K$^{0}_{\rm S}$- and (anti-)$\Lambda$-hadron correlations in pp collisions at $\sqrt{s} = 13$ TeV

Two-particle azimuthal correlations are measured with the ALICE apparatus in pp collisions at $\sqrt{s} = 13$ TeV to explore strangeness- and multiplicity-related effects in the fragmentation of jets and the transition regime between bulk and hard production, probed with the condition that a strange meson (K$^{0}_{\rm S}$) or baryon ($\Lambda$) with transverse momentum $p_{\rm T}>3$ GeV/c is produced. Azimuthal correlations between kaons or $\Lambda$ hyperons with other hadrons are presented at midrapidity for a broad range of the trigger ($3<p_{\rm T}^{\rm trigg}<20$ GeV/$c$) and associated particle $p_{\rm T}$ (1 GeV/$c$ $<p_{\rm T}^{\rm assoc}<p_{\rm T}^{\rm trigg}$), for minimum-bias events and as a function of the event multiplicity. The near- and away-side peak yields are compared for the case of either K$^{0}_{\rm S}$ or $\Lambda$($\overline{\Lambda}$) being the trigger particle with that of inclusive hadrons (a sample dominated by pions). In addition, the measurements are compared with predictions from PYTHIA 8 and EPOS LHC event generators.


Introduction
Particle production as a function of the event charged-particle multiplicity in proton-proton (pp) collisions at the LHC has revealed interesting patterns. Clearly, in the soft (bulk) particle production domain with low transverse momentum (p T 4 GeV/c), several experimental measurements indicate features in high-multiplicity pp collisions similar to those observed in nucleus-nucleus collisions. These include long-range correlations in pseudorapidity [1,2], large azimuthal anisotropies [3,4] and strangeness production [5,6].
These measurements are theoretically interpreted in terms of a combination of initial-state collective dynamics (colour-glass condensate) [7] or as a hydrodynamic-like (final-state) collective flow [8]. Quantifying the relative contributions of initial-and final-state phenomena is a challenge, both experimentally and theoretically (see reviews [9,10]). These phenomena are also modelled in Monte Carlo (MC) event generators, like PYTHIA8 [11] or EPOS LHC [12]. For example, a basic experimental finding in pp collisions, the increase of the average transverse momentum with the event multiplicity is realized in these two models very differently. In PYTHIA 8, in events with several partonic scatterings, termed Multiple Parton Interactions (MPI), the respective color strings cut (reconnect) each other, leading to a redistribution of energy from particle production to transverse momentum. In the EPOS LHC model, a parametrised hydrodynamic evolution of a small volume with high density of thermalised matter (core) is used. In both models the respective parameters were tuned using the Run 1 data at the LHC, without explicit inclusion of particle correlations [12,13].
In PYTHIA8, correlations among the final state hadrons are realized through transversely extended strings, exerting on each other transverse shoves [14] that mimic collective dynamics, akin to that of a (long-lived) quark-gluon medium. The shoving model of hadronisation was recently used to discern within a PYTHIA8 study [15] possible effects of jet quenching in pp collisions. This prominent characteristic of nucleus-nucleus collisions, remains undetected in high-multiplicity pp or p-Pb collisions [16], perhaps not surprisingly, given the much smaller spatial extension of the dense system, compared to the nucleus-nucleus case. Experimentally, it was recently shown that in pp collisions the near-side longrange (in pseudorapidity) ridge yield (of bulk particles) in high-multiplicity events remains present for events which are additionally biased, through either a Z boson [17], a leading high-p T particle or a jet [18]. These findings are interesting per se and also motivate the quest to find or exclude jet quenching in high-multiplicity events in small collision systems, with differences in the observed effects on gluon, light and heavy quark jets.
At LEP, differences between quark-and gluon-initiated jets in e + -e − annihilations have been revealed in several measurements. Gluon jets are characterised by a larger charged-particle multiplicity than quark jets [19,20]. Moreover, in the relative production of K 0 S mesons and Λ hyperons to charged particles, it was found that the relative production of Λ is ≈30% higher in gluon than in quark jets, while the relative K 0 S production was found to be approximately the same [21]. In the present article, such studies of particle production and correlations are continued, exploring the effect of a strangeness bias, both in form of a meson (K 0 S ) or a baryon (Λ) with p T > 3 GeV/c. The correlations between kaons or Λ(Λ) hyperons with other hadrons are studied at midrapidity in pp collisions at √ s = 13 TeV for a broad range of the trigger (3 < p trigg T < 20 GeV/c) and associated particle p T (1 GeV/c < p assoc T < p trigg T ), for minimum bias events and as a function of the event multiplicity measured at forward rapidities. Such correlations encode effects of fragmentation, hadronisation and parton showering as well as possible collectivity and jet quenching. The complex overlap of these aspects is probed through the experimental handles of particle species and p T , inducing different kinematic and flavour biases. The near-and away-side peak yields are compared for the case of either K 0 S or (anti-)Λ as a trigger particle with that of inclusive hadrons (a sample dominated by pions). The measurements are, in addition, compared with the PYTHIA 8 and EPOS LHC event generators. The article is organised as follows: Section 2 outlines the experimental setup and the data sample; Section 3 describes the analysis, while Section 4 presents the results; a summary and an outlook are given in Section 5.

Experiment and data sample
The inclusive charged hadron, K 0 S meson and (anti-)Λ hyperon identification at midrapidity is performed using the tracking detectors of the ALICE central barrel located in a solenoidal magnet, which provides a magnetic field of 0.5 T oriented along the beam direction. A detailed description of the ALICE experiment and its performance can be found in [22,23].

Event selection
For the data taking, a minimum bias (MB) trigger is employed, provided by the V0 detector, which consists of two forward scintillator arrays covering the pseudorapidity ranges −3.7 < η < −1.7 and 2.8 < η < 5.1. The MB trigger signal consists of a coincident signal in both arrays. All events selected in this analysis are required to have a reconstructed primary collision vertex (PV) within the longitudinal interval |z vtx | < 10 cm from the nominal interaction point in order to ensure uniform detector performance. Beam-gas events are rejected using timing cuts with the V0 detector. Moreover pile-up events are rejected based on the Silicon Pixel Detector (SPD) information. The total number of analysed pp collisions at √ s = 13 TeV, measured during the LHC Run 2 data-taking period in years 2016-2018 by ALICE is 1.58 × 10 9 corresponding to integrated luminosity of about 27 nb −1 .
For the MC event generators, the multiplicity classes are selected with the trigger-corrected percentile calculation, applied to the distribution of charged primary particles produced in the η acceptance of the V0 detectors.

Primary hadron and V 0 selection
Primary charged tracks (denoted as h) are reconstructed in the pseudorapidity range |η| < 0.8 using the Inner Tracking System (ITS), which consists of six layers of silicon detectors around the beam pipe, and the Time Projection Chamber (TPC), consisting of a large cylindrical drift volume filled with nearly 90 m 3 either of Ar/CO 2 (88/12, in 2016 and 2018) or Ne/CO 2 /N 2 (90/10/5 in 2017) and read out by multi-wire proportional chambers. Combining the information from these two detectors, the primary charged-track sample is created by applying selection criteria in order to suppress the contamination from secondary particles following previous studies [25]. The number of crossed pad rows in the TPC is required to be at least 70 (out of a maximum of 159) and the minimal ratio to the number of findable clusters (geometrically possible assignable clusters to a track) is 0.8. Only tracks with a fraction of shared clusters with other tracks smaller than 0.4 are accepted. The distance of closest approach (DCA) to the PV is required to be within an elipsoid with semi-axes of 2.4 cm and 3.2 cm in the xy-plane and z-direction, respectively. Every track is required to have a fit quality for both TPC and ITS, characterised by goodness-of-fit values χ 2 per cluster smaller than 4 and 36 for the TPC and ITS, respectively. Only K 0 S -and (anti-)Λ-hadron correlations in pp collisions at √ s = 13 TeV ALICE Collaboration tracks with a hit in the two most inner layers of ITS are selected. The kink topologies produced by decays are rejected. The selected sample of primary charged particles is dominated by hadrons. The electrons constitute less than 1%.
The K 0 S mesons and Λ(Λ) baryons (V 0 particles) are reconstructed in the rapidity range |y| < 0.5 via their most probable decay channels [26] and exploiting their characteristic (V 0 ) decay topology: The identification and reconstruction follows previous measurements presented in [27] and [28]. The identification of the daughter tracks is performed via specific energy loss dE/dx in the TPC, which is required to be within ±3σ from the expected mean value for pions or protons (for more details see [23]). The track quality criteria are the same as for the primary global tracks described above. The pairs of identified daughter tracks are combined to V 0 candidates, which are accepted if their invariant mass is within 3σ (1σ for K 0 S is in the range 0.0039-0.0075 GeV/c 2 and for Λ in 0.0021-0.0033 GeV/c 2 depending on p T ) from the nominal value. The combinatorial contribution is suppressed by applying selection criteria based on the topological variables summarised in Table 1. Here, the V 0 decay radius is the distance between the point where the V 0 decays (secondary vertex) and the PV. The DCA xy to PV is the distance of closest approach between the daughter track and the PV. The θ PA refers to the pointing angle, which is the angle between the momentum vector of the V 0 candidate and the line connecting the primary and secondary vertex. The reconstructed proper lifetime of an individual particle is defined as mL/p, where m is the particle mass, L is the distance between primary and secondary vertex and p is the particle momentum. The mean life cτ is listed in [26] and its value is 2.68 cm and 7.89 cm for K 0 S and Λ(Λ), respectively. It can happen that a certain pair reconstructed as K 0 S candidate can have an invariant mass of Λ(Λ) under the pπ assumption for the daughter tracks. Such pairs are not accepted neither as K 0 S nor as Λ(Λ) candidates. Table 1 quotes under the competing rejection entry the mass on which this criterion is applied for both K 0 S and Λ. Besides the topological selections, a bunch-off pile-up (by the high frequency collisions, some tracks from previous bunch-crossing remain in TPC when current collision happen) removal criterion is required where at least one of the V 0 daughter tracks is reconstructed both in ITS and TPC or has a signal in the Time-Of-Flight detector.

The correlation function
In the dihadron correlation approach, the first hadron is the trigger particle, here either a primary charged particle (hadron) or an identified K 0 S meson or Λ(Λ) hyperon with p T in range 3-20 GeV/c. Since the K 0 S -and (anti-)Λ-hadron correlations in pp collisions at √ s = 13 TeV ALICE Collaboration Λ-h and Λ-h correlation functions are compatible, as expected for this collision energy, the results are combined and reported in the following as (Λ + Λ)-h. The second particle is the associated particle, in this case, always a primary charged particle with a kinematic requirement 1 GeV/c <p assoc T < p trigg T . By calculating the differences in the azimuthal angle and pseudorapidity for each of such pairs, three types of correlation functions are constructed: h-h, K 0 S -h and (Λ + Λ)-h. For h-h correlations, pairs with invariant mass (IM) within ±5 MeV/c 2 of the mass of K 0 S or Λ(Λ) or from γ conversions are not accepted. The contribution from decays of the K * (892) and φ mesons, ∆ resonances and D mesons was checked and found negligible. In the case of (Λ + Λ)-h correlations, this restriction is applied to pairs with IM of a cascade (Σ, Ξ, Ω).An example of a raw K 0 S -h correlation function is shown in Fig. 1 (left panel). At (∆ϕ, ∆η) = (0, 0), one can observe the near-side peak, which originates mostly from particle pairs fragmented within the same jet. Bose-Einstein correlations, strong decays of high-mass resonances and final state interactions may have also a small contribution for the h-h case. Due to momentum conservation, jets are produced back-to-back in the transverse plane. Thus, a second peak around π in ∆ϕ is expected, which is smeared in the ∆η direction, because the particles can obtain an additional longitudinal boost related to the varied center-of-mass frame of the partonic collision. In the selection of the trigger particle, the near-side jet is fully reconstructed in the longitudinal direction, but the away-side jet is not necessarily (fully) within the detector acceptance. The procedure of getting fully corrected 2dimensional per-trigger yield is schematically written in Eq 1. Here, d 2 N raw pair d∆ϕd∆η (∆ϕ, ∆η) is the uncorrected correlation function, ε trigg ,ε assoc and ε pair are correction factors further described in Sec. 3.2 and N trigg is the number of the trigger particles. Afterwards, the 2-dimensional per-trigger yield is projected on the ∆ϕ axis and integrated (see Eq. 2) in the intervals |∆ϕ| < 0.9 and |∆ϕ − π| < 1.4 to obtain the near-side and away-side yield, respectively, denoted as Y ∆ϕ in Eq. 2.

Corrections
The corrections are described in the same order as they were applied to the data. All MC-based corrections are calculated using events from PYTHIA8.210 (Monash 2013 tune) [13,29], with particle propagation through the detector by means of GEANT3 [30]. The detection inefficiencies are corrected with the single particle efficiency factor, calculated in MC and applied as weight (1/ε trigg ×1/ε assoc ) for each pair. This factor was calculated separately for trigger and associated particles as a function of p T , η, ϕ and PV position. In the case of primary charged particles, a p T -dependent contamination factor is also part of the weight to account for the amount of secondary particles in the sample. This is defined as a ratio of only primary tracks to all reconstructed ones.
Imperfect detector acceptance within |η| < 0.8 range is corrected with the mixed-event method, where trigger particles from one event are correlated with associated particles from different events. Thus, no physical correlations are present. The mixed-event correlation function has a typical triangular shape determined by the η acceptance. An example of this function is shown in the middle plot of Fig. 1 where a plateau is visible. This is caused by different ranges in η for trigger (K 0 S ) and associated particles (h). The mixed-event correlation is already scaled to unity with a scaling factor equal to the average of bins with ∆η = 0. In the following, the actual correlation function is divided by the mixed-event one to eliminate the detector acceptance effects as illustrated in Fig. 1. This correction is schematically written as 1/ε pair in Eq. 1. In some cases, due to the finite binning in multiplicity and PV position in z-direction, the mixed-event correlation does not match the shape of the background perfectly. For this reason, a so called "wing" correction is performed. Here the correlation function is scaled once more with a 2D distribution constant in ∆ϕ and dependent on ∆η in order to get a flat distribution in ∆η at the away-side. This correction is never larger than 2% and only affects the h-h correlation function. A similar effect was observed also in a previous analysis [31].
For the reconstruction of K 0 S mesons and Λ(Λ) baryons, some of the candidates selected with the topological criteria are in fact combinatorial background. Since the shape of the correlation function does not need to be the same for the signal and background, a second correlation function is calculated, where candidates from two intervals from outside the invariant mass peak (m V 0 − 9σ to m V 0 − 6σ and m V 0 + 6σ to m V 0 + 9σ ) are taken as trigger particles. These give the same width as the signal region in the invariant mass spectrum. The second "side-band" correlation function is subtracted from the signal one. The number of trigger particles is in addition corrected for purity, defined as a ratio of number of signal V 0 candidates over all candidates within the invariant mass acceptance region.
In the case of Λ(Λ) being the trigger particle, the feed-down contribution from decays of Ξ baryons (reconstructed following [6]) baryons is subtracted in a similar way as for the combinatorial background. For this case, the (Ξ − + Ξ + )-h correlation function in every p T and multiplicity bin is calculated, scaled with the detection efficiency of Λ(Λ) from Ξ decays and subtracted from the (Λ + Λ)-h correlation function. Similarly, the feed-down fraction is subtracted from the number of trigger particles. It is assumed that the production rates of charged and neutral Ξ baryons are equal and the feed-down fraction from Ω is negligible. This correction has an effect of 5% on the final near-side yields for low p T and smaller than 1% for high p T .
After projecting the per-trigger yield on the ∆ϕ axis, the underlying event background is subtracted with the ZYAM (Zero Yield At Minimum) method [32]. The background is assumed to be flat and estimated as the average value of six bins outside the jet peaks to reduce the statistical fluctuations.

Systematic uncertainties
The sources of systematic uncertainties of the per-trigger yields in the minimum bias sample are listed in Tab. 2. These are estimated by varying track-selection criteria and other parameters in the analysis. The significance of each source of systematic uncertainty was checked according to the Barlow criterion [33]. Within this procedure a threshold value (1 σ ) is set, based on which each variation can be checked, whether it is within statistical fluctuations or a real systematic difference. If a certain variation did not pass the test, this contribution was not accounted for in the total systematic uncertainty, which K 0 S -and (anti-)Λ-hadron correlations in pp collisions at √ s = 13 TeV ALICE Collaboration Table 2: Summary of the main sources and values of the relative systematic uncertainties (expressed in %) for the per-trigger yields in the MB sample. The abbreviation "negl." stands for negligible (smaller than 0.1%) and "rej." means that this variation was rejected due to the Barlow  For the uncertainty related to the ∆ϕ integration window, the window is varied around the nominal values (|∆ϕ| < 0.9 and |∆ϕ − π| < 1.4) within ±0.1. For the yields for the h-h correlations, on both near-and away-side, the contribution to the total uncertainty is around 0.4% for all multiplicity classes. For the yields for K 0 S -h and (Λ + Λ)-h correlations, the value varies within 0.4-2% for both near-and away-side.
The PV selection along the z-axis (z vtx ) is decreased from ±10 cm to ±7 cm from the interaction point in order to estimate the uncertainty connected to the detector acceptance effects. The uncertainty is smaller than 0.3% in all multiplicity classes for the yields from h-h correlation function. It is in the range 0.7-2.3% and 0.7-2.7% for the near-side yield in case of K 0 S -h and (Λ + Λ)-h yields, respectively. For the away-side, this source contributes with 1.7-4.5% and 0.7-4.9% in case of K 0 S -h and (Λ + Λ)-h yields, respectively.
The number of bins in z vtx used for the event-mixing classes is changed from 9 to 7 to account for the uncertainty connected with the detector acceptance. For the yields triggered with an unidentified hadron, the contribution from this source is smaller than 0.5% at both sides for all multiplicity classes. This uncertainty is in the range 0.5-2.7% and 0.4-1.5% for the near-side yield triggered with K 0 S and (Λ + Λ), respectively and within 1.2-5.2% and 0.8-2.8% for the away-side.
The contribution to the systematic uncertainty resulting from the yield calculation method is estimated by fitting each jet peak with a double-gaussian function and integrating the fit function to calculate the pertrigger yield instead of calculating the yield directly by the bin counting method as default. This leads to an uncertainty around 1% for the near-side and to a value smaller than 0.2% for the away-side for the h-h yields in all multiplicity classes. For most multiplicity classes this source was rejected by the Barlow criterion for the K 0 S trigger. The non-rejected contribution is 1.1% and 0.7% for the near-and awayside, respectively. The accounted contribution to the uncertainty of yields triggered with (Λ + Λ) is in the range 0.3-0.8% and 0.2-3.4% for the near-side and away-side yields, respectively.
The ∆η range is varied within 0.1 around its nominal value |∆η| < 1 in order to estimate the uncertainty related to the near-side jet acceptance. This is estimated to be within 0.3-0.9%, 0.6-1.9%, 0.4-2.4% for h-h, K 0 S -h and (Λ + Λ)-h yields in all multiplicity classes, respectively. The scale factor for the mixed-event correlation function is varied, which gives a negligible contribution to the total systematic uncertainty for h-h yields for both sides. This contribution for K 0 S -h ((Λ + Λ)-h) yields is estimated as 0.7-1.5% (0.2-0.4%) and 0.9-2% (0.2-0.5%) for the near and away-side yields, respectively, in different multiplicity classes.
In order to estimate the systematic uncertainty connected to the V 0 reconstruction, the values for the topological selection are varied around the nominal values. Its value is, for different multiplicity classes, in the range 1.5-5.8% (1.9-5.6%) and 2.2-7.5% (2-5.5%) for the K 0 S (Λ + Λ) triggered yields at the nearand away-side, respectively.
The ranges for the signal and for background in the invariant mass distributions are varied in order to estimate the uncertainty related to the subtraction of the contribution from misidentified K 0 S or (Λ + Λ). This source is rejected by the Barlow criterion for the K 0 S -h yields and has a value in the range 0.5-3.9% and 1.1-4.3% for the (Λ + Λ)-h triggered yields, for the near-and away-side, respectively.
The systematic uncertainty associated with the primary track selections is estimated by selecting tracks with slightly varied criteria. These are the same as the ones used for global tracks, but there is a tighter and p T -dependent DCA requirement in the xy-plane, which means that tracks with a DCA in the xy-plane larger than 0.0105 + 0.0350/p 1.1 T are rejected. This uncertainty is smaller than 0.7% for both the nearand away-side yield for h-h for all multiplicity classes. The uncertainty intervals for K 0 S ((Λ + Λ)) triggered yields are estimated as 0.9-2.4% (0.4-3.5%) and 1.3-3.9% (0.2-3.1%) for the near-and awayside yields, respectively.
The range used for the estimation of the wing correction scaling factor is varied in order to calculate the uncertainty related to this method. This contribution is not dependent on the event multiplicity.
The Ξ − (Ξ + ) reconstruction uncertainty contributes to the uncertainty of yields triggered by (Λ + Λ). The correction procedure is checked with a Monte Carlo closure test. Two correlation functions are calculated, the first one with generated MC particles and the second one with MC particles reconstructed after GEANT3 propagation using the full reconstruction and correction chain as for the experimental data. The ratio of these two correlation functions is expected to be unity. This is the case for the h-h and K 0 S -h correlation functions, but there is a residual departure from unity for (Λ + Λ)-h correlation function at the near-side of up to 2.5%, which is accounted as a systematic uncertainty.

Results and discussion
The ∆ϕ projections of the correlation functions for the three different trigger particles are shown for two p trigg T intervals, 3 < p trigg T < 4 GeV/c and 9 < p trigg T < 11 GeV/c, in Fig. 2. Included are also the correlation functions predicted by MC event generators widely used by the LHC collaborations: PYTHIA8 with the standard Monash tune, which includes colour re-connection as final-state effects [13], PYTHIA8 Monash tune with shoving [14] and EPOS LHC [12]. It is important to note that the PYTHIA 8 Monash  Δϕ (rad) Δϕ (rad) Δϕ (rad) and EPOS LHC tunings were based on single-particle spectra and underlying event observables, but did not include particle correlations in azimuth. The shoving strength parameter g is here set to g=3 and in addition the upper p T cut for the shoving mechanism is turned off. None of the models describes quantitatively the correlation functions consistently for the three trigger particle species. For the low p trigg T , both PYTHIA8 tunes overestimate the peaks on the near-and away-side, while EPOS LHC underestimates them significantly for all trigger particles except for the K 0 S . In the high p trigg T interval, the shoving tune of PYTHIA8 is underestimating the near-side peak for all trigger particles except for K 0 S -h case, but describes well the away-side peak. The description of EPOS LHC and PYTHIA8 Monash is similar in both p The per-trigger yields, obtained by integrating the ∆ϕ projections of the correlation function for the intervals |∆ϕ| < 0.9 (near-side) and |∆ϕ − π| < 1.4 (away-side) are studied as a function of p trigg T , p assoc T and event-activity class for the three trigger particle species and compared with the MC event generators. The results are described in the following sections.

Per-trigger yields
The per-trigger yields are shown in Fig. 3 as a function of the p trigg T for different event-activity classes. An increasing trend with p trigg T is observed, as expected, as higher energetic jets have increasingly more associated particles.
For a more quantitative inspection of the event-activity dependence, the ratio between the yield in each event class and the yield for minimum bias is given in Fig. 4. Different trends are visible for the nearand away-side peaks. A clear multiplicity ordering for the near-side can be observed, events with higher multiplicity exhibiting the highest yields. This behaviour is most obvious for the h-h correlations, but it is significant on the near-side also for the V 0 -triggered yields.
For the away-side this ordering is reverted, in particular with the increase of the p T of the trigger particle. Given the uncertainties, this trend is less significant for the K 0 S -h and (Λ + Λ)-h correlations. The finding is qualitatively reproduced in PYTHIA8 simulations and can be understood considering that the location 0-1% (x2 ) 5 1-3% (x2 ) 4 3-7% (x2 ) 3 7-15% (x2 ) 2 15-50% (x2 )  of the away-side jet is not fixed in η. The requirement of a low (high) multiplicity in the V0 detectors at larger rapidity, biases the events towards configurations where the away-side jet is within (outside) the central acceptance, thus increasing (decreasing) the per-trigger yield at the away-side. The near-side jet is by construction in the central pseudorapidity acceptance, though the multiplicity measurement in the V0 detectors may still be influenced by long range correlations (flow-like) and fragmentation biases.  This jet bias, although expected and roughly understood, is interesting, as it gives insights on particle production mechanisms. It is further investigated through the comparison with model predictions and through normalisation of the yields for K 0 S -h and (Λ + Λ)-h to those for h-h.
The p assoc T per-trigger yield spectra for different p trigg T intervals are shown in Fig. 5. A decreasing trend with p assoc T is observed, as expected, as the probability for creation of associated particle with high p T decreases with p T . Note, that due to the kinematic requirement p assoc T <p trigg T , the yields triggered with lower p T particle do not cover the full p assoc T range.

Comparison with model predictions
The ratios of model predictions to data for the integrated per-trigger yields are shown in Fig. 6 for the near-and away-side yields as a function of p trigg T for minimum bias events and event classes selected on their activity. The first finding is that the trends in the model descriptions of the data are largely the same for h-h, K 0 S -h and (Λ + Λ)-h correlations. The event-activity dependence is reproduced by PYTHIA8 calculations, for both the standard tune and with shoving, the latter clearly offering a better description. The dependence is not reproduced by EPOS LHC.
For the near-side, PYTHIA8 with colour re-connection describes well the yields for high p T trigger particles while it overestimates the yields at low-p T . This is valid for all multiplicity classes and holds for the three species of trigger particle. This is a consequence of the good description of the hard QCD processes in PYTHIA8, which do not depend on the event multiplicity. The shoving mechanism improves the intermediate sector, at the price of degrading the harder sector. It is apparent that allowing shoving for large p T , as done for the simulations presented here, is not entirely physical. The medium-hard and softer regime remains a challenge and is a subject of current theoretical attention [34]. For the away-side, the shoving mechanism describes the data better than the standard PYTHIA8. In EPOS LHC the eventactivity dependence seen in data is not described well: a stronger event-activity dependence is observed in the model, which underpredicts the data for higher event multiplicities and either overpredicts it (for the near-side) or describes it well (for the away-side) for the lower event-activity classes. Model / Data EPOS LHC Figure 6: Models to data ratio of integrated per-trigger yields as a function of p trigg T for different multiplicity classes on the near-side (top panels) and away-side (bottom panels) for three MC event generators: PYTHIA8 Monash with colour re-connection (left), PYTHIA8 with shoving (middle) and EPOS LHC (right). Note, for plotting purpose, the arbitrary shifts for the vertical axis are given in the legend. The bands represent combined systematic and statistical uncertainties from data and models.
The features of the data-model comparison are dramatically different in Fig. 7, where the model to data per-trigger yield ratio is shown as a function of p assoc T for minimum bias collisions. Here, the triggerparticle dependence is rather different in the models. PYTHIA8 predicts, for both the standard settings and for the shoving mechanism, in particular for the near-side and in dependence of p trigg T , a much stronger dependence on the trigger particle than seen in the data, while EPOS LHC describes the data well. For high values of p trigg T , the data are described well in the whole p assoc T range. This reflects that the full fragmentation process in a hard scattering is well modelled. It is important to note that PYTHIA8 Monash describes quite well the measured p T dependence of the ratio (Λ + Λ)/K 0 S in jets with p T > 10 GeV/c. However, the ratio in MB collisions is not described well, in particular for p T < 4 GeV/c [35].
It is interesting to examine the differences between PYTHIA8 with the standard settings and with the shoving mechanism. Clearly, the shoving mechanism describes the medium-hard processes better, corresponding roughly to 3 < p trigg T < 5 GeV/c and 1 < p assoc T < 5 GeV/c, while the harder processes are underestimated. This is visible in particular in Fig. 6 for all trigger-particle species for different eventactivity classes, while in case of the p assoc T dependence shown in Fig. 7 the shoving mechanism leads to a poorer description of the data compared to the standard settings. The EPOS LHC model gives a rather different description of the data compared to PYTHIA8. In contrast to the rather poor description of the p trigg T and event-class dependence (Fig. 6) the dependence on p assoc T (Fig. 7) is rather well described for different p trigg T intervals and for the three trigger-particle species.

Comparison of hadron-and strangeness-triggered yields
In order to compare more quantitatively the correlation yields for different trigger-particle species, ratios to the per-trigger yields for h-h are calculated. These ratios are shown as a function of p trigg T in Fig. 8 for the near-and away-side, while Fig. 9 shows them as a function of p assoc T . The data indicate that intervals on the near-side (top panels) and away-side (bottom panels) for three MC models: PYTHIA8 Monash with colour re-connection (left), PYTHIA8 with shoving (middle) and EPOS LHC (right). Note that for plotting purpose, the arbitrary shifts for the vertical axis are given in the legend. The bands represent combined systematical and statistical uncertainties for data and statistical for models. the differences between charged-hadron (a sample dominated by pions) triggered yields and either K 0 S or (Λ + Λ) triggered yields are small and have a weak dependence on the event-activity class. All three models describe the trends seen in the ratios better than it was the case for yields itself, a consequence of the earlier finding that the model-data disagreements are very similar for the three trigger-particle species.
At closer examination, one observes that a difference between different trigger-particle species is visible for the near-side. The yield ratios Y K 0 S −h ∆ϕ /Y h−h ∆ϕ are smaller than unity and flat with p trigg T in all multiplicity classes, which indicates that jets triggered with K 0 S mesons contain less particles than the unbiased (inclusive) jets and this feature does not depend on the hardness of the process (p trigg T ) or event multiplicity. In contrast to that, the Y (Λ+Λ)−h ∆ϕ /Y h−h ∆ϕ ratio increases with p trigg T . Potentially, this could be explained with a bias towards gluon jets, which contain more particles [19] and have relative enhanced production of Λ hyperons [21]. In the right column in the left plot of Fig. 9, it is visible that this effect in the data is pronounced for the soft part of harder jets (low p assoc T for high p trigg T ). A decreasing trend of the ratio can also be observed with increasing p assoc T . This suggests that a jet triggered with either a K 0 S or a Λ or Λ particle has a smaller amount of associated particles with higher p T than a jet triggered with an unidentified hadron with the same p T . This decreasing trend is reproduced by the considered models.
To check if the difference in the ratios for the near side triggered with K 0 S and (Λ + Λ) can be caused by the differences between quark and gluon jets, a separated PYTHIA 8 study was performed, selecting exclusive hard processes containing only quarks (q + q → q + q) or gluons (g + g → g + g) in the final state. The results of this study are shown in Fig. 10 for MB collisions in comparison with the data. It is visible that the ratio is almost identical for the K 0 S -triggered yields for both quark and gluon jets. In this case, for both processes the ratio is flat as a function of p trigg T and decreasing with p assoc T . Nevertheless, a clear difference between the two processes is observed in the ratios of yields triggered with (Λ + Λ). The ratio for the gluon-jet process is increasing with p trigg T and is higher, while it is flat and smaller   for the quark jets. A systematic difference is visible also in the p assoc T dependence, where the ratio from gluon jets is significantly higher than the one from quark jets. Although the p T distributions of hadrons in the simulated exclusive processes may be different than in MB collisions, it is expected that the observed difference is generic and explains at least some of the trends seen in the data.
In contrast, for the away-side, the ratios as a function of p trigg T are compatible with unity within the uncertainties as shown in the right part of Fig. 8, thus no dependence on the trigger particle species (K 0 S or (Λ + Λ)) is seen. The deviation of some bins from unity is caused by the fluctuations affecting the underlying event estimation. A similar trend is also observed in the p assoc T dependence in the right plot of Fig. 9. This fits to the expectation that there is no bias in the away-side jet, since the associated production of strangeness is not dominated by hard processes, i.e. initial production of a ss pair leading to two strangeness induced jets. This is confirmed by the comparison with models, which predict ratios for the away-side around unity (Fig. 8).

Summary and conclusions
Charged-hadron, K 0 S and (Λ + Λ) triggered correlation functions are measured at the LHC in pp collisions at √ s = 13 TeV with the ALICE apparatus. The integrated per-trigger yields are extracted for both near-and away-side and studied as a function of event multiplicity, p trigg T and p assoc T . A dependence on the event-multiplicity is observed, which may be explained at the near-side by an interplay of fragmentation and of collective-like effects such as the long-range ridge. For the away-side the primary effects are likely due to a selection bias, where the away-side jet is within the V0 detector acceptance causing smaller away-side yields for high-multiplicity classes. This bias was overcome by studying the ratios       of yields for K 0 S or (Λ + Λ) as trigger particle over that for inclusive hadrons. For the near-side, different trends were observed for yield ratios triggered by K 0 S and (Λ + Λ). While the Y . A PYTHIA8 study of the respective exclusive processes reveals that the difference is caused by the bias towards gluon jets through triggering with Λ or Λ hyperon. In the p assoc T dependence of these K 0 S -and (anti-)Λ-hadron correlations in pp collisions at √ s = 13 TeV ALICE Collaboration yield ratios, a decreasing trend of the ratio can be observed with increasing p assoc T , suggesting a smaller amount of associated particles with higher p T in the jets triggered with a V 0 particle than in jets triggered with an unidentified hadron with the same p T . This trend can be reproduced by the considered models. However, on the away-side, no clear difference between the trigger-particle species is observed.
All the measured quantities are compared with model predictions. PYTHIA8 with the standard Monash tune can describe the data for high p trigg T (hard processes) while the shoving mechanism works better at intermediate p trigg T . The comparison of data with the EPOS LHC model reveals that the model predicts a significantly stronger multiplicity dependence than seen in the data. The ratios of yields for K 0 S or (Λ + Λ) trigger particles to those for inclusive (charged) hadrons are qualitatively well described by all the considered models, except for EPOS LHC at the near-side for the (Λ + Λ) triggered yield ratios.  [28] ALICE Collaboration, K. Aamodt et al., "Strange particle production in proton-proton collisions at √ s=0.9 TeV with ALICE at the LHC", Eur. Phys. J. C (2011) , arXiv:1012.3257 [nucl-ex].