Event shapes and jets in e^{+}e^{-} and pp collisions
EEVENT SHAPES AND JETS IN π + π β AND PP COLLISIONS
M. Sas , J. Schoppink Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands Physics Department, Yale University, New Haven CT, U.S.A.February 1, 2021
Abstract
In high energy particle collisions the shape of the event,i.e. the relative distribution of particles in momentum space,is often used to try to select events with certain topologies.It is claimed that an event shape observable like transversesphericity is able to discriminate between jet-like eventsand events that are dominated by soft production from theunderlying event.In this paper we investigate the relationship between theshape of the event and the number of jets found in the respec-tive event for both π + π β and pp collisions using the PYTHIAmodel. In π + π β collisions, we find that the transverse spheric-ity of the event can be used effectively to either enhance orsuppress the fraction of jets found in the selected sample,and can even discriminate between single, two, and multi-jettopologies. However, contrary to current literature, we findthat in pp collisions this does not hold. It is shown that thetransverse sphericity as well as the particle multiplicity issensitive to the number of multi-parton interactions. INTRODUCTION
Transverse sphericity is an event shape observable thathas been used throughout the particle physics communityas a way to characterize the configuration of the momentumvectors of the final state particles as either pencil-, sphere-like, or anything in between. Pencil-like events are typicallyassociated with events that have a di-jet structure, and sphere-like events with those containing mostly soft processes andan absence of jets [1, 2].Historically, quantifying the shape of the event involvedcalculating the thrust axis, i.e. the axis which maximizes theinner product of the final-state particle momentum vectors.As such, the thrust axis aligns with the average momentumof the particles and is a good approximation for the mainproduction axis of the event, especially for π + π β collisions[3β7], where to leading order there are two partons producedwith opposite momenta. For this collision system pencil-likeevents should correspond to a di-jet structure, and sphericalevents to multi-jet topologies [8β11].This paper addresses whether this holds for pp collisionsat RHIC and top LHC energies, where there are more sub-leading processes in addition to the initial hard scattering[12, 13]. This paper presents the results of an investigationon how the transverse sphericity ( π T ) correlates with jet pro-duction, using simulated π + π β and pp collisions. In addition,correlations between ( π T ) and other event characteristics,such as leading parton π T , particle multiplicity, and numberof multi-parton interactions are studied. ANALYSIS METHOD
The analysis presented in this paper is performed usingsimulated π + π β and pp collisions, using the PYTHIA8.1event generator [14], with the settings listed in Table 1. Thecenter-of-mass energy of the π + π β dataset corresponds to themass of the π boson, which is also the energy at which theLEP collider operated. For the pp datasets the beam energiesare chosen to be the same as the nominal operating energy atthe RHIC and the LHC in Run 2, both using the Monash 2013tune. Furthermore, the pp datasets are generated twice, oncewith multi-parton interactions (MPI) turned on, and oncewith MPI turned off. This will be used to study the sphericitydistributions with and without MPI in pp collisions. Trackswith π T > MeV / π and | π | < are selected for theanalysis, and in the case of the π + π β dataset only the hadronicfinal states are considered.The transverse sphericity is calculated using π T = π π + π , (1)where π and π , with π > π , are the two eigenvalues ofthe transverse momentum matrix π πΏπ₯π¦ , which is given by π πΏπ₯π¦ = (cid:205) π π π ,π βοΈ π π π ,π (cid:20) π π₯,π π π₯,π π π¦,π π π¦,π π π₯,π π π¦,π (cid:21) , (2)where π π ,π , π π₯,π , and π π¦,π , are the components of the mo-mentum vectors of particle π in transverse, π₯ , and π¦ direction,respectively.These equations essentially project all the particles of theevent onto the π₯ β π¦ plane and determine the eigenbasis ofthe transverse momentum matrix. As such, π T is sensitiveto the relative orientation of the momentum vectors, where π = is for pencil-like events, i.e. π T βΌ , and π βΌ π forsphere-like events, i.e. π T βΌ .Furthermore, the number of jets contained in each event isobtained by employing the FastJet package [15]. We choseto use the anti β π π‘ algorithm with a jet radius of π = . andminimum jet energy of πΈ = GeV. As this study is purelybased on model calculations, it is chosen to only includestatistical uncertainties that are proportional to the number ofevents as generated in the respective dataset. In all cases thedatasets are large enough to lead to statistically significantconclusions.
RESULTS
The distributions of the transverse sphericity π T for therespective datasets as well as for events with different num-bers of reconstructed mid-rapidity jets are shown in Fig. 1. a r X i v : . [ h e p - ph ] J a n ystem β π PYTHIA8.1 settings π + π β GeV π decay to quarkspp GeV Monash tune, MPI-ONpp
GeV Monash tune, MPI-OFFpp TeV Monash tune, MPI-ONpp TeV Monash tune, MPI-OFFTable 1: Data sets used.The top left figure shows first of all that the π T distributionfor π + π β collisions has a maximum around π T βΌ . , witha long tail towards higher values. This is consistent withthe picture that lepton collisions, to leading order, producetwo outgoing quarks that fragment into final state particles.The π T distributions for the pp datasets have a mean around π T βΌ . for MPI-ON, and π T βΌ . for MPI-OFF. Clearly,pp collisions produce a much broader distribution with alarger mean. There is no abundance of events with a pencil-like configuration, which is consistent with the idea thatpp collisions involve many more processes compared to theβcleanerβ π + π β collisions, tending to be more spherical dueto the overall higher particle multiplicities produced by alarger number of independent processes.Figure 1 shows the π T distributions for the number ofmid-rapidity jets reconstructed in the events, for π jets = , , , + . In the top right figure, the simulated π + π β colli-sions are dominated by 2-jet events at lower π T . For slightlyhigher values, π jets = + contributes the most, after whichfor π T > . the events with π jets = take over and dominatethe contribution to the inclusive sample. Single jet eventsexhibit a broad distribution that have a maximum at lowervalues of π T . For pp collisions, strikingly, the entire sampleis dominated by events that do not have a jet that passes theselection criteria. This is consistent with the notion that, eventhough the collision energy is much higher, pp collisionshave on average significantly fewer high momentum jets inthe final state compared to π + π β collisions, as the rapiditydistribution is wider and tracks with | π | < are selected.For the pp dataset with MPI-ON at β π = TeV, contraryto the same distributions found at β π = GeV, the singleand multi-jet events are more pronounced for higher valuesof π T , while for the datasets with MPI-OFF the events con-taining a jet have a lower sphericity value. This indicatesthat multi-parton interactions do not play a major role atRHIC energies.To better quantify the effect of making a selection in π T on the number of jets in the sample, the respective distribu-tions for the highest of the most pencil- and sphere-likeevents are integrated and the fraction of each to the inclusivedistribution is calculated. The results of this calculation aregiven in Table 2. First, it shows that π + π β collisions havejets in all but . of the events, while this fraction ofnon-jet events rises to . and . for pp collisionsat β π = TeV with MPI-ON and MPI-OFF, respectively.Most of the π + π β collisions contain jets, followed by + jets. For pp collisions the majority of events do not containa jet, followed by single-jet events. These events are mostlikely events where one of the two jets is outside of the detec-tor acceptance, i.e. the majority of the higher π T constituenttracks have | π | > . In π + π β collisions the fraction of eventscontaining π jets = increases from . for all eventsto . for the most pencil-like events. It decreasesfrom . to . for pp collisions at β π = TeV withMPI-ON and slightly increases for the case with MPI-OFF.For the most sphere-like events, the fraction of eventswithout a jet in π + π β collisions increases from . for allevents to . in the most spherical-like events, followedby a sizeable contribution from π jets = + . Selecting onspherical events in pp collisions doesnβt change the fractionsof events that have a jet like it does for π + π β collisions, butshows an increase in π jets = from . to . for ppcollisions at β π = TeV with MPI-ON. As jets are so rarein pp collisions at β π = GeV, none of the selections havea significant effect on the π jets fractions. These results indi-cate that for π + π β collisions a selection on the sphericity isable to enhance a specific amount of jets within that sample,while for pp collisions there is no such strong correlation.Now, since the correlation between the shape of the eventand the number of reconstructed jets in pp collisions is ratherweak, it would be interesting to establish if there is anotherevent characteristic that correlates well with the event shape.The distributions of the π T of the leading parton within theevent for pencil-like and sphere-like events for π + π β , pp(MPI-OFF), and pp (MPI-ON) collisions are shown in Fig.2. Similar to the previous results, the most pencil-likeevents (low π T ) and most sphere-like events (high π T )are used to obtain the results. It indicates that selectingpencil- rather than sphere-like events leads to an increase ofthe mean π T of the leading parton of βΌ for π + π β colli-sions. This is consistent with the previous results presentedin Fig. 1, as multi-jet topologies correlate with higher valuesof π T . Interestingly, for pp collisions, the mean π T of theleading parton is larger for sphere-like events compared topencil-like events for the case with MPI-ON, while it is notthe case with MPI-OFF. This observation is consistent withthe conclusions taken from Table 2.The distributions for the number of multi-parton interac-tions for pp collisions (MPI-ON) are shown in Fig. 3, forpencil- and sphere-like events (left), as well as for the eventswith the lowest and highest final state particle multi-plicities (right). It shows that events with higher sphericityand higher multiplicity both increase the mean number ofmulti-parton interactions, which can be understood from theidea that sphericity correlates with multiplicity. Moreover, π MPI increases more when selecting the events with highestmultiplicity instead of the most sphere-like configuration,and also more strongly excludes lower π MPI . Thus, the multi-plicity of the event is found to be a better observable to selectevents with a larger number of multi-parton interactions inpp collisions. jets ( % ) , All π jets ( % ) , pencil-like π jets ( % ) , sphere-likeData Set energy MPI 0 1 2 3+ 0 1 2 3+ 0 1 2 3+ π + π β GeV β . . . . . . . . . . . . pp GeV ON > . < . < . < . > . < . < . < . > . < . < . < . pp GeV OFF > . < . < . < . > . . < . < . > . < . < . < . pp TeV ON . . . . . . . . . . . . pp TeV OFF . . . . . . . . . . . . Table 2: Percentage of events containing π jets = , , , + jets with πΈ > GeV, for ensembles of all events, the mostpencil-like events, and most sphere-like events as calculated using the transverse sphericity π T . CONCLUSIONS
The analysis presented in this paper investigates the re-lationship between the shape of the event, the number ofreconstructed jets, and other event characteristics such as theparticle multiplicity, π T of the leading parton, and the num-ber of multi-parton interactions. In Fig. 1 it is shown thatthe π T distributions are qualitatively different for π + π β andpp collisions, as most π + π β collisions produce a pencil-likeshape, while the particles produced in a pp collisions are onaverage in a more sphere-like configuration. Also, it turnsout that a large percentage of π + π β collisions contain a recon-structed jet, while this is not the case for pp collisions. Thecorrelation between the transverse sphericity π T and the num-ber of reconstructed jets in π + π β collisions enables the use ofthis observable to discriminate between di-jet and multi-jettopologies. Surprisingly, it turns out that in pp collisions(MPI-ON) π T is not strongly correlated to π jets , as any selec-tion in π T results in a sample dominated by π jets = . Thus,these results suggest that pp collisions with a pencil-likeshape are by no means more jet-like compared to eventswithout a selection on their shape.Furthermore, the results shown in Fig. 3 indicate a strongcorrelation between π T and the number of multi-parton in-teractions. The average number of these interactions in-creases relatively more for pp collisions at β π = TeVcompared to pp collisions at β π = GeV. However, asFig. 3 (right) shows, the mean number of multi-parton in-teractions increase even more between events with low andhigh multiplicities. These observations are consistent withthe idea that π T correlates with the particle multiplicity, i.e.a large number of multi-parton interactions lead to a moresphere-like configuration with increased multiplicity. As itis experimentally impossible to directly measure the π MPI ,it would be very interesting to use π T , as well as the eventmultiplicity, to explore pp collisions with small and largeamounts of multi-parton interactions and compare them tomodel predictions. ACKNOWLEDGEMENTS
This work was supported by the Netherlands Organisationfor Scientific Research (NWO). This work was supported inpart by the Office of Nuclear Physics of the U.S. Departmentof Energy. Work supported by the US DOE under awardnumber DE-SC004168.
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10 1 T d S d N = 91 GeVs collisions, - e + ePYTHIA8.1 Inclusive = 0 jets
N = 1 jets
N = 2 jets
N = 3+ jets N T S - - - - - - - - - -
10 1 T d S d N = 200 GeVspp collisions, PYTHIA8.1MPI-ON Inclusive = 0 jets
N = 1 jets
N = 2 jets
N = 3+ jets N T S - - - - - - - - - -
10 1 T d S d N = 200 GeVspp collisions, PYTHIA8.1MPI-OFF Inclusive = 0 jets
N = 1 jets
N = 2 jets
N = 3+ jets N T S - - - - -
10 1 T d S d N = 13 TeVspp collisions, PYTHIA8.1MPI-ON Inclusive = 0 jets
N = 1 jets
N = 2 jets
N = 3+ jets N T S - - - - -
10 1 T d S d N = 13 TeVspp collisions, PYTHIA8.1MPI-OFF Inclusive = 0 jets
N = 1 jets
N = 2 jets
N = 3+ jets N Figure 1: Transverse sphericity distributions ( π T ) for simulated π + π β and pp collisions (top left), and differentiated forthe amount of jets reconstructed in the events ( π jets = , , , +) for each respective dataset. The inclusive distributionsare normalized to unity. The inclusive and π jets = distributions for the pp collisions dataset at β π = GeV areindistinguishably close.
T,leading parton p - - -
10 1 T dpd N > = 41.0 GeV/c T ,
= 20.9 GeV/c T ,
= 0.9 GeV/c T ,
= 1.5 GeV/c T ,
T,leading parton p - - - - - T dpd N > = 1.2 GeV/c T ,
= 1.4 GeV/c T ,
T,leading parton p - - - T dpd N > = 3.8 GeV/c T ,
= 6.0 GeV/c T ,
T,leading parton p - - T dpd N > = 6.3 GeV/c T ,
= 4.9 GeV/c T ,
Figure 2: The distributions for the π T of the leading parton for pencil-like (low π T ) and sphere-like (high π T ) events, ascalculated for each respective dataset. The mean of each distribution is given in the figure. MPI N - - - -
10 1 M P I d N d N > = 0.5 MPI ,
MPI , MPI N - - - - 10 1 M P I d N d N > = 0.8 MPI Low Mult, MPI High Mult, MPI N - - - - 10 1 M P I d N d N > = 0.6 MPI , MPI , MPI N - - - - 10 1 M P I d N d N > = 0.9 MPI Low Mult, MPI High Mult, Figure 3: The distributions of the number of multi-parton interactions for pencil- and sphere-like events (left), as well asevents with low and high multiplicity (right), as calculated for simulated pp (MPI-ON) collisions at β π = GeV (top)and β π =13