Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions

At sufficiently high temperature and energy density, nuclear matter undergoes a transition to a phase in which quarks and gluons are not confined: the Quark-Gluon Plasma (QGP) [1]. Such an extreme state of strongly-interacting QCD (Quantum Chromo-Dynamics) matter is produced in the laboratory with high-energy collisions of heavy nuclei, where an enhanced production of strange hadrons is observed [2-6]. Strangeness enhancement, originally proposed as a signature of QGP formation in nuclear collisions [7], is more pronounced for multi-strange baryons. Several effects typical of heavy-ion phenomenology have been observed in high-multiplicity proton-proton (pp) collisions [8,9]. Yet, enhanced production of multi-strange particles has not been reported so far. Here we present the first observation of strangeness enhancement in high-multiplicity pp collisions. We find that the integrated yields of strange and multi-strange particles relative to pions increases significantly with the event charged-particle multiplicity. The measurements are in remarkable agreement with p-Pb collision results [10,11] indicating that the phenomenon is related to the final system created in the collision. In high-multiplicity events strangeness production reaches values similar to those observed in Pb-Pb collisions, where a QGP is formed.

The production of strange hadrons in high-energy hadronic interactions provides a way to investigate the properties of QCD, the theory of strongly-interacting matter.Unlike up (u) and down (d) quarks, which form ordinary matter, strange (s) quarks are not present as valence quarks in the initial state, yet they are sufficiently light to be abundantly created during the course of the collisions.In the early stages of high energy collisions, strangeness is produced in hard (perturbative) 2 → 2 partonic scattering processes by flavour creation (gg → s s, q q → s s) and flavour excitation (gs → gs, qs → qs).Strangeness is also created during the subsequent partonic evolution via gluon splittings (g → s s).These processes tend to dominate the production of high transverse momentum (p T ) strange hadrons.At low p T non perturbative processes dominate the production of strange hadrons.In string fragmentation models the production of strange hadrons is generally suppressed relative to hadrons containing only light quarks, as the strange quark is heavier than up and down quarks.The amount of strangeness suppression in elementary (e + e − and pp) collisions is an important parameter in Monte Carlo (MC) models.For this reason, measurements of strange hadron production place constraints on these models.
The abundances of strange particles relative to pions in heavy-ion collisions from top RHIC (Relativistic Heavy-Ion Collider) to LHC (Large Hadron Collider) energies do not show a significant dependence on either the initial volume (collision centrality) or the initial energy density (collision energy).With the exception of the most peripheral collisions, particle ratios are found to be compatible with those of a hadron gas in thermal and chemical equilibrium and can be described using a grand canonical statistical model [12,13].In peripheral collisions, where the overlap of the colliding nuclei becomes very small, the relative yields of strange particles to pions decrease and tend toward those observed in pp collisions, for which a statistical-mechanics approach can also be applied [14,15].Extensions of a pure grand-canonical description of particle production, like statistical models implementing strangeness canonical suppression [16] and core-corona superposition [17,18] models, can effectively produce a suppression of strangeness production in small systems.However, the microscopic origin of enhanced strangeness production is not known, and the measurements presented in this Letter may contribute to its understanding.Several effects, like azimuthal correlations and mass-dependent hardening of p T distributions, which in nuclear collisions are typically attributed to the formation of a strongly-interacting quark-gluon medium, have been observed in high-multiplicity pp and proton-nucleus collisions at the LHC [8][9][10][11][19][20][21][22][23][24][25].Yet, enhanced production of strange particles as a function of the charged-particle multiplicity density (dN ch /dη) has so far not been observed in pp collisions.The study of pp collisions at high multiplicity is thus of considerable interest as it opens the exciting possibility of a microscopic understanding of phenomena known from nuclear reactions.
In this Letter, we present the multiplicity dependence of the production of primary strange (K 0 S , Λ, Λ) and multi-strange (Ξ − , Ξ + , Ω − , Ω + ) hadrons in pp collisions at the centre-of-mass energy of √ s = 7 TeV.Primary particles are defined as all particles created in the collisions, except those coming from weak decays of light-flavour hadrons and of muons.The measurements have been performed at midrapidity 1 , |y| < 0.5, with the ALICE detector [26] at the LHC.Similar measurements of the multiplicity and centrality dependence of strange and multi-strange hadron production have been performed by ALICE in proton-lead (p-Pb) collisions at a centre-of-mass energy per nucleon pair √ s NN = 5.02 TeV [10,11] and in lead-lead (Pb-Pb) collisions at √ s NN = 2.76 TeV [6,27].The measurements reported here have been obtained in pp collisions at √ s = 7 TeV for events having at least one charged particle produced in the pseudorapidity2 interval |η| < 1 (INEL>0), corresponding to about 75% of the total inelastic crosssection.In order to study the multiplicity dependence of strange and multi-strange hadron production, the sample is divided into event classes based on the total ionisation energy deposited in the forward detectors, covering the pseudorapidity regions 2.8 < η < 5.1 and −3.7 < η < − 1.   Particle/antiparticle production yields are identical within uncertainties.The p T distributions of K 0 S , Λ + Λ, Ξ − + Ξ + and Ω − + Ω + (in the following denoted as K 0 S , Λ, Ξ and Ω) are shown in Figure 1 for a selection of event classes with progressively decreasing dN ch /dη .The mean pseudorapidity densities of primary charged particles dN ch /dη are measured at midrapidity, |η| < 0.5.The p T spectra become harder as the multiplicity increases, with the hardening being more pronounced for higher mass particles.A similar observation was reported for p-Pb collisions [10] where this and several other features common with Pb-Pb collisions are consistent with the appearance of collective behavior at high-multiplicity [8,11,[19][20][21][22][23].In heavy-ion collisions these observations are successfully described by models based on relativistic hydrodynamics.In this framework, the p T distributions are determined by particle emission from a collectively expanding thermal source [28].The blast-wave model [29] is employed to analyse the spectral shapes of K 0 S , Λ and Ξ in the common highest multiplicity class (class I).A simultaneous fit to all particles is performed following the approach discussed in [10] in the p T ranges 0-1.5, 0.6-2.9 and 0.6-2.9GeV/c, for K 0 S , Λ and Ξ, respectively.The best-fit describes the data to better than 5% in the respective fit ranges, consistent with particle production from a thermal source at temperature T fo expanding with a common transverse velocity β T .The resulting parameters, T fo = 163 ± 10 MeV and β T = 0.49 ± 0.02, are remarkably similar to the ones obtained in p-Pb collisions for an event class with comparable dN ch /dη [10].[30][31][32] and to results obtained in p-Pb and Pb-Pb collisions at the LHC [6,10,11].For Pb-Pb results the ratio 2Λ / (π + + π − ) is shown.The indicated uncertainties all represent standard deviations.
The p T -integrated yields are computed from the data in the measured ranges and using extrapolations to the unmeasured regions.In order to extrapolate to the unmeasured region, the data were fitted with a Tsallis-Lévy [10] parametrization, which gives the best description of the individual spectra for all particles and all event classes over the full p T range (Figure 1).Several other fit functions (Boltzmann, m T -exponential, p T -exponential, blast-wave, Fermi-Dirac, Bose-Einstein) are employed to estimate the corresponding systematic uncertainties.The fraction of the extrapolated yield for the highest(lowest) multiplicity event class is about 10(25)%, 16(36)%, 27(47)% for Λ, Ξ and Ω, respectively, and is negligible for K 0 S .The uncertainty on the extrapolation amounts to about 2(6)%, 3(10)%, 4(13)% of the total yield for Λ, Ξ and Ω, respectively, and it is negligible for K 0 S .The total systematic uncertainty on the p T -integrated yields amounts to 5(9)%, 7(12)%, 6(14)% and 9(18)% for K 0 S , Λ, Ξ and Ω, respectively.A significant fraction of this uncertainty is common to all multiplicity classes and it is estimated to be about 5%, 6%, 6% and 9% for K 0 S , Λ, Ξ and Ω, respectively.In Figure 2, the ratios of the yields of K 0 S , Λ, Ξ and Ω to the pion (π + + π − ) yield as a function of dN ch /dη are compared to p-Pb and Pb-Pb results at the LHC [6,10,11].A significant enhancement of strange to non-strange hadron production is observed with increasing particle multiplicity in pp collisions.The behaviour observed in pp collisions resembles that of p-Pb collisions at a slightly lower centre-of-mass energy [11], in terms of both the values of the ratios and their evolution with multiplicity.As no significant dependence on the centre-of-mass energy is observed at the LHC for inclusive inelastic collisions, the origin of strangeness production in hadronic collisions is apparently driven by the characteristics of the final state rather than by the collision system or energy.At high multiplicity, the yield ratios reach values similar to the ones observed in Pb-Pb collisions, where no significant change with multiplicity is observed beyond an initial slight rise.Note that the final-state average charged-particle density dN ch /dη , which changes by over three orders of magnitude from low-multiplicity pp to central Pb-Pb, will in general be related to different underlying physics in the various reaction systems.For example, under the assumption that the initial reaction volume in both pp and p-Pb is determined mostly by the size of the proton, dN ch /dη could be used as a proxy for the initial energy density.In Pb-Pb collisions, on the other hand, both the overlap area as well as the energy density could increase with dN ch /dη .Nonetheless, it is a non-trivial observation that particle ratios in pp and p-Pb are identical at the same dN ch /dη, representing an indication that the final-state particle density might indeed be a good scaling variable between these two systems.
Figure 3 shows that the yield ratios Λ/K 0 S = (Λ + Λ)/2K 0 S and p/π = (p + p)/(π + + π − ) do not change significantly with multiplicity, demonstrating that the observed enhanced production rates of strange hadrons with respect to pions is not due to the difference in the hadron masses.The results in Figures 2  and 3 are compared to calculations from MC models commonly used for pp collisions at the LHC: PYTHIA8 [30], EPOS LHC [31] and DIPSY [32].The kinematic domain and the multiplicity selections are the same for MC and data, namely, dividing the INEL>0 sample into event classes based on the total charged-particle multiplicity in the forward region.The observation of a multiplicity-dependent enhancement of the production of strange hadrons along with the constant production of protons relative to pions cannot be simultaneously reproduced by any of the MC models commonly used at the LHC.The model which describes the data best, DIPSY, is a model where interaction between gluonic strings is allowed to form "color ropes" which are expected to produce more strange particles and baryons.
To illustrate the evolution of the production of strange hadrons with multiplicity, Figure 4 presents the yield ratios to pions divided by the values measured in the inclusive INEL>0 pp sample, both for pp and p-Pb collisions.The observed multiplicity-dependent enhancement with respect to the INEL>0 sample follows a hierarchy determined by the hadron strangeness.We have attempted to describe the observed strangeness hierarchy by fitting the data presented in Figure 4 an the empirical function of the form where S is the number of strange or anti-strange valence quarks in the hadron, (h/π) In summary, we have presented the multiplicity dependence of the production of primary strange (K 0 S , Λ, Λ) and multi-strange (Ξ − , Ξ + , Ω − , Ω + ) hadrons in pp collisions at √ s = 7 TeV.The results are obtained as a function of dN ch /dη measured at midrapidity for event classes selected on the basis of the total charge deposited in the forward region.The p T spectra become harder as the multiplicity increases.The mass and multiplicity dependences of the spectral shapes are reminiscent of the patterns seen in p-Pb and Pb-Pb collisions at the LHC, which can be understood assuming a collective expansion of the system in the final state.The data show for the first time in pp collisions that the p T -integrated yields of strange and multi-strange particles relative to pions increase significantly with multiplicity.These particle ratios are similar to those found in p-Pb collisions at the same multiplicity densities [11].The observed enhancement increases with strangeness content rather than with mass or baryon number of the hadron.Such behaviour cannot be reproduced by any of the MC models commonly used, suggesting that further developments are needed to obtain a complete microscopic understanding of strangeness production and indicating the presence of a phenomenon novel in high-multiplicity pp collisions.The evolution of strangeness enhancement seen at the LHC steadily increases as a function of dN ch /dη from low multiplicity pp to high multiplicity p-Pb and reaches the values observed in Pb-Pb collisions.This may point towards a common underlying physics mechanism which gradually compensates the strangeness suppression in fragmentation.Further studies extending to higher multiplicity in small systems are essential, as they would demonstrate whether strangeness production saturates at the thermal equilibrium values predicted by the grand canonical statistical model [12,13] or continues to increase.The remarkable similarity of strange particle production in pp, p-Pb and Pb-Pb collisions adds to previous measurements in pp, which also exhibit characteristic features known from high-energy heavy-ion collisions [8-11, 19-23, 25] and are understood to be connected to the formation of a deconfined QCD phase at high temperature and energy density.

A Methods
A detailed description of the ALICE detector and of its performance can be found in [26,33].We briefly outline the main detectors utilized for this analysis.The V0 detectors are two scintillator hodoscopes employed for triggering, background suppression and event-class determination.They are placed on either side of the interaction region at z = 3.3 m and z = − 0.9 m, covering the pseudorapidity regions 2.8 < η < 5.1 and −3.7 < η < − 1.7, respectively.Vertex reconstruction, central-barrel tracking and charged-hadron identification are performed with the Inner Tracking System (ITS) and the Time-Projection Chamber (TPC), which are located inside a solenoidal magnet providing a 0.5 T magnetic field.The ITS is composed of six cylindrical layers of high-resolution silicon tracking detectors.The innermost layers consist of two arrays of hybrid Silicon Pixel Detectors (SPD) located at average radii 3.9 and 7.6 cm from the beam axis and covering |η| < 2.0 and |η| < 1.4, respectively.The TPC is a large cylindrical drift detector of radial and longitudinal size of about 85 < r < 250 cm and −250 < z < 250 cm, respectively.It provides charged-hadron identification information via ionisation energy loss in the fill gas.
The data were collected in 2010 using a minimum-bias trigger requiring a hit in either the V0 scintillators or in the SPD detector, in coincidence with the arrival of proton bunches from both directions.The contamination from beam-induced background is removed offline by using the timing information and correlations in the V0 and SPD detectors, as discussed in details in [33].Events used for the data analysis are further required to have a reconstructed vertex within |z| < 10 cm.Events containing more than one distinct vertex are tagged as pileup and are discarded.The remaining pileup fraction is estimated to be negligible, ranging from about 10 −4 to 10 −2 for the lowest and highest multiplicity classes, respectively.A total of about 100 million events has been utilised for the analysis.
The mean pseudorapidity densities of primary charged particles dN ch /dη are measured at midrapidity, |η| < 0.5, for each event class using the technique described in [34].The dN ch /dη values, corrected for acceptance and efficiency, as well as for contamination from secondary particles and combinatorial background, are listed in Table A.1.The relative RMS width of the corresponding multiplicity distributions ranges from 68% to 30% for the lowest and highest multiplicity classes, respectively.The corresponding fractions of the INEL>0 cross-section are also summarized in Table A.1.

Strange K 0
S , Λ and Λ and multi-strange Ξ − , Ξ + , Ω − and Ω + candidates are reconstructed via topological selection criteria and invariant-mass analysis of their characteristic weak decays [35]: Details on the analysis technique are described in [10,36,37].The results are corrected for detector acceptance and reconstruction efficiency calculated using events from the PYTHIA6 (tune Perugia 0) MC generator [38] with particle transport performed via a GEANT3 [39] simulation of the ALICE detector.The contamination to Λ (Λ) yields from weak decays of charged and neutral Ξ baryons (feed-down) is subtracted using a data-driven approach [10].The study of systematic uncertainties follows the analysis described in [10,36,37].Contributions common to all event classes (N ch -independent) are estimated and removed to determine the remaining uncertainties which are uncorrelated across different multiplicity intervals.The main sources of systematic uncertainty and their corresponding values are summarized in Table A.2.The results on pion and proton production have been obtained following the analysis method discussed in [40]. 7.

Fig. 1 :
Fig. 1: p T -differential yields of K 0 S , Λ + Λ, Ξ − + Ξ + and Ω − + Ω + measured in |y| < 0.5.The results are shown for a selection of event classes, indicated by roman numbers in brackets, with decreasing multiplicity.The error bars show the statistical uncertainty, whereas the empty boxes show the total systematic uncertainty.The data are scaled by different factors to improve the visibility.The dashed curves represent Tsallis-Lévy fits to each individual distribution to extract integrated yields.The indicated uncertainties all represent standard deviations.

Fig. 2 :
Fig.2:p T -integrated yield ratios to pions (π + + π − ) as a function of dN ch /dη measured in |y| < 0.5.The error bars show the statistical uncertainty, whereas the empty and dark-shaded boxes show the total systematic uncertainty and the contribution uncorrelated across multiplicity bins, respectively.The values are compared to calculations from MC models[30][31][32] and to results obtained in p-Pb and Pb-Pb collisions at the LHC[6,10,11].For Pb-Pb results the ratio 2Λ / (π + + π − ) is shown.The indicated uncertainties all represent standard deviations.

Fig. 3 :
Fig.3: Particle yield ratios Λ/K 0 S = (Λ + Λ)/2K 0 S and p/π = (p + p)/(π + + π − ) as a function of dN ch /dη .The yield ratios are measured in the rapidity interval |y| < 0.5.The error bars show the statistical uncertainty, whereas the empty and dark-shaded boxes show the total systematic uncertainty and the contribution uncorrelated across multiplicity bins, respectively.The values are compared to calculations from MC models[30][31][32] in pp collisions at √ s = 7 TeV and to results obtained in p-Pb collisions at the LHC[10].The indicated uncertainties all represent standard deviations.

Fig. 4 :
Fig. 4: Particle yield ratios to pions normalised to the values measured in the inclusive INEL>0 pp sample.The results are shown for pp and p-Pb collisions, both normalised to the inclusive INEL>0 pp sample.The error bars show the statistical uncertainty.The common systematic uncertainties cancel in the double-ratio.The empty boxes represent the remaining uncorrelated uncertainties.The lines represent a simultaneous fit of the results with the empirical scaling formula in Equation 1.The indicated uncertainties all represent standard deviations.
measured hadron-to-pion ratio and the charged-particle multiplicity density in INEL>0 pp collisions, respectively, and a and b are free parameters.The fit describes the data well, yielding a = 0.083 ± 0.006, b = 1.67 ± 0.09, with a χ 2 /ndf of 0.66.
. The sums of the contributions common to all event classes are listed separately as N ch -independent systematics.

Table A . 2 :
The uncertainties are the quadratic sum of statistical and systematic contributions and represent standard deviations.Main sources and values of the relative systematic uncertainties (standard deviations expressed in %) of the p T -differential yields.The values are reported for low, intermediate and high p T