Evolution of strange and multi-strange hadron production with relative transverse multiplicity activity in underlying event

In this work, relative Underlying Event (UE) transverse multiplicity activity classifier ($R_{\rm {T}}$) is used to study the strange and multi-strange hadron production in proton-proton collisions. Our study with $R_{\rm {T}}$ would allow to disentangle these particles which are originating from the soft and hard QCD processes. We have used the PYTHIA 8 MC with different implementation of color reconnection and rope hydronisation models to demonstrate the proton-proton collisions data at $\sqrt{s}$ = 13 TeV. The relative production of strange and multi-strange hadrons are discussed extensively in low and high transverse activity region. In this contribution, the relative strange hadron production is enhanced with increasing $R_{\rm {T}}$. This enhancement is significant for strange baryons as compared to mesons. In addition, the particle ratios as a function of $R_{\rm {T}}$ confirms the baryon enhancement in newCR, whereas Rope model confirms the baryon enhancement only with strange quark content. An experimental confirmation of such results will provide more insight into the soft physics in the transverse region which will be useful to investigate various tunes based on hadronization and color reconnection schemes.


I. INTRODUCTION
In recent times, the most important discoveries in proton-proton (pp) collisions are the evidence of collectivity [1][2][3][4][5] and strangeness enhancement [6][7][8]. They are remarkably similar to those observed in heavy-ion collisions at RHIC and LHC, where these features are attributed to the production of a deconfined hot and dense medium, known as the Quark-Gluon Plasma (QGP) [9,10]. The measurement of strange hadron production in minimum-bias events in pp collision at LHC energies has shown enhancement as a function of multiplicity density [6,[11][12][13][14]. One of the important conclusion from that study was most of the Quantum Chromodynamics (QCD) based Monte-Carlo (MC) models could not reproduce the data qualitatively. Strange quarks in pp collisions can be produced in the hard scattering via flavor excitation/creation and gluon splitting [15]. In soft scattering at low transverse momentum, strange quark pairs can be produced via non-perturbative processes. However, production of strange quark being heavier is suppressed relative to hadrons containing only up and down quarks. The hadronic final states in minimum-bias events are the product of hard (perturbative) partonparton scattering and soft scattering which is called Underlying Event (UE) [16][17][18]. The major contribution to the UE activity comes from multiple-parton interactions (MPI) in the same pp collision [19,20], initial and final state radiation, beam-beam remnants, and color reconnection (CR) [21]. MPI plays significant role in the particle production at LHC energies [7,22,23]. Measurements related to hadron yields in minimum-bias (inelastic) collisions are convoluted with the hard scattering and the soft UE activity [24]. The majority of minimum-bias collisions at LHC energies are soft, with a typical transverse momentum scale less than 2 GeV/c [25][26][27][28].
In this paper, we attempt to disentangle the hard QCD-process and investigate the hadron production, in particular strange and multi-strange particles in the transverse region dominated by the soft QCD process. The novel relative transverse multiplicity variable (R T ) has an excellent discriminating power to probe collective effects in hadronization [29]. Furthermore, the multiplicity distribution associated with the UE exhibits Koba-Nielsen-Olesen (KNO) scaling [30]. The relative transverse multiplicity variable, R T , serves as a perfect tool to study strange hadron production yield and transverse momentum spectra from low to high underlying event activity. The UE measurement with charged-particle jets showed dependence on the charged-particle jet radius, possibly due to the selection bias [31]. However, in this work the highest transverse momentum chargedparticle is used as a leading-object to define UE regions. The kinematical variables and acceptances are selected to match with ALICE detector [32] in order to compare results directly with the ALICE which has an excellent particle identification capabilities. Neutral strange particle production in underlying event as a function of arXiv:2004.06056v1 [hep-ph] 13 Apr 2020 leading p T was first reported by CMS [33] in pp collision at √ s =7 TeV. The results showed constant strange to charged-particle ratios beyond the plateau region.
In current study, PYTHIA 8 (version 8.301) MC event generator along with three different models which incorporates various color flow and hadronization mechanisms to qualitatively describe various aspects of the underlying event activity is used. The Monash 2013 tune (labeled as "Monash") [34] whose parameters are tuned to latest LHC data (run I and II) is used as a reference model. In addition to particle decays and soft-QCD modeling, PYTHIA 8 features leading-logarithmic initial-and final-state parton showers, Lund string hadronization, and MPI models [35,36]. Furthermore, new QCD based color-space model which allows strings to form between leading and non-leading color connected parton [37] is considered. When this model (which allows color-epsilon and anti-epsilon structure formation) is combined with PYTHIAs model for junction fragmentation [38], it gives rise to a new source of baryon production. This novel model (labeled as "newCR") can describe average transverse momentum of charged particles and also production rates of baryons. The third model (labeled as "Rope") is based on the rope hadronization formalism [39,40] which describes the interactions between the overlapping Lund strings in transverse space to combine into color ropes. Such color ropes are expected to give more strange particles and baryons. In these models, minimum-bias (inelastic) events are generated for proton-proton collision at center of mass energy, √ s = 13 TeV.

II. EVENT SELECTION AND OBSERVABLES
The UE properties are derived based on the leading charged-particle direction in the event. This chargedparticle is expected to have the direction of the parton produced with the highest transverse momentum in the hard scattering. The event is classified into three topological regions: (i) Towards, (ii) Away and (iii) Transverse region in terms of the azimuthal angle difference ∆φ between the directions of the leading charged-particle and that of any other particle in the event as shown in Figure 1. The particles produced in the toward region are spanned by the azimuthal angle |∆φ| < 60 • , and in the away region, |∆φ| > 120 • , which is expected to be dominated by the hard scatterings. The UE activity can be best studied in the transverse region, 60 • < |∆φ| < 120 • .
Traditionally, observable such as average multiplicity of charged-particles or average scalar sum of chargedparticles p T per event is measured as a function of leading charged-particle track transverse momentum (p lead T ). The charged-particle density in the transverse region rises steeply for low values of p lead T and reaches a plateau. The UE activity is classified in the plateau region (5 < p lead T < 40 GeV/c) to define relative transverse activity variable, R T . The R T is defined as the ratio of multiplicity of the inclusive charged-particles and identified strange hadrons to its event-averaged multiplicity R T = Ninc Ninc . The R T variable is useful tool to differentiate events with higher-than-average (R T > 1) from lower-than-average (R T < 1) UE activity, irrespective of center of mass energy or any fiducial requirements on the observable. The event-averaged multiplicity N inc , (and width) for "Monash", "newCR", and "Rope" model is 7.72 (4.94), 7.97 (4.94), and 7.65 (4.85) respectively.

III. RESULTS AND DISCUSSION
In this work, all the results are discussed by taking Monash as a reference model to understand the particle production mechanism with respect to newCR and Rope models. Figure 2 (left panel) shows average number of MPI in an event as a function of log 10 (R T ) for transverse region in three different models. The average number of MPI increases steeply with log 10 (R T ) beyond 0, which corresponds to R T ∼ 1 and it is 10-15% higher for newCR and Rope models. The highest event activity at log 10 (R T ) 0.5 has twice the average number of MPI as compared to log 10 (R T ) = 0. Mean transverse momentum ( p T ) of charged-particle as a function of R T in transverse region is compared with the ALICE data [41] and MC models as shown in the right panel of Figure 2. The p T increases with R T for all the three MC models and qualitatively explains the ALICE data. The color reconnection present in all the three models allows interaction between the strings which generate flow-like effects in the final state. An increase in p T with R T is attributed to  the presence of CR between the interacting strings. The p T is higher for the Monash as compared to newCR and Rope models by 3-5% below R T 3. This can be explained as the number of MPIs are almost 10-15% higher for newCR and Rope as compared to the Monash model, and this contributes to more soft QCD processes, which results in the lower value of p T . The average ratios of the production rates of strange hadron to the average rates of the pions as a function of p lead T in the transverse region are shown in Figure 3. To probe any sensitivity to relative strangeness enhancement, strange hadron yields are normalized to pion yields. Moreover, this ratio also factor out any contribution from differences in the overall multiplicity spectra of the tunes and MC models. The average strange particle production relative to pions increases significantly at low lead p T , eventually reaching plateau region at around 1-3 GeV/c. The average ratios for different particles are scaled by different factors to improve the visibility. The similarity between production rates of strange hadrons ratios and charged particles [41] as a function of p lead T confirms the impact-parameter picture of multiple parton interactions in pp collisions, in which the centrality of the collision and the MPI activity are correlated. Strange hadrons with higher mass attains the plateau at higher leading p T . The newCR and Rope models predict higher production of strange baryons as compared to strange mesons. The production rate of Ω (|S| = 3) with p lead T , in newCR and Rope models are ∼ 10 and ∼ 3 times higher as compared to Monash, respectively in the plateau region. The relative yields are similar in case of Λ and Ξ in Rope model. However, higher production rates (∼ 30%) are predicted in newCR model for Λ as compared to Ξ. The particle production in different p T region has different origins and thus p T -differential ratios provides more differential understanding about the particle production and hadronisation. The p T -differential ratio of strange and multistrange hadrons to pions in the transverse region for integrated R T is shown in Figure 4. A universal trend in the relative production of strange hadrons with p T can be seen, which finally reaches a plateau beyond 2-4 GeV/c for all the three models. The plateau shifts towards the high p T value for heavier strange particles, which can be attributed to collectivity like effects originating from the color reconnection by boosting the emitted particles to higher momenta. Comparison with Monash shows an increase in strange meson production by (10-20 %) in p T region 0.5-1.5 GeV/c as shown in Figure 4 (left panel) for Rope model. However, in higher p T region production rates in both Rope and newCR model are suppressed. Significant differences in strange baryons rates are observed among the MC models as shown in Figure  4 (right panel). The magnitude is highest for the Ω, by up to a factor of 10 for Rope, and 4 for newCR model in the p T region between 0-3 GeV/c. The Rope and newCR models comparison for Λ and Ξ shows 2-3 times higher production rates in the p T region 0-3 GeV/c. The behavior of the strange hadron production normalized to pions with R T is a useful tool to understand different hadronization models. Comprehensive study has been performed for strange hadrons both in low (R T < 1) and high R T (R T > 1) region which corresponds to low and high UE activity in the transverse region. The ratio of average strange hadron yield to pions as shown in Figure 5, increases with increasing R T for all the MC models. This increase in yield ratios with R T , particularly for R T > 1 can be attributed to the higher multiple partonic interactions as shown in Figure 2 (left panel). In case of strange mesons, Monash shows higher production rates with R T , whereas Rope and newCR model shows 10-15% less production. On the other hand, for strange baryon, enhancement is significantly higher as compared to mesons. The highest production rate is predicted for multi-strange baryon (Ω) in Rope model fol-lowed by newCR, this trend is consistent with our earlier observation with leading p T as shown in Figure 3. Enhancement in newCR as compared to Monash can be understood as an introduction of the junctions structure during the color reconnection phases which favors the baryon enhancement over mesons. Further contribution to strange and multi-strange hadrons in Rope model comes from additional production of strangeness and diquarks due to interacting strings which forms ropes and consequently hadronizes. The particle production chemistry in UE is investigated by measuring different particle yield ratios which are sensitive to different hadron masses, baryon/meson, and strangeness content with R T , as shown in Figure 6. We observe dependence for baryon to meson ratios as a function of R T for p/φ and Λ/K 0 S . The Λ/K 0 S ratio has highest production rate in Rope model (∼ 2.5 times) followed by newCR (∼ 2 times) as compared to Monash in high relative transverse activity region. The p/φ ratio obtained from the newCR and Rope model have similar production rates as proton being non-strange particle do not have further contributions from Rope model. The individual particle yields increases with R T , however, the effective baryon to baryon (Ξ/Λ) or meson to meson (φ/K 0 S ) ratios cancel-out, which results in the independent behavior with R T .

IV. SUMMARY AND CONCLUSION
We have extensively studied the strange and multistrange particle production in the transverse region as a function of leading p T and transverse multiplicity activ-  ity in pp collisions at √ s = 13 TeV. Three different models with different implementation of hadronization and color reconnection are used to study the dependence of the particle production in the transverse region using the PYTHIA 8 event generator. In this paper, an attempt has been made to disentangle the soft and hard QCD processes and look into the particle production in more differential manner using transverse UE activity classifier R T . The newCR model includes baryon enhancement due to junctions structure introduction during the color reconnection stage. Whereas, Rope model incorporates strangeness enhancement due to surplus production of strangeness and di-quarks compared to Monash as a function of R T . The steep rise of p T in the transverse region as a function of R T is qualitatively explained by all the three models. These models underestimate p T at low transverse activity region (R T < 1) for the ALICE data, whereas overestimate at higher R T values. The average strange particle production relative to pions as a function of leading p T increases significantly at low leading p T , eventually reaching plateau region at around 1-3 GeV/c. A systematic shift in the knee of the plateau towards the higher value of leading p T with the heavier hadrons is observed. An enhancement of baryons relative to pions with leading p T is predicted in newCR model and additional production in Rope model. The production rate of baryon with highest strangeness, Ω, in the plateau region for newCR and Rope models are ∼ 10 and ∼ 3 times higher as compared to Monash, respectively. The p T -differential particle ratios in the transverse region shows the evolution of the spectral shape for both strange mesons and baryons in low-p T region between 0-3 GeV/c. A strong increased production of strange baryons in the newCR and Rope model around 1 GeV/c is observed. The ratio of average strange hadron yield to pions increases as a function of R T in all the MC mod-els. Monash shows higher production rates with R T for strange mesons, whereas Rope and newCR model show higher production rates for strange baryons. The p/φ and Λ/K 0 S ratios as a function of R T confirms the baryon enhancement in newCR, whereas Rope model is responsible for baryon enhancement with strange quark content. Moreover, meson to meson and baryon to baryon ratios do not show significant dependence on R T . Previous studies show that most of the MC models do not explain the enhancement of strange hadron production in pp collision as a function of charged-particle multiplicity density. Our study with transverse multiplicity activity classifier provides qualitative evidence of increase in strange hadron production in the underlying event. An experimental confirmation of these results will provide more insight into the soft physics in the transverse region as a function of R T . This will further help to tune various hadronization and color reconnection schemes which can better explain particle production in pp collision.