Insights on strange quark hadronization in small collision system with ALICE: multiple strange hadrons and $\Sigma^{\pm}$ baryons

Among the most iconic results of Run-1 and Run-2 of the LHC is the observation of enhanced production of (multi-)strange to non-strange particles, gradually rising from low-multiplicity to high-multiplicity pp or p--Pb collisions and reaching values close to those measured in peripheral Pb--Pb collisions. The observed behaviour cannot be quantitatively reproduced by any of the available QCD-inspired MC generators. In this contribution two extensions of this study are presented: the measurement of $\Sigma$ baryons and the first measurement of the full Probability Density Function (PDF) for $K^{0}_{S}$, $\Lambda$, $\Xi^{-}$ and $\Omega^{-}$, therefore extending the study of strangeness production beyond the average of the distribution. This novel method represents a unique opportunity to test the connection between charged and strange particle multiplicity production.


Introduction
Among several probes of the Quark-Gluon Plasma (QGP) formation, the so-called Strangeness Enhancement (SE) was one of the first proposed [2] and observed experimentally [3].In addition, to confirm the SE at the highest center-of-mass energy [4][5][6], the ALICE Collaboration carried out a comprehensive study of strange hadron production (relative to pions) as a function of the charged-particle multiplicity [1].The main finding is that strangeness enhances progressively with multiplicity, across different colliding systems and center-ofmass energies [1,7,8].The invariance of the SE pattern on the colliding system suggested that the mechanisms at play in high-multiplicity pp interactions could be the same as those involved in particle formation in Pb-Pb collisions.Moreover the increase, previously unexpected in pp interactions, is proportional to the strangeness content being the highest for the triple-strange Ω.However, the observed behaviour cannot be quantitatively reproduced by any of the available QCD-inspired models, suggesting that further developments are needed to obtain a complete microscopic understanding of strangeness production.

Σ baryon production
The measurement of the Σ hyperon production is an important addition to what shown in [1] since it has the same strangeness content of Λ but it is charged.The ALICE Collaboration investigated the Σ + → p + π 0 decay mode (branching ratio of 51.57%) in pp collisions at √ s = 13 TeV by reconstructing the π 0 → γ + γ using two independent reconstruction methods [9]: in the first one, each photon is reconstructed from conversion γ → e + e − (PCM), while in the second one, one photon is reconstructed from conversion and one is measured in the calorimeters (PCM-Calo).On the left of Fig. 1 the p T spectrum obtained for Σ + and its charge conjugate anti-particle is shown and compared with different models.EPOS LHC [12] and Pythia8 [13] are both able to reproduce the p T shape, but only EPOS LHC describes the yields satisfactorily.The Collaboration also measured for the first time the Σ production in pp collisions at √ s = 5.02 TeV reconstructing the decay into a anti-neutron (by means of the PHOton Spectrometer calorimeter [10]) and a charged pion (Σ − → π − + n, branching ratio of 99.848%).On the right of Fig. 1 the p T spectrum for Σ − obtained with this very promising new technique is shown and compared to phenomenological models.

Multiple strange hadron production
In order to extend all the above observations to the measurement of the full PDF a new technique based on counting the number of strange particles event-by-event in pp collisions at √ s = 5.02 TeV has been adopted.Signal extraction has been performed investigating a procedure based on signal/background weights obtained from the data after the application of selective cuts on topological features of the weak decay and particle identification.As a first step, a fit to the 1-dimensional invariant mass spectrum given by the sum of a function for the signal and one for the background was performed in different p T and multiplicity bins.In this way, for each invariant mass it is possible to define a probability that the candidate is signal (ratio between the value of the signal function and the total one) or background (ratio between the value of the background function and the total one).After this first step, all events are re-analysed in order to apply the procedure to all N candidates per event.Event by event, each candidate is considered, associating the probability for it to be signal or background (from previous step) which depends on the invariant mass and transverse momentum.Then, all the products of the different probabilities associated to each candidate were computed and were grouped according to the total signal yield.Consequently, it is possible to obtain that all candidates are signal, are background, or all the intermediate situations, having for each event with N candidates a full ), P(n Λ ) (P(n Λ )), P(n Ξ − ) (P(n Ξ + )) and P(n Ω − ) (P(n Ω + )) for the integrated multiplicity (0-100 %).Results obtained for particles have been reported as full points, while for the antiparticles as open ones.In both figures the lines are not fit, they connect only data points.
probability spectrum spanning from 0 to N. Summing the result obtained for each event, it was possible to measure the reconstructed spectra for each multiplicity class.To estimate the correction for the detector response, MC productions with realistic strange particle p T distributions and detector conditions have been used to perform a uni-dimensional bayesian unfolding procedure [11], leading to the corrected PDF for K 0 S , Λ, Ξ − and Ω − .Results are reported in Fig. 2, for K 0 S in several multiplicity classes (left) and for all the analyzed particles for the integrated multiplicity (right).The probability to produce more than one particle per event (e.g. 2) increases with the event charged-particle multiplicity moving from blue to red points consistently across the full PDF.This result represents a unique opportunity to test the connection between charged and strange particle multiplicity production all the way to very "extreme" situations, e.g.spanning from events with 7 K 0 S at low average multiplicity -where < dN/dη > |η|<0.5 ∼ 3, with potential large fluctuations -to events with 0 K 0 S at high multiplicity -where < dN/dη > |η|<0.5 ∼ 20.

Average probability for the production yields
From the measurement of P(n part ) it is possible to calculate the average probability < Y n−part > for the production of n particles using the Eq. 1 that contains the combinatorial factor and the probability to produce i−particles per event of a given species (the i-th bin of the PDF for the particle of interest).
In Fig. 3, the average production yield of 1, 2, 3, 4 and 5 K 0 S as a function of the charged particle multiplicity are reported on the left.The increase with multiplicity is more than linear for the production of multiple strange hadrons.Comparing the results with Pythia8 Monash [13], Pythia8 + Ropes (with QCD-Color Reconnection) [14] and EPOS LHC [12], one can see that the agreement worsens as the number of particles per event increases.S respectively in black, red, blue, orange and green, as a function of the charged particle multiplicity compared with Pythia8 Monash [13], Pythia8 + Ropes (with QCD-CR) and EPOS LHC [12] models.Right: Ratio < Y nΛ > / < Y nK 0 S > as a function of the charged particle multiplicity compared with Pythia8 Monash [13], Pythia8 + Ropes (with QCD-CR) [14] and EPOS LHC [12] models.
Moreover, the production yields of more than one particle allow to evaluate the ratio < Y nΛ > / < Y nK 0 S > as a function of the multiplicity which is a very important quantity to disentangle baryon from strangenes-related effects in the multiplicity-dependent enhancement pattern.This is reported in the right side of Fig. 3, where an increasing pattern is observed when looking at multiple strange particle production.This increasing pattern is rather well reproduced by Pythia8 + Ropes (with QCD-CR), where specific mechanisms are implemented, which lead to an effective baryon enhancement.All these observations suggest that in every strange-hadron/π [1,8] plots as a function of multiplicity the observed enhancement can be partly attributed to strangeness and partly to baryon number.

Figure 1 .
Figure 1.Left: p T spectrum obtained for Σ + and its charge conjugate anti-particle in pp collisions at √ s = 13 TeV.Right: p T spectrum obtained for Σ − in pp collisions at √ s = 5.02 TeV.

Figure 2 .
Figure 2. Le f t: The probability to produce n K 0 S per event for several multiplicity classes.Right: P(n K 0 S