Multiplicity-dependent production of heavy mesons with strangeness in small systems at LHCb

. The phenomenon of strangeness enhancement, originally proposed as a signature of quark-gluon plasma formation, has received considerable new interest following recent observations in small collision systems. LHCb is uniquely well suited to study such e ﬀ ects in the heavy quark sector, down to very low transverse momentum. Here we will present new LHCb results on the production rates of B 0s relative to B 0 mesons versus multiplicity in pp collisions. Potential implications for the hadronization mechanism of heavy quarks and our understanding of the factorization of fragmentation functions will be discussed


Introduction
The Quark Gluon Plasma (QGP) is a state of matter in which quarks and gluons are not confined within hadrons, but evolve as quasi-free particles.The QGP is of great interest to the scientific community since it constitutes a somewhat unexplored region in the Quantum Chromo Dynamics phase diagram.Besides, it is predicted to have been formed microseconds after the Big Bang and to constitute the inner core of neutron stars [1].
The production of the QGP requires achieving high energy densities.Theoretical [2] and experimental evidence [3,4] agree that it is possible to reach this colour deconfinement in the laboratory when colliding two heavy nuclei.In these kinds of collisions, there are several indicators for the formation of the QGP.An enhancement in the production of hadrons with strange valence quarks with respect to light hadrons in heavy-ion collisions has long been considered a probe of the QGP [5].Only in collisions with a high number of participating nucleons (participants) is the density high enough to produce the QGP.In a collision of two heavy ions, the charged particle multiplicity is highly correlated to the number of participants [6], so a strangeness enhancement with multiplicity can be associated with plasma production.
Over recent years there has been an increase in interest in the search for QGP traits in smaller collision systems, such as pPb and pp.For instance, the ALICE collaboration has measured a strangeness enhancement in high multiplicity pp collisions [7].The LHCb measurements of the ratio of B 0 s to B 0 cross sections, σ B 0 s /σ B 0 , as a function of charged particle multiplicity and p T [8] constitutes a new test for the presence of QGP properties in small collision systems.
The production mechanism of hadrons (hadronisation) in hadronic collisions is substantially affected by the nature of the colliding matter.B mesons are exceptional probes for hadronisation for two main reasons: There are no b quarks in the beam protons, thus their production is dominated by hard parton scatterings in the initial stages of the collisions [9] and, due to their large mass, their production is well described by pQCD [10][11][12].
The usual hadronisation mechanism for B mesons in hadronic collisions is called fragmentation, where showers of partons produced by outgoing quarks form into hadrons [13,14].However, in the case of a very dense medium, readily available quarks with overlapping wavefunctions can combine into colour singlets, hadronising through coalescence.Coalescence is especially important in high-energy heavy ion collisions where the QGP is formed [15].In pp collisions, if hadronisation via coalescence emerges as a mechanism for forming final state B hadrons, the production of B 0 s (s,b) relative to B 0 (d,b) mesons could increase with particle multiplicity.

B 0
s /B 0 production ratio with multiplicity

Data Sample and Selection
The pp collisions data used for these measurements were collected by the LHCb experiment at a centre of mass energy √ s = 13 TeV, corresponding to a total integrated luminosity of 5.4 fb −1 .The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed to study heavy flavour physics at the LHC [16].LHCb is composed of several subdetectors.The LHCb tracking system consists of the VErtex LOcator system (VELO) and four planar tracking stations.The VELO is a silicon strip tracking detector that encloses the beams' interaction point (primary vertex).The main tracks and N back tracks for NoBias events (blue squares) and B 0 signal events (red circles).The vertical scale is arbitrary.From [8].
purpose of the VELO is to reconstruct the primary vertices.Particle identification in LHCb is provided by four different detectors: the calorimeter system, the two RICH stations (that use Cherenkov radiation) and the muon stations.
A simulation sample was used in order to account for the effects of the reconstruction and the selection.The pp events are generated using Pythia [17,18] with a specific LHCb configuration [19].Decays of unstable particles are described by EvtGen [20] and the detector response is mimicked by Geant4 [21,22] as described in Ref. [23].
The yields of B 0 s and B 0 are both measured through the same decay channel, that gives similar yields for the two mesons.
Only events with one primary vertex are considered.The events are further selected through triggers that select the decay J/ψ → μ − μ + .In order to identify the B meson candidates within these events, certain kinematic and particle-identification requirements are implemented to the tracks of the daughter particles.
The sample is divided into multiplicity classes.The multiplicity is characterised by the number of tracks reconstructed by the VELO (N VELO tracks ), and a subset of these that point backwards with respect to LHCb (N back tracks ), in the pseudorapidity interval −3.5 < η < −1.5.The distributions of N VELO tracks and N back tracks are shown in Figure 1, both for NoBias events and for B 0 signal events.NoBias events do not have any selection, aside from requiring a bunch crossing and a primary vertex.The B 0 events distribution was achieved by applying the sPlot method [24] to remove the background from the selected sample.
The NoBias events are used to normalise the multiplicity.Precisely, for each of the N VELO tracks /N back tracks intervals, the measurement is quoted in terms of the number of tracks at the centre of the interval, divided by the mean number of tracks in NoBias events.These take the values N VELO  tracks NoBias = 37.7 and N back tracks NoBias = 11.1, with negligible uncertainties.

Determination of the B 0 s /B 0 production ratio
The ratio of cross-sections σ B 0 s /σ B 0 is calculated as Here, N B 0 s and N B 0 are the measured yields for B 0 s and B 0 , respectively, and is the ratio of the branching ratios to the decay in Eq. 1.The four remaining factors are the ratios of LHCb acceptance and the trigger, particle identification and reconstruction efficiencies, in order of appearance.
For each of the multiplicity (and p T ) intervals that the data sample is divided into, the yield ratios are determined through a likelihood fit on the J/ψπ + π − invariant mass spectrum.The PDFs 1 that model the two signals are Crystal Ball functions, which have tail parameters constrained to values determined by the simulation.The background is modelled by an exponential function.Figure 2 shows examples of the fit for two multiplicity ranges.
The ratios of the acceptances and the efficiencies are found to be consistent with unity and with uncertainties of ∼ 1%, due to the similarities of the B 0 s and B 0 decays.However, for the case of the reconstruction efficiencies, the ratio is significantly different from one, ε reco B 0 /ε reco B 0 s = 0.86 ± 0.04, for the full data sample.The reason for this is that, due to its larger mass, the π + π − spectrum for the B 0 s is dominated by the intermediate-mass resonances f 0 (980) and f 0 (1500) [25], while for the B 0 the main contribution is that of the lower-mass ρ 0 (770) [26], the reconstruction of which is less efficient.

Results
The B 0 s to B 0 ratio was measured for the full integrated sample and found to be σ B 0 s /σ B 0 = 0.30 ± 0.01 ± 0.03, being the first uncertainty from statistical and the second from systematic sources.
The ratio was studied for several normalised multiplicity intervals, defined for both N VELO tracks and N back tracks .These results are shown in Figure 3.The ratio consistently increases with N VELO tracks , which is not the case for N back tracks .Previous measurements from e + e − collisions at the Υ(5S ) and Z 0 resonances [27] are represented and show good agreement with the data at low multiplicity.
In order to understand to a greater extent what is the mechanism responsible for the increase in the ratio with N VELO tracks , the data sample is divided into p T intervals.Figure 4 shows the results for three p T regimes.For the lowest p T interval, 0 < p T < 6 GeV/c, where the B mesons have p T smaller or similar to their mass, the ratio shows an increasing behaviour with N VELO tracks .If the data is fit to a linear model, the slope differs from zero by 3.4 standard deviations.At the higher p T intervals, 6 < p T < 12 GeV/c and 12 < p T < 20 GeV/c, no such multiplicity dependence is found, and the results are consistent with the measurements from e + e − collisions. 1 Probability Distribution Functions

Conclusion and Future Prospects
The cross-section ratio σ B 0 s /σ B 0 is found to be consistent with previous measurements from e + e − collisions for high p T and for low p T at relatively low multiplicity.
There is an enhancement of the B 0 s meson production with respect to the B 0 production with global event multiplicity at low p T , but not with backward multiplicity.The lack of dependence on backward multiplicity could indicate that the mechanism responsible for the increase in the ratio is related to the local particle density in a similar rapidity interval as the B mesons.These measurements are qualitatively consistent with the emergence of quark coalescence as an additional hadronisation mechanism: the increase of the ratio at high multiplicity only happens for B 0 s mesons with low p T and relatively low velocity, that have more overlap with the low-p T bulk of the s quarks produced in the collision, creating b − s pairs through co-alescence; while at high-p T they hadronise via fragmentation, as in e + e − collisions.
The LHCb Collaboration is progressing on a similar analysis for the ratio of D + s to D + mesons with multiplicity in pPb collisions.Other related work includes the study of the production of Ξ + c in pPb collisions and of light strange hadrons and their dependence with multiplicity for pp and pPb collisions.

Figure 1 .
Figure 1.Distribution of N VELOtracks and N back tracks for NoBias events (blue squares) and B 0 signal events (red circles).The vertical scale is arbitrary.From[8].