, in which two pairs of pπ decayed from two Λ particles from the same event; (2) two ridges that correspond to a pπ pair from a Λ decay paired with a combinatorial background pair; (3) a continuum that originates from a combinatorial background pπ pair matched to a different background pπ pair.
Second, a M inv distribution is constructed by a US pπ pair and a like-sign (LS) pπ pair. The US–LS mass distribution is to estimate the two background contributions. It is then subtracted from the US–US distribution, leaving an M inv distribution containing only the Λ hyperon candidates. The subtracted M inv distribution is subsequently fitted with a 2D Gaussian function. Only pairs within ±2σ around the mean are selected for further analysis. The same selection procedure is repeated for \({K}_{{\rm{S}}}^{0}\) mesons. All of the aforementioned distributions are constructed using four distinct particles.
Only Λ and \(\bar{\Lambda }\) hyperon candidates that are at mid-rapidity (|y| < 1), with transverse momentum p T within 0.5 < p T < 5.0 GeV c−1 are selected for the analysis. The average transverse momentum ⟨p T ⟩ of the reconstructed Λ hyperons is 1.35 GeV c−1 (for \({K}_{{\rm{S}}}^{0}\) mesons, it is 1.14 GeV c−1). Further in the analysis, the selected pairs are divided into groups based on their relative kinematics (Δϕ and Δy). The numbers of selected signal hyperon pairs is summarized in Extended Data Table 2. The signal-to-background ratios (S/B) of the selected hyperon pairs do not heavily depend on this relative kinematics and are in the range \(7 < S/{B}_{\Lambda \bar{\Lambda }} < 8\) for \(\Lambda \bar{\Lambda }\) pairs and in the range 3 < S/B ΛΛ < 4 for both ΛΛ and \(\bar{\Lambda }\bar{\Lambda }\) pairs.
ME correction
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