Evidence for modification of $b$ quark hadronization in high-multiplicity $pp$ collisions at $\sqrt{s} = 13$ TeV

The production rate of $B^{0}_{s}$ mesons relative to $B^{0}$ mesons is measured by the LHCb experiment in $pp$ collisions at a center-of-mass energy $\sqrt{s} = 13$ TeV over the forward rapidity interval $2<y<4.5$ as a function of the charged particle multiplicity measured in the event. Evidence at the 3.4$\sigma$ level is found for an increase of the ratio of $B^{0}_{s}$ to $B^{0}$ cross-sections with multiplicity at transverse momenta below 6 GeV/$c$, with no significant multiplicity dependence at higher transverse momentum. Comparison with data from $e^{+}e^{-}$ collisions implies that the density of the hadronic medium may affect the production rates of $B$ mesons. This is qualitatively consistent with the emergence of quark coalescence as an additional hadronization mechanism in high-multiplicity collisions.

Measurements of B mesons at colliders offer unique probes of the hadronization process by which single quarks evolve into color-neutral hadrons.In contrast to light quarks, the large mass of b quarks suppresses their production via non-perturbative processes.In addition there is no b content in the valence quark distribution of the incoming beam particles [1].Therefore, production of b b pairs at hadron colliders is dominated by hard parton-parton interactions in the initial stages of the collisions, and is well described by perturbative QCD calculations [2][3][4].
The fraction of b quarks that pair with an s quark to form B 0 s mesons, f s , and the fraction that pair with a light d quark to form B 0 mesons, f d , are determined through the hadronization process.One mechanism for hadronization is fragmentation, where showers of partons produced by outgoing quarks form into hadrons [5,6].Measurements of B hadron production in e + e − collisions at the Υ (5S) [7][8][9] and Z 0 [10-13] resonances give consistent values for the ratio f s /f d , which is often interpreted as evidence for the universality of b quark fragmentation assumed by QCD factorization theorems [14].However, measurements at hadron colliders have shown that the ratio f s /f d has a dependence on the collision center-of-mass energy and the B meson transverse momentum p T [15][16][17][18][19].The fraction of b quarks which hadronize into baryons also varies with p T [20,21].Additionally, recent measurements have shown that charm quark hadronization differs between e + e − and pp collisions [22].The reason for these variations is not immediately clear, and may be explained by hadronization mechanisms other than fragmentation [23].
An alternative hadronization process, quark coalescence, can occur when a quark produced in the collision combines with another quark to form a color singlet hadron.Models incorporating coalescence are successful at reproducing a range of measurements from fixed-target experiments and colliders [24][25][26][27][28]. Coalescence calculations generally require multiple quark wavefunctions to overlap in position and velocity, so the fraction of hadrons produced by this mechanism is expected to increase with the number of quarks produced in the collision.The effect is expected to be most prominent at relatively low p T , which is the range where the bulk of the particles created in the collision are found.Coalescence can also lead to enhanced production of baryons at low p T , and is especially important in high-energy heavy ion collisions where a large volume of deconfined quark-gluon plasma (QGP) is formed [29][30][31].Data from the CMS collaboration has shown that B 0 s production may be enhanced relative to B + production in PbPb collisions when compared to pp collisions [32,33].However, significant uncertainties and the relatively high p T range covered by that data preclude drawing firm conclusions on the influence of coalescence on B hadronization.
Recent measurements in pp collisions have shown some behaviors similar to those associated with the formation of QGP in collisions of heavy nuclei [34][35][36].Among these effects is an enhanced yield of light-quark baryons and mesons with strangeness in collisions where a relatively large number of charged particles are produced [37], which was originally proposed as a QGP signature [38].If hadronization via coalescence emerges as a mechanism for forming final state B hadrons, then the production rates of B 0 s hadrons could increase relative to the production of B 0 hadrons as particle multiplicity increases.
This Letter describes 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 .Both the B 0 s and B 0 candidates are reconstructed through their decays to the J/ψπ + π − final state, where the J/ψ decays into a µ + µ − pair.This decay mode provides similar yields for both B 0 s and B 0 mesons.Here multiplicity is represented by the number of charged tracks reconstructed in a silicon strip detector that surrounds the pp interaction region, the LHCb VELO detector [39,40].These measurements use a sample of pp collisions collected at a center-of-mass energy √ s = 13 TeV, corresponding to an integrated luminosity of 5.4 fb −1 .
The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, described in detail in Refs.[41,42].Events considered in this analysis are required to satisfy a series of triggers designed to select the decay J/ψ → µ + µ − and have one reconstructed pp interaction point (primary vertex).Each muon candidate is required to penetrate the hadron absorber layers in the LHCb muon system and have p T > 500 MeV/c.Candidate J/ψ mesons are formed from pairs of oppositely charged muon candidates that have an invariant mass near the known J/ψ mass and originate from a vertex that is displaced from the primary vertex.Charged pion candidates are identified by the response of the LHCb ring-imaging Cherenkov detectors, and are required to have total momentum p > 3 GeV/c and transverse momentum p T > 750 MeV/c.Candidate µ + µ − π + π − combinations that form a good quality common vertex are retained, and the tracks are refit with kinematic constraints that fix the µ + µ − invariant mass to the known J/ψ mass, and require all four tracks to have the same origin point [43].
Simulation is required to model the effects of the detector acceptance and the selection requirements.In the simulation, pp collisions are generated using Pythia [44] with a specific LHCb configuration [45].Decays of unstable particles are described by EvtGen [46].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [47] as described in Ref. [48].The p T distributions of the simulated B 0 s and B 0 mesons, the invariant mass distributions of π + π − pairs from their decays, and simulated event multiplicity distributions are weighted to match background-subtracted distributions that are extracted from the data using the sPlot method [49].
The multiplicity metrics used in this analysis are the total number of charged tracks reconstructed in the VELO detector, N VELO tracks , and the subset of VELO tracks that point in the backward direction, away from the LHCb spectrometer, N back tracks .The backward tracks cover a pseudorapidity interval of approximately −3.5 < η < −1.5, providing a multiplicity estimate that is measured in a different region than the signal.The VELO detector and its performance are described in detail in Refs.[39,40].Figure 1 shows the distributions of N VELO tracks and N back tracks for both NoBias events and B 0 signal events with one reconstructed primary vertex, which requires at least five reconstructed tracks.NoBias events are selected based on the Large Hadron Collider beam clock, which indicates that a bunch crossing has occurred, without any other trigger requirements.The distributions for B 0 signal events are extracted from the data, and background is removed using the sPlot method [49].The results are quoted in terms of normalized multiplicity, defined as the number of tracks at the center of a given multiplicity interval divided by the mean number of tracks in NoBias events, which are ⟨N VELO tracks ⟩ NoBias = 37.7 and ⟨N back tracks ⟩ NoBias = 11.1, with negligibly small uncertainties.For comparison, the mean number of N VELO tracks and N back tracks are 71.1 ± 0.1 and 17.4 ± 0.3 for B 0 signal events, respectively, where the uncertainty is due to the statistical uncertainty on the track distributions.In some respects, the lowand high-multiplicity data samples approach the hadronic environments achieved in e + e − collisions and heavy-ion collisions, respectively.The sample containing signal events is divided into intervals of multiplicity, and in each interval a likelihood fit is performed on the J/ψπ + π − invariant mass spectrum to  determine the ratio of B 0 s to B 0 yields.Examples of the J/ψπ + π − mass distribution in low-and high-multiplicity intervals are shown in Fig. 2.An increase of the B 0 s yield relative to the B 0 yield in the high-multiplicity interval is apparent.The B 0 s and B 0 peaks are each represented in the fit by a sum of two Crystal Ball functions, which have tail parameters constrained to values determined by simulation.The background contribution is represented by an exponential function, which is found to provide a good description of the purely combinatorial J/ψπ ± π ± mass spectrum with like-sign dipions.All multiplicity intervals are fit simultaneously, where the signal shapes are constrained to be the same in each interval, but their normalization and the background parameters are allowed to vary.The B 0 s and B 0 line shapes are nearly identical, and variations of the fit functions have a negligible effect on the extracted ratio of B 0 s to B 0 yields.The ratio of cross-sections σ B 0 s /σ B 0 is found by calculating where N B 0 s /N B 0 is the ratio of B 0 s to B 0 signal yields returned by the fit, B B 0 /B B 0 s is the ratio of B 0 to B 0 s branching fractions to J/ψπ + π − [19,50], and s , and ε reco B 0 /ε reco B 0 s are ratios of the LHCb acceptance and the trigger, particle identification, and reconstruction efficiencies for B 0 to B 0 s mesons, respectively.Due to the similarities of the B 0 s and B 0 decays, many systematic uncertainties partially cancel in this ratio of cross sections.The ratio of the LHCb acceptance for the decays ε acc B 0 /ε acc B 0 s is found, using simulation, to be consistent with unity, with an uncertainty of ∼ 1% due to the uncertainty on the weights applied to the simulation in order to match the data.The ratio of trigger efficiencies ε trig s is determined from data to be consistent with unity, with an uncertainty of ∼ 1%, using techniques described in Ref. [51], where the uncertainty comes from statistical uncertainties on the data sample.The ratio of particle identification efficiencies ε PID B 0 /ε PID B 0 s is found using calibrated samples of identified muons and pions obtained from the data, and is consistent with unity with an uncertainty of ∼ 1% due to the finite size of the calibration sample.The only term with a significant difference from unity is the ratio of reconstruction efficiencies, which is found to be ε reco B 0 /ε reco B 0 s = 0.86 ± 0.04 for the p T -integrated sample.This is due to the difference in the dipion mass distributions produced in the B 0 s and B 0 decays: the B 0 s decay is dominated by contributions from intermediate f 0 (980) and f 0 (1500) states [52], which are reconstructed with higher efficiency than the lower-mass ρ 0 (770) intermediate state that is significant in B 0 decays [53].The uncertainty on this correction is due to the statistical uncertainty on the weights extracted from the data that are applied to the simulation in order to match the measured B meson p T and dipion mass distributions.
The ratio of cross-sections for the multiplicity-integrated samples is found to be σ B 0 s /σ B 0 = 0.30 ± 0.01 ± 0.03, where the first uncertainty is statistical and the second is systematic.This measurement agrees with previous LHCb measurements of f s /f d using different decay channels [19] within 1.5 standard deviations.
The multiplicity dependence of σ B 0 s /σ B 0 is shown in Fig. 3, for two different multiplicity metrics.The vertical error bars (boxes) represent point-to-point uncorrelated (fully correlated) uncertainties, while the horizontal error bars represent the bin width.Numerical values are given in the supplemental material [54].In the left panel, the ratio shows an increasing trend with the total VELO multiplicity, where multiplicity is normalized to the mean value found in NoBias collisions.Also shown are the σ B 0 s /σ B 0 values measured in e + e − collisions at the Υ (5S) and Z 0 resonances [55], which are in good agreement with the data at low multiplicity.The right panel shows the same ratio versus the normalized N back tracks .No significant dependence is observed on the multiplicity measured in the backward region.The dependence on total multiplicity, compared to the lack of dependence on multiplicity measured at backward rapidity, could indicate that the mechanism responsible for the increase in the σ B 0 s /σ B 0 ratio is related to the local particle density in a similar rapidity interval as the B mesons themselves.
The multiplicity dependence of σ B 0 s /σ B 0 is shown in three different intervals of B meson p T in Fig. 4. Numerical values are given in the supplemental material [54].The lowest p T interval, 0 < p T < 6 GeV/c, encompasses B mesons with p T approximately equal to or less than their mass.In this p T interval, at low multiplicity the σ B 0 s /σ B 0 ratio is consistent with values measured in e + e − collisions, and increases with multiplicity.A line fit to these data returns a slope of 0.075 ± 0.022 (N VELO tracks /⟨N VELO tracks ⟩ NoBias ) −1 , which differs from zero by 3.4 standard deviations and thereby provides evidence for an increase of the the σ B 0 s /σ B 0 ratio.This fit considers only the point-to-point uncorrelated uncertainties; since all data points must move simultaneously within the correlated uncertainties, they have no effect on the extracted slope.
For comparison, the ratio of cross sections calculated by the PYTHIA event generator is also shown.Events are generated with and without color reconnection (CR), a process which allows partons produced by from different interactions in the collision to be connected by color lines [56,57].Color reconnection was introduced to model charged particle production in hadron collisions, and is thought to be especially important in highmultiplicity collisions where multiple-parton interactions are significant.Both sets of PYTHIA calculations show a rise with multiplicity, which is more pronounced when CR is included.The PYTHIA models agree with the data at relatively low multiplicity, but both scenarios give values that are lower than the central values of the data at high multiplicity.
The measurements in higher p T intervals, 6 < p T < 12 GeV/c and 12 < p T < 20 GeV/c, display no significant dependence on multiplicity and are consistent with data from e + e − collisions.This behavior is expected in a scenario where low-p T b quarks with relatively low velocity recombine with s quarks produced in high-multiplicity collisions, while the wavefunctions of higher p T b quarks have less overlap with the low-p T bulk of the quarks produced in the collision.These high-p T b quarks would thereby dominantly hadronize via fragmentation in vacuum, as in e + e − collisions, rather than via coalescence.Again, both sets of PYTHIA calculations show a rising trend, which is more pronounced when color reconnection is included.However, here the uncertainties on the data prevent  discrimination between the two scenarios.Lines fit to the 6 < p T < 12 GeV/c and 12 < p T < 20 GeV/c data have slopes that are consistent with zero within 0.2 and 1.3 standard deviations, respectively.
In summary, LHCb measurements in pp collisions at √ s = 13 TeV show evidence that the production of B 0 s mesons is enhanced relative to B 0 mesons in collisions with high charged-particle multiplicity, indicating that strangeness enhancement is present in B hadron production.In collisions with relatively low charged-particle multiplicity, and for B mesons with p T > 6 GeV/c, the rate of B 0 s production relative to B 0 production is consistent with what is measured in e + e − collisions.These measurements are qualitatively consistent with expectations based on the emergence of quark coalescence as an additional hadronization mechanism, rather than fragmentation alone.These results could indicate that interactions of the b quarks with the local hadronic environment influence the hadronization process, thereby breaking factorization of b quark hadronization between e + e − and hadron collisions.

Figure 1 :
Figure1: Distribution of the number of VELO tracks and backward tracks for NoBias events (red) and B 0 signal events (blue), each with only one primary vertex.The vertical scale is arbitrary.

Figure 3 :
Figure 3: Ratio of cross sections σ B 0 s /σ B 0 versus the normalized multiplicity of a) all VELO tracks, and b) backward VELO tracks.The vertical error bars (boxes) represent point-to-point uncorrelated (fully correlated) uncertainties.The horizontal bands show the values measured in e + e − collisions.

Figure 4 :
Figure 4: Ratio of cross sections σ B 0 s /σ B 0 versus normalized multiplicity in the transverse momentum ranges a) 0 < p T < 6 GeV/c, b) 6 < p T < 12 GeV/c, and c) 12 < p T < 20 GeV/c.The vertical error bars (boxes) represent point-to-point uncorrelated (fully correlated) uncertainties.The horizontal bands show the values measured in e + e − collisions and the horizontal lines show PYTHIA calculations with and without (w/o) color reconnection.