Particle-level kinematic fingerprints and the multiplicity of neutral particles from low-energy strong interactions
aa r X i v : . [ h e p - ph ] D ec Particle-level kinematic fingerprints and the multiplicityof neutral particles from low-energy strong interactions
Federico Colecchia ∗ Brunel University London, Kingston Lane, Uxbridge UB8 3PH, UK
The contamination, or background, from uninteresting low-energy strong interactions is a majorissue for data analysis at the Large Hadron Collider. In the light of the challenges associated with theupcoming higher-luminosity scenarios, methods of assigning weights to individual particles have recentlystarted to be used with a view to rescaling the particle four-momentum vectors. We propose a differentapproach whereby the weights are instead employed to reshape the particle-level kinematic distributionsin the data. We use this method to estimate the number of neutral particles originating from low-energystrong interactions in different kinematic regions inside individual collision events. Given the parallelnature of this technique, we anticipate the possibility of using it as part of particle-by-particle eventfiltering procedures at the reconstruction level at future high-luminosity hadron collider experiments.
Keywords:
The subtraction of contamination from low-energyphysics processes described by Quantum Chromo-dynamics (QCD) is a critical task at the LargeHadron Collider (LHC). The impact of such a cor-rection is going to become even more significant inthe upcoming scenarios whereby the high-energyparton scattering of interest will be superimposedwith a higher number of low-energy interactionsassociated with collisions between other protons,the so-called pileup events.Pileup results in the presence of multiple ver-tices inside collision events, which often makes thestudy of rare processes particularly challenging.Subtraction techniques are well established, andtypically combine tracking information for charged particles with estimates of the energy flow asso-ciated with neutral particles that originate fromlow-energy QCD interactions [1]. However, whilethe information provided by the tracking detectorscan significantly ease the task of assigning chargedparticles a vertex of origin, that of associating neu-tral particles with a probability of their originatingfrom low-energy QCD interactions as opposed tothe high-energy parton scattering of interest is amuch harder task.A number of pileup subtraction techniqueshave been proposed over the years and are part ofthe core reconstruction pipelines at hadron colliderexperiments. With a view to achieving improvedperformance at higher luminosity, techniques thatwork at the level of individual particles inside col-lision events have recently been proposed [2, 3, 4]and are being evaluated at the LHC. In particular,particle weighting methods have been presentedwhereby individual particles are assigned a proba-bility for their origin in soft QCD interactions asopposed to the signal hard parton scattering. Theweights are typically used either to rescale the par- ∗ Email: [email protected] Whenever neutral particles are referred to in the text, neutrinos are not considered. BACKGROUND ticle four-momentum vectors [2] or in conjunctionwith multiple interpretations of the data [5].In this article, we propose a different approachwhereby the weights are instead employed to re-shape the particle-level kinematic distributions in-side individual collision events.We build on a view of events as mixtures of par-ticles originating from different physics processes,namely a signal hard parton scattering and back-ground low-energy strong interactions .Due to the quantum nature of the underly-ing physics, the kinematic distributions of parti-cles originating from a given process, e.g. fromlow-energy strong interactions, normally exhibit acertain degree of variability across collisions. Inother words, individual events can be associatedwith distinctive particle-level pileup kinematic pat-terns, or “fingerprints”, as discussed in section 5.4.We report on the use of this technique onsimulated data and show that our algorithm pro-duces reasonable estimates of the number of neu-tral pileup particles in different kinematic regionsinside events regardless of whether or not parti-cles originating from the hard parton scatteringare present. To our knowledge, this is the firstmethod of estimating how neutral pileup particlesare distributed in different kinematic regions insideindividual events thereby taking into account theinherent variability across collisions.We expect this technique to improve further onthe resolution of the missing transverse energy ,as well as on the estimates of particle isolation inhigher-luminosity regimes.Missing transverse energy plays an importantrole in a number of physics analysis scenarios atthe LHC, particularly with regard to searches fornew particles beyond the Standard Model, whichis the currently-accepted model of particle inter-actions. Notable examples are the search for DarkMatter candidates, i.e. for new particles that couldexplain ∼
85% of the mass of the universe currentlynot accounted for, as well as searches for new parti-cles predicted by the theory of supersymmetry and by theories that postulate the existence of extra di-mensions. Moreover, missing transverse energy isan essential ingredient in the study of a number ofStandard Model processes, such as the decay of therecently-discovered Higgs-like boson to pairs of τ leptons, as well as processes that involve W bosonsand top quarks in the final state.In our previous studies, we proposed the ideaof filtering individual events particle by particle atthe reconstruction level in order to improve on therejection of contamination from low-energy stronginteractions in high-luminosity hadron collider en-vironments. The algorithm that we describe in thisarticle is a simplified deterministic variant of theMarkov Chain Monte Carlo technique that we usedin [6, 7].It is our opinion that the simplicity and par-allelisation potential of this technique make it apromising candidate for inclusion in particle-by-particle event filtering procedures at the recon-struction level at future high-luminosity hadroncollider experiments.We see this algorithm as complementary to theparticle weighting methods that have been recentlyproposed at the LHC. Since our technique is basedon a different approach, we expect its combina-tion with state-of-the-art algorithms to result inimproved performance at higher pileup rates. Asmore particle weighting methods are proposed, wealso envisage the possibility of combining the dif-ferent weights, e.g. in the context of a multivariateframework, with a view to exploiting all the infor-mation available in the data at the level of individ-ual particles. Historically, methods of subtracting contaminationfrom soft QCD interactions have been developedwith a view to correcting observables associatedwith hard jets, i.e. with collections of final-stateparticles produced by the showering and hadroni-sation of scattered high-energy partons. It is worth noticing that, while the idea of assigning individual particles a single process of origin is per se conceptuallyflawed in hadron collider environments due to the presence of colour connection, the use of particle weights provides therequired flexibility in interpreting the origin of individual particles. Missing transverse energy is the event-level energy imbalance measured on a plane perpendicular to the direction of thecolliding particle beams. THE APPROACH
The state of the art includes a number of tech-niques that are often based on different principles,and that are typically used in combination at theATLAS and CMS experiments at the LHC.In this context, an important role is played bycorrection procedures that relate to the concept ofjet area [8], which provides a measure of the sus-ceptibility of jets to contamination from low-energyparticles. A core ingredient of jet area-based algo-rithms is the estimation of an event-level soft QCDtransverse momentum density based on the pileupjets in the event. With such methods, which arecore ingredients of the official reconstruction andanalysis pipelines at the LHC, the correction ap-plied to the total transverse momentum of a hardjet of interest is proportional both to the jet areaand to an estimate of the soft QCD transverse mo-mentum density in the event. However, techniquesbased on jet area are not designed to describe dif-ferences in soft QCD energy flow between differentkinematic regions inside collision events, and theupcoming high-luminosity regimes are likely to callfor the development of dedicated methods.With the introduction of jet substructure tech-niques, soft QCD contamination started to bestudied in terms of individual components insidehard jets, thereby exploiting the hierarchical struc-ture of jets. This has resulted in an importantsuite of new tools for reconstruction and analysisat the LHC, particularly with regard to jet groom-ing [9, 10, 11, 12, 13] and jet cleansing [14].In general terms, the algorithmic evolution out-lined above has gradually moved toward more “lo-cal” estimates of soft QCD contamination that takeinto account the variability across collisions as wellas inhomogeneity inside individual events. Thishas ultimately led to the development of methodsworking at the level of individual particles as themost fine-grained level of information available inthe data. Notable examples are PUPPI [1, 2], Soft-Killer [3] and the particle-level technique presentedin [4].For instance, PUPPI exploits the existence ofcollinear singularities in the physics that underlies the showering process. This makes it possible toassign individual particles weights that reflect thelikelihood of them originating from the hard par-ton scattering as opposed to soft QCD interactions.Specifically, the weights rely on a measure of prox-imity between particles in a space defined in termsof particle transverse momentum, p T , pseudorapid-ity , η , and azimuthal angle, ϕ . The probability density functions (PDFs) that de-scribe the kinematics of particles originating fromsoft QCD interactions as opposed to a hard par-ton scattering reflect the properties of the under-lying physics processes, and describe the expectedshapes of the corresponding particle-level distribu-tions. However, even when the processes involvedare exactly the same, individual collision eventscontain independent, and therefore different, real-isations of the underlying quantum processes, andthe shapes of the corresponding particle-level dis-tributions are for this reason generally different indifferent events. In other words, the shape of thekinematic distribution of particles originating fromsoft QCD interactions is generally event-specific,i.e. each event can in principle be associated withits own particle-level soft QCD kinematic “finger-print”.A key aspect of our approach is the idea of us-ing the particle weights to estimate the shape ofthe soft QCD kinematic distribution in terms ofparticle η and p T inside individual events, therebytaking into account the inherent variability acrosscollisions due to the presence of statistical fluctua-tions in the data. Given an estimate of the neutralsoft QCD particle fraction in each event, this isequivalent to estimating the corresponding numberof neutral soft QCD particles in different ( η, p T ) bins.Although the actual numbers of particles orig-inating from background soft QCD interactionsas opposed to the signal hard scattering are notknown, given a signal model, it is possible to es- The transverse momentum, p T , of a particle is defined as the absolute value of the component of the particle momentumvector on a plane perpendicular to the direction of the colliding beams. Particle pseudorapidity, η is a kinematic quantity expressed in terms of the particle polar angle in the laboratory frameby η = − log [ tan ( θ/ . THE ALGORITHM timate the expected number of signal particles, ν s ( η, p T ) , in each ( η, p T ) region. On the otherhand, the expected number of background parti-cles normally cannot be estimated due to the non-perturbative nature of the underlying physics pro-cesses.If n ∗ s ( η, p T ) and n ∗ b ( η, p T ) denote the unknowntrue numbers of signal and background soft QCDparticles in each ( η, p T ) bin, then n ( η, p T ) = n ∗ s ( η, p T ) + n ∗ b ( η, p T ) , where n ( η, p T ) is the corre-sponding number of particles in the data. In gen-eral, whenever an event exhibits an excess of par-ticles in a given ( η, p T ) region as compared to theaverage number, it is not known to what extentthe excess originates from a soft QCD interactionas opposed to the hard scattering. However, whenone considers LHC events with a number of ver-tices in line with what is expected in the upcom-ing higher-luminosity regimes, the final-state par-ticle multiplicities associated with soft QCD back-ground interactions and with the signal hard scat-tering are such that the expected number of signalparticles is typically much lower than the numberof background particles, i.e. h ν s ( η, p T ) i ≪ h n ∗ b ( η, p T ) i , (1)where the average is taken over the ( η, p T ) space. This also implies that the statistical fluc-tuations on the number of particles in a given ( η, p T ) region are typically dominated by the fluc-tuations on the number of soft QCD particles, i.e. h σ n s ( η, p T ) i ≪ h σ n b ( η, p T ) i . Under such condi-tions, it is reasonable to express the estimatednumber of soft QCD particles in terms of ˆ n b ( η, p T ) ≃ n ( η, p T ) − ν s ( η, p T ) (2)In the following, we estimate the shape of theparticle-level ( η, p T ) distribution of neutral softQCD particles inside individual events using anevent-level estimate of the neutral soft QCD par-ticle fraction, as well as PDF templates obtainedfrom high-statistics control samples. The proce-dure is outlined below:1. Control samples are first used to estimatethe shapes of the expected ( η , p T ) distribu- tions of neutral final-state particles originat-ing from soft QCD interactions and from thesignal hard parton scattering. Such distri-butions reflect the properties of the underly-ing physics processes, and their shapes cor-respond to what is expected from an averageover multiple events.2. The overall fraction of neutral soft QCD par-ticles in each event is estimated based on thecorresponding charged particle fraction.3. The above information is used to defineweights that reflect the probability for indi-vidual particles to originate from soft QCDinteractions as opposed to the hard scatter-ing.4. The weights are employed to reshape theparticle-level ( η , p T ) distribution in the data,with a view to estimating the number of neu-tral soft QCD particles in different kinematicregions event by event. For the purpose of this study, the particle-level ( η, p T ) space is each event has been subdivided intobins of widths ∆ η = 0 . and ∆ p T = 0 . GeV/c.We focus on particles with < p T < GeV/c,which are the majority of those produced by softQCD interactions. The algorithm consists of thefollowing steps, along the lines discussed in the pre-vious section:1 Obtain the shapes of the particle-level ( η, p T ) PDFs from the high-statistics control sam-ples. In the following, f ( η, p T ) and f ( η, p T ) will denote the PDFs of neutral particles orig-inating from soft QCD interactions and fromthe signal hard scattering, respectively.2 In each event, estimate the overall fraction ofneutral soft QCD particles, α ( n )0 , in terms ofthe corresponding charged particle fraction, α ( c )0 : ˆ α ( n )0 = min ( kα ( c )0 , α ( c )0 ) (3) A similar line of reasoning applies to a depletion in the number of particles. RESULTS
The role of the correction factor k , which isestimated from Monte Carlo as described insection 5, is to correct on average for the dif-ference between neutral and charged particlekinematics. This includes a correction for thenumber of charged particles with p T below500 MeV/c that do not reach the tracking de-tectors. Taking the minimum in (3) ensuresthat ˆ α ( n )0 is always lower than 1.3 Combine the above information into particleweights: w ( η, p T ) = ˆ α ( n )0 f ( η, p T )ˆ α ( n )0 f ( η, p T ) + ˆ α ( n )1 f ( η, p T ) , (4)with α ( n )0 + α ( n )1 = 1 . The quantity w ( η, p T ) provides an estimate of the probability for in-dividual particles in each ( η, p T ) bin to orig-inate from soft QCD interactions as opposedto the hard parton scattering of interest.4 Use w ( η, p T ) to reshape the ( η, p T ) distri-bution of neutral particles in the data in or-der to estimate the distribution of neutralsoft QCD particles in each event. The ex-pected number of neutral soft QCD particles, ˆ n b ( η, p T ) , is estimated in terms of ˆ n b ( η, p T ) = w ( η, p T ) n ( η, p T ) , (5)where n ( η, p T ) is the corresponding numberof neutral particles in the data. Given the ex-pected number ˆ n b ( η, p T ) , the unknown num-ber of neutral soft QCD particles in each ( η, p T ) bin can be treated as a random vari-able following a binomial distribution withmean given by (5) and standard deviation σ ˆ n b = p nw (1 − w ) . (6)It should be noted that (5) is equivalent to(2) if one uses w to calculate ν s , i.e. if ν s /n = 1 − w .5 Estimate the number of neutral soft QCDparticles in each ( η, p T ) bin in terms of: ˆ n b = w n ± p nw (1 − w ) (7)It is worth noticing that the algorithm is in-herently parallel, since different bins can be pro-cessed independently. It is our opinion that thesimplicity and parallelisation potential of this tech-nique make it a promising candidate for inclusionin future particle-level event filtering proceduresupsteam of jet reconstruction at high-luminosityhadron collider experiments.In this article, we have used the weights de-fined in (4) to illustrate this approach. However, itshould be emphasised that the idea of employingthe weights to reshape the particle-level ( η, p T ) dis-tribution inside individual events does not requirethis choice of weights, and can in principle be usedin conjunction with any particle weighting proce-dure, as discussed in section 5.3. We discuss the results of a feasibility study of thisapproach on Monte Carlo data at the generatorlevel. We used Pythia 8.176 [15, 16] to generate1,000 events, each consisting of a gg → t ¯ t hard par-ton scattering at √ s = 14 TeV superimposed with50 soft QCD interactions to simulate the presenceof pileup.
We generated control sample data sets contain-ing ∼ , particles originating from the signal gg → t ¯ t hard scattering and ∼ , particlesassociated with background soft QCD interactions.These data sets were used to obtain the shapes ofthe ( η, p T ) PDFs of signal and background neu-tral particles. The latter reflect the particle-levelkinematic signatures of the underlying physics pro-cesses, from which the corresponding distributionsin the data generally deviate due to the presenceof statistical fluctuations.Figure 1 displays the corresponding ( η, p T ) dis-tributions of neutral soft QCD particles (a) and ofneutral particles from the hard scattering (b), eachnormalised to unit volume.5 .2 Event-by-event neutral particle fractions 5 RESULTS η -4-3-2-101234 [ G e V / c ] T p Control sample: backgroundControl sample: background (a) η -4-3-2-101234 [ G e V / c ] T p Control sample: signalControl sample: signal (b)
Figure 1: Particle-level ( η, p T ) distributions from the high-statistics control samples in the region − < η < , < p T < GeV/c, as described in the text. (a) Neutral soft QCD particles. (b) Neutral particles fromthe hard parton scattering. The plots have been rotated around the z axis in order to make the kinematicsignatures more clearly visible. One of the pieces of information required by thechoice of weights that we have made for the pur-pose of this study is an event-by-event estimate ofthe overall fraction of neutral particles originatingfrom soft QCD interactions.We estimate the neutral pileup particle fractionin each event in terms of the corresponding chargedfraction. We apply a correction factor, k , thatrepresents an average over multiple Monte Carloevents according to (3), i.e ˆ α ( n )0 = min ( k ˆ α ( c )0 , α ( c )0 ) ,where α ( n )0 and α ( c )0 are the overall neutral andcharged pileup particle fractions in the event, re-spectively. Specifically, the correction factor isgiven by k = < α MC,n /α MC,c > , where α MC,n ( α MC,c ) is the fraction of neutral (charged) pileupparticles estimated from Monte Carlo, and the av-erage is taken over the 1,000 events generated inthis study.Figure 2 displays the ratio between the fractionof neutral pileup particles and the correspondingquantity for charged particles in the events gen-erated. The results shown in the following have been obtained using k = 1 . , which correspondsto the mean of the distribution in figure 2. Multi-ple runs of the algorithm were performed whereby k was varied within 5% of its nominal value, andproduced consistent results. For the purpose of this study, the particle weightshave been defined as a function of the fraction ofneutral soft QCD particles in each event as wellas of the control sample PDF templates, accordingto (4). To our knowledge, this is the first par-ticle weighting method that directly exploits theparticle-level kinematic signatures of the underly-ing physics processes in the ( η, p T ) space. We seethis choice of weights as complementary to thoseadopted in the recently-proposed algorithms thatuse measures of proximity between particles de-fined in terms of particle p T , η and ϕ .According to the above choice of weights, allparticles in the same ( η, p T ) bin are assigned thesame weight. However, as previously noticed, theidea of employing the weights to reshape the dis-tribution in the data is more general and can inprinciple be used in conjunction with any parti-6 .4 Soft QCD kinematic fingerprints 5 RESULTS c0 α / n0 α Entries 1000Mean 1.019RMS 0.009662
Figure 2: Distribution of the ra-tio between the fraction of neutralsoft QCD particles and the corre-sponding fraction of charged par-ticles, α MC,n /α MC,c from MonteCarlo, over the events generated inthis study. Additional informationis given in the text.cle weighting method. In fact, if S ( η, p T ) denotesthe set of particles in each ( η, p T ) bin in the dataand n ( η, p T ) the corresponding particle multiplic-ity, rescaling n ( η, p T ) by P i ∈ S ( η,p T ) w i /n ( η, p T ) re-duces to (5) when w i ≡ w ( η, p T ) .In other words, rescaling the ( η, p T ) distribu-tion in the data in order to estimate the numberof soft QCD particles across the particle kinematicspace is equivalent to setting the bin contents to afunction of the data that is given by P i ∈ S ( η,p T ) w i .If it were known which particles in the event origi-nate from the hard scattering and which from softQCD interactions, the weights would be either 0or 1. With reference to those ( η, p T ) bins thatcontain no signal particles, i.e. where all particlesin the bin originate from soft QCD interactions, w i ≡ w ( η, p T ) = 1 and P i ∈ S ( η,p T ) w i = n ∗ b ( η, p T ) .With regard to those bins, the problem of estimat-ing the number of soft QCD particles becomes triv-ial, and ˆ n b ( η, p T ) = n ( η, p T ) . Correspondingly, theuncertainty associated with the estimated numberof soft QCD particles, according to (6), becomeszero.In reality, it is only possible to estimate a prob-ability for individual particles to originate from ei-ther process, also in the light of the role playedby colour connection, and w i ∈ [0 , . The resultspresented in the following show that our methodproduces reasonable estimates of the number ofneutral soft QCD particles in different ( η, p T ) binsregardless of whether or not particles originatingfrom the signal hard scattering are present. In general, the accuracy of ˆ n b ( η, p T ) is expected toincrease with increasing accuracy of the weights.It is worth noticing that the use of w ( η, p T ) is associated with a relatively coarse-grained de-composition of the ( η, p T ) space, particularly alongthe η axis. However, as mentioned above, we arenot proposing to use these weights in isolation,but rather in combination with other particle-levelmetrics, such as those presented in [2].It should also be emphasised that w ( η, p T ) encodes properties of the underlying physics pro-cesses that are not employed by other meth-ods, and we expect the combined use of differ-ent weights to be beneficial. For instance, someof the results presented in [2] seem to suggestover-subtraction of soft QCD particles, wherebyparticles originating from the hard scattering areerroneously misidentified as pileup-related. Weforesee the possibility of implementing optimisedparticle weighting algorithms that make use ofall the particle-level information available in thedata, thereby further improving on the perfor-mance of pileup subtraction in high-luminosity en-vironments. A key aspect of our approach is the use of bin-by-bin estimates of the neutral soft QCD particle frac-tions in order to estimate how the correspondingparticles are distributed across the ( η, p T ) spacein each event. This method therefore takes into7 .5 Soft QCD particle counting 5 RESULTS account the variability of the shape of the softQCD particle distribution across collisions, i.e. itenables the estimation of event-specific soft QCDkinematic “fingerprints” at the particle level.The performance of the algorithm is illustratedin the following with regard to one of the MonteCarlo events generated in this study, chosen as areference. Consistent results were obtained on allevents analysed.Figure 3 (a) displays the true particle-level( η , p T ) distribution of neutral soft QCD particlesin the reference event. As shown by a compari-son with the corresponding high-statistics controlsample distribution in figure 1 (a), the particle-level ( η, p T ) soft QCD distribution inside individ-ual events generally exhibits local features that arewashed out when multiple events are lumped to-gether. We illustrate here the proposed use of particleweights to reshape the particle-level ( η, p T ) distri-bution in the data, using the weights defined insection 5.3 as an example. The objective is to es-timate ˆ n b ( η, p T ) , which describes how soft QCDneutral particles are distributed across the ( η, p T ) space inside individual events. A tentative esti-mate could in principle be obtained using the con-trol sample ( η, p T ) PDF templates, f and f , interms of N ( n ) α ( n )0 f ( η, p T ) α ( n )0 f ( η, p T ) + α ( n )0 f ( η, p T ) , (8)where N ( n ) is the total number of neutral par-ticles in the event. However, although this relieson an event-by-event estimate of the neutral softQCD particle fraction, it cannot account for the in-homogeneity of the distribution of soft QCD par-ticles that is typically observed inside individualevents.If the unknown true probability densities for aparticle with transverse momentum p T and pseu-dorapidity η to originate from the signal hard scat-tering and from background soft QCD interac-tions are denoted by f ∗ ( η, p T ) and f ∗ ( η, p T ) , the true fractions of background and signal particlesinside each ( η, p T ) bin are f ∗ ( η, p T )∆ η ∆ p T and f ∗ ( η, p T )∆ η ∆ p T , respectively, where ∆ η and ∆ p T are the widths of the bins along the η and p T axes.In reality, f ∗ and f ∗ are not known, and we usethe corresponding control sample PDF templatesin (4) to estimate the local fractions of soft QCDparticles.If the unknown true number of soft QCD par-ticles, n ∗ b ( η, p T ) , is higher than the correspondingaverage number due to fluctuations in the data,a fraction w ( η, p T ) of the excess will add to theestimated number of neutral soft QCD particlesin that ( η, p T ) bin. At the same time, a fraction − w ( η, p T ) will be associated with the hard par-ton scattering. A similar line of reasoning can beapplied to a situation whereby fluctuations lead toa depletion in terms of the number of soft QCDparticles with respect to the average. In otherwords, ˆ n b ( η, p T ) is generally expected to reflect thetrue distribution n ∗ b ( η, p T ) more accurately than(8).While ˆ n b ( η, p T ) represents the expected num-ber of neutral soft QCD particles, the unknownactual number can be treated as a random vari-able following a binomial distribution with mean n ( η, p T ) w ( η, p T ) and standard deviation given by(6). The estimated ( η, p T ) distribution of neutralsoft QCD particles in the event chosen to illus-trate our method is shown in figure 3 (b). As canbe seen, the local features of the distribution dueto the presence of fluctuations in the data are rea-sonably described, e.g. the excess at η ≃ . and p T ≃ . GeV/c.The same results are shown in figure 4, wherethe estimated number of soft QCD particlesacross the ( η, p T ) space is superimposed with aheatmap corresponding to the relative uncertaintyon ˆ n b ( η, p T ) . As expected, the uncertainty ishigher in lower-statistics bins, i.e. w is a morereliable estimate of the local fraction of soft QCDparticles in more highly-populated bins.Based on these results, we expect the use ofthis technique in conjunction with the recently-proposed particle weighting methods to be partic-ularly beneficial in the region p T < MeV/c,which contains most of the particles originatingfrom soft QCD interactions.8 .5 Soft QCD particle counting 5 RESULTS η -4-3-2-101234 [ G e V / c ] T p Monte Carlo truth: backgroundMonte Carlo truth: background (a) η -4-3-2-101234 [ G e V / c ] T p Estimated distribution: backgroundEstimated distribution: background (b)
Figure 3: (a) True particle-level ( η, p T ) distribution of neutral soft QCD particles from one of the MonteCarlo events generated in this study. The plot highlights the deviation of the shape of the distributionfrom that of the corresponding control sample template due to the presence of statistical fluctuations inthe data. (b) The corresponding particle-level ( η, p T ) distribution of neutral soft QCD particles estimatedusing this algorithm as detailed in the text. η -4-3-2-101234 [ G e V / c ] T p Control sample background weights, w Control sample background weights, w (a) η -5 -4 -3 -2 -1 0 1 2 3 4 5 [ G e V / c ] T p (%) b n/ b n σ
19 23 20 21 37 23 29 16 31 34 26 21 16 21 22 25 19 26 12 12 16 13 23 22 21 19 37 22 32 29 32 34 16 43 36 33 28 24 20 24 18 14 19 23 25 26 21 24 21 29 16 29 28 26 30 20 16 18 20 16 16 16 18 18 19 18 18 17 18 15 28 18 15 9 16 11 14 10 16 13 6 9 8 16 10 12 13 17 17 16 15 12 12 14 7 10 13 16 15 11 3 8 9 10 11 8 10 8 8 13 11 18 13 12 7 10 8 3 9 11 2 7 3 7 7 8 7 6 6 13 9 8 16 6 10 10 7 6 6 4 6 5 1 4 5 12 12 12 6 13 8 6 12 8 9 5 5 6 6 4 4 2 10 3 2 5 7 5 7 5 10 7 3 3 8 4 4 8 7 1 4 3 6 3 3 3 4 7 6 4 2 8 1 8 9 4 5 4 3 1 1 2 4 3 6 9 1 4 6 2 8 4 2 4 3 3 4 2 5 3 1 3 3 4 1 4 4 4 4 3 2 1 3 4 1 1 2 1 1 2 3 7 2 2 2 2 3 2 5 3 3 2 2 1 1 2 2 1 1 2 2 5 3 4 2 1 4 2 4 1 3 2 1 1 2 1 2 1 3 2 2 3 2 2 3 2 3 2 1 3 1 2 3 3 4 2 1 2 3 2 1 1 3 2 2 1 1 1 2 1 4 2 2 1 2 1 1 1 2 2 1 1 1 1 1 1 5 2 3 1 3 1 1 1 1 2 3 1 1 5 2 4 2 2 1 1 2 2 1 2 1 2 1 1 1 1 1 1 (%) b n/ b n σ (b) Figure 4: (a) Particle weights as defined in the text. (b) Relative uncertainty on the estimated numberof neutral soft QCD particles, σ ˆ n b / ˆ n b , represented as a heatmap superimposed to ˆ n b ( η, p T ) . Additionalinformation is provided in the text. 9 .5 Soft QCD particle counting 5 RESULTS η -4 -2 0 2 40.40.60.811.21.41.6 < 0.05 GeV/c T Control sample / truth: 0 < p < 0.05 GeV/c T Control sample / truth: 0 < p (a) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.1 GeV/c T Control sample / truth: 0.05 GeV/c < p < 0.1 GeV/c T Control sample / truth: 0.05 GeV/c < p (b) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.15 GeV/c T Control sample / truth: 0.1 GeV/c < p < 0.15 GeV/c T Control sample / truth: 0.1 GeV/c < p (c) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.2 GeV/c T Control sample / truth: 0.15 GeV/c < p < 0.2 GeV/c T Control sample / truth: 0.15 GeV/c < p (d) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.25 GeV/c T Control sample / truth: 0.2 GeV/c < p < 0.25 GeV/c T Control sample / truth: 0.2 GeV/c < p (e) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.3 GeV/c T Control sample / truth: 0.25 GeV/c < p < 0.3 GeV/c T Control sample / truth: 0.25 GeV/c < p (f) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.35 GeV/c T Control sample / truth: 0.3 GeV/c < p < 0.35 GeV/c T Control sample / truth: 0.3 GeV/c < p (g) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.4 GeV/c T Control sample / truth: 0.35 GeV/c < p < 0.4 GeV/c T Control sample / truth: 0.35 GeV/c < p (h) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.45 GeV/c T Control sample / truth: 0.4 GeV/c < p < 0.45 GeV/c T Control sample / truth: 0.4 GeV/c < p (i) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.5 GeV/c T Control sample / truth: 0.45 GeV/c < p < 0.5 GeV/c T Control sample / truth: 0.45 GeV/c < p (j)
Figure 5: Ratio between the control sample and the true ( η, p T ) distribution of neutral soft QCD particlesas a function of particle η . The ratios are shown in different p T bins in the region < p T < . GeV/c.The distributions are normalised to unit volume. The error bars correspond to one Poisson standard de-viation on the control sample bin contents as described in the text. (a) < p T < . GeV/c. (b) . GeV/c < p T < . GeV/c. (c) . GeV/c < p T < . GeV/c. (d) . GeV/c < p T < . GeV/c. (e) . GeV/c < p T < . GeV/c. (f) . GeV/c < p T < . GeV/c. (g) . GeV/c < p T < . GeV/c. (h) . GeV/c < p T < . GeV/c. (i) . GeV/c < p T < . GeV/c. (j) . GeV/c < p T < . GeV/c.10 .6 Missing transverse energy resolution 5 RESULTS
In order to verify the agreement between theshapes of the estimated and of the true ( η, p T ) dis-tributions of neutral soft QCD particles, we com-pared the estimated distribution to the true oneusing Monte Carlo truth information in different p T bins. Figure 5 displays the ratio between thecontrol sample ( η, p T ) distribution of neutral softQCD particles and the corresponding true distribu-tion in the reference event as a function of particle η in p T bins of width 0.05 GeV/c between 0 and0.5 GeV/c. The error bars correspond to one Pois-son standard deviation on the number of particlesin the control sample. The plots highlight the ef-fect of statistical fluctuations in the data, which areresponsible for the observed discrepancies betweenthe shapes of the particle-level distributions insideindividual events and the “average” shape that cor-responds to the high-statistics control sample.The corresponding ratio between the estimatedand the true distribution in the reference event isdisplayed in figure 6, which shows a significantly-improved agreement. The error bars are calculatedbased on (6).Table 1 further illustrates the performance ofthis technique on the same event presented in theplots. The figures in the table correspond to binswith < p T < . GeV/c and | η | ≤ . with atleast two particles in the data, i.e. n ( η, p T ) ≥ .The columns correspond to the centres of the η and p T bins, to n ∗ s , n ∗ b , w , ˆ n b , σ ˆ n b , ∆ w = w − w ∗ , andto p T ∆ w .As pointed out in section 5.3, although this ap-proach is being presented with reference to sce-narios where the number of signal particles is onaverage much lower than the number of soft QCDparticles, the task of estimating the latter becomestrivial in the limit where the number of signal par-ticles is zero, since in that case w ( η, p T ) = 1 and ˆ n b ( η, p T ) = n ∗ ( η, p T ) . However, in practice, it isnot known which bins contain particles originatingfrom the signal hard scattering and which do not.With a view to verifying that our results aremore accurate than those that would be obtainedif the presence of signal particles in the data wasneglected, the deviation of the estimated numberof neutral soft QCD particles from the correspond-ing true value, ∆ˆ n b = ˆ n b − n ∗ b , was compared tothe true number of signal particles, n ∗ s . Figure 7 displays | ∆ˆ n b | /n ∗ s in those bins that contain morethan 1 particle in the data, at least one of whichoriginating from the signal hard scattering. Theabsolute difference between the estimated numberof neutral soft QCD particles and the unknowntrue number averaged over the events analysed inthis study was found to be h| ∆ˆ n b |i avg ≃ . , where h·i denotes the average over those bins that con-tain at least 1 background particle, and the sub-script “ avg ” refers to the average over the events.The average absolute error on ˆ n b on the data setanalysed was therefore found to be lower than 1particle.It should also be emphasised that, although weare not explicitly proposing our algorithm with ref-erence to pileup subtraction inside jets, we alsoenvisage the possibility of combining this methodwith state-of-the-art jet calibration techniques, e.g.using local estimates of neutral pileup particle mul-tiplicity as constraints in jet substructure algo-rithms. In this section, we employ a similar approach to [2]whereby the weights are used to rescale the particlefour-momentum vectors, with a view to assessingthe impact of the weights defined in section 5.3 onthe resolution of the missing transverse energy, /E T .A full analysis of the impact on /E T resolutionat the LHC is outside the scope of this article. Weare here providing a preliminary estimate concen-trating on the effect of pileup, assuming 50 verticesper event.It is worth recalling that the measurement of /E T relies on information that is provided by in-dependent sources, such as the calorimeters, thetrackers and the muon subdetectors, and that itis sensitive both to pileup contamination and tobeam-induced effects [17].In particular, /E T is one of the observables thatare most significantly affected by contaminationfrom soft QCD interactions at hadron colliders. Itis estimated that each additional pileup interactionat the LHC adds . ÷ . GeV in quadrature tothe Particle Flow /E T resolution and, although ex-isting methods have been shown to be extremely11 .6 Missing transverse energy resolution 5 RESULTS η -4 -2 0 2 40.40.60.811.21.41.6 < 0.05 GeV/c T Estimated / truth: 0 < p < 0.05 GeV/c T Estimated / truth: 0 < p (a) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.1 GeV/c T Estimated / truth: 0.05 GeV/c < p < 0.1 GeV/c T Estimated / truth: 0.05 GeV/c < p (b) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.15 GeV/c T Estimated / truth: 0.1 GeV/c < p < 0.15 GeV/c T Estimated / truth: 0.1 GeV/c < p (c) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.2 GeV/c T Estimated / truth: 0.15 GeV/c < p < 0.2 GeV/c T Estimated / truth: 0.15 GeV/c < p (d) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.25 GeV/c T Estimated / truth: 0.2 GeV/c < p < 0.25 GeV/c T Estimated / truth: 0.2 GeV/c < p (e) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.3 GeV/c T Estimated / truth: 0.25 GeV/c < p < 0.3 GeV/c T Estimated / truth: 0.25 GeV/c < p (f) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.35 GeV/c T Estimated / truth: 0.3 GeV/c < p < 0.35 GeV/c T Estimated / truth: 0.3 GeV/c < p (g) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.4 GeV/c T Estimated / truth: 0.35 GeV/c < p < 0.4 GeV/c T Estimated / truth: 0.35 GeV/c < p (h) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.45 GeV/c T Estimated / truth: 0.4 GeV/c < p < 0.45 GeV/c T Estimated / truth: 0.4 GeV/c < p (i) η -4 -2 0 2 40.40.60.811.21.41.6 < 0.5 GeV/c T Estimated / truth: 0.45 GeV/c < p < 0.5 GeV/c T Estimated / truth: 0.45 GeV/c < p (j)
Figure 6: Ratio between the estimated ( η, p T ) distribution of neutral soft QCD particles and the corre-sponding true distribution. The ratios are shown in different p T bins of width 0.05 GeV/c in the region < p T < . GeV/c. The distributions are normalised to unit volume. The error bars correspond to onebinomial standard deviation on the bin contents as described in the text. (a) < p T < . GeV/c. (b) . GeV/c < p T < . GeV/c. (c) . GeV/c < p T < . GeV/c. (d) . GeV/c < p T < . GeV/c. (e) . GeV/c < p T < . GeV/c. (f) . GeV/c < p T < . GeV/c. (g) . GeV/c < p T < . GeV/c. (h) . GeV/c < p T < . GeV/c. (i) . GeV/c < p T < . GeV/c. (j) . GeV/c < p T < . GeV/c.12 .6 Missing transverse energy resolution 5 RESULTS
Table 1: Subset of the results obtained on the event chosen to illustrate the performance of this technique.The figures correspond to ( η, p T ) bins with < p T < . GeV/c and | η | ≤ . , and with at least twoparticles in the data, i.e. n ( η, p T ) ≥ . The columns correspond to the centres of the η and p T bins, to n ∗ s , n ∗ b , w , ˆ n b , σ ˆ n b , ∆ w , and p T ∆ w . η p T (GeV/c) n ∗ s n ∗ b w ˆ n b σ ˆ n b ∆ w p T ∆ w (GeV/c)-2.25 0.025 3 20 0.946 21.7 1.1 0.022 0.0005-2.25 0.075 3 16 0.946 18 1 0.039 0.0029-2.25 0.125 2 24 0.945 24.6 1.2 -0.011 -0.0014-1.75 0.025 4 25 0.938 27.2 1.3 0.019 0.0005-1.75 0.075 3 34 0.945 35 1.4 -0.009 -0.0007-1.75 0.125 3 18 0.939 19.7 1.1 0.023 0.0029-1.25 0.025 4 12 0.938 15 1 0.093 0.0023-1.25 0.075 2 20 0.94 20.7 1.1 -0.008 -0.0006-1.25 0.125 2 22 0.937 22.5 1.2 -0.016 -0.002-0.75 0.025 3 28 0.937 29 1.4 -0.007 -0.0002-0.75 0.075 3 29 0.935 29.9 1.4 -0.011 -0.0008-0.75 0.125 5 16 0.933 19.6 1.1 0.08 0.01-0.25 0.025 2 32 0.937 31.9 1.4 -0.03 -0.0007-0.25 0.075 3 26 0.935 27.1 1.3 -0.005 -0.0004-0.25 0.125 1 28 0.934 27.1 1.3 -0.047 -0.00590.25 0.025 4 22 0.935 24.3 1.3 0.026 0.00060.25 0.075 3 29 0.933 29.9 1.4 -0.013 -0.0010.25 0.125 2 14 0.932 14.9 1 0.005 0.00060.75 0.025 4 17 0.933 19.6 1.1 0.048 0.00120.75 0.075 4 30 0.94 31.9 1.4 0.008 0.00060.75 0.125 2 27 0.936 27.2 1.3 -0.024 -0.00311.25 0.025 1 15 0.939 15 1 -0.026 -0.00061.25 0.075 4 12 0.943 15.1 0.9 0.098 0.00731.25 0.125 5 23 0.941 26.3 1.2 0.048 0.0061.75 0.025 3 18 0.939 19.7 1.1 0.023 0.00061.75 0.075 3 40 0.943 40.6 1.5 -0.017 -0.00131.75 0.125 2 24 0.944 24.6 1.2 -0.012 -0.00152.25 0.025 2 20 0.941 20.7 1.1 -0.006 -0.00022.25 0.075 2 34 0.945 34 1.4 -0.023 -0.00172.25 0.125 2 28 0.944 28.3 1.3 -0.019 -0.002313 .6 Missing transverse energy resolution 5 RESULTS η -5 -4 -3 -2 -1 0 1 2 3 4 5 [ G e V / c ] T p
1 1 5 3 4 4 3 2 4 4 1 3 2 1 3 1 2 2 1 1 2 3 3 2 3 3 3 4 4 3 2 2 1 1 1 5 1 1 4 2 3 2 5 1 2 2 5 2 2 1 4 3 2 3 1 3 1 3 4 2 1 3 3 1 2 1 3 4 4 3 1 1 2 1 3 1 3 1 1 2 1 2 4 1 1 1 2 1 1 1 2 1 2 1 2 3 1 2 2 1 2 2 1 1 2 3 2 1 1 1 1 2 2 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1 2 1 1 1 1 2 3 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
Figure 7: True number of parti-cles originating from the signal hardscattering, n ∗ s ( η, p T ) , superimposedwith a heatmap corresponding to | ∆ˆ n b | /n ∗ s in those bins that con-tain more than one particle in thedata, at least one of which originat-ing from the signal hard scattering.Additional information is given inthe text. η -5 -4 -3 -2 -1 0 1 2 3 4 5 ( G e V / c ) T p | (MeV/c) T p ∆ |
19 23 20 21 37 23 29 16 31 34 26 21 16 21 22 25 19 26 12 12 16 13 23 22 21 19 37 22 32 29 32 34 16 43 36 33 28 24 20 24 18 14 19 23 25 26 21 24 21 29 16 29 28 26 30 20 16 18 20 16 16 16 18 18 19 18 18 17 18 15 28 18 15 9 16 11 14 10 16 13 6 9 8 16 10 12 13 17 17 16 15 12 12 14 7 10 13 16 15 11 3 8 9 10 11 8 10 8 8 13 11 18 13 12 7 10 8 3 9 11 2 7 3 7 7 8 7 6 6 13 9 8 16 6 10 10 7 6 6 4 6 5 1 4 5 12 12 12 6 13 8 6 12 8 9 5 5 6 6 4 4 2 10 3 2 5 7 5 7 5 10 7 3 3 8 4 4 8 7 1 4 3 6 3 3 3 4 7 6 4 2 8 1 8 9 4 5 4 3 1 1 2 4 3 6 9 1 4 6 2 8 4 2 4 3 3 4 2 5 3 1 3 3 4 1 4 4 4 4 3 2 1 3 4 1 1 2 1 1 2 3 7 2 2 2 2 3 2 5 3 3 2 2 1 1 2 2 1 1 2 2 5 3 4 2 1 4 2 4 1 3 2 1 1 2 1 2 1 3 2 2 3 2 2 3 2 3 2 1 3 1 2 3 3 4 2 1 2 3 2 1 1 3 2 2 1 1 1 2 1 4 2 2 1 2 1 1 1 2 2 1 1 1 1 1 1 5 2 3 1 3 1 1 1 1 2 3 1 1 5 2 4 2 2 1 1 2 2 1 2 1 2 1 1 1 1 1 1 (a) |> (GeV/c) T p ∆ <| Entries 1000Mean 0.02059RMS 0.004436 (b)
Figure 8: (a) Absolute difference between the estimated and the true particle weight multiplied by the par-ticle p T , | ∆ p T | , shown as a heatmap superimposed to the estimated number of neutral soft QCD particles, ˆ n b ( η, p T ) . As expected, the rescaled particle p T , w p T , is a better estimate of the true value in the low- p T region, which is more densely populated by soft QCD particles. (b) Distribution of the average | ∆ p T | , h| ∆ p T |i , over the events analysed in this study. The average is weighted with the number of particles inthe data, n ( η, p T ) , and is taken over the ( η, p T ) space. Additional information is provided in the text.14 CONCLUSIONS AND OUTLOOK useful below 35 vertices per event [1], there is still amargin for improvement. Moreover, it is not clearwhat the performance of the existing techniques isgoing to be like as the number of vertices per eventincreases.The pileup-related contribution to the /E T res-olution associated with the use of the weights de-fined in section 5.3 is a function of the deviationof w ( η, p T ) from the corresponding true value, w ∗ ( η, p T ) . Specifically, when w ( η, p T ) is usedto rescale the four-momentum of a particle withtransverse momentum p T , a deviation of the weightfrom its true value results in a fraction of the parti-cle p T being assigned to the wrong physics process.If ∆ w ( η, p T ) = w ( η, p T ) − w ∗ ( η, p T ) denotes thedeviation of the particle weight from its true value,the amount of incorrectly-assigned p T for that par-ticle is given by ∆ p T ( η, p T ) = p T ∆ w ( η, p T ) .Figure 8 (a) displays the estimated numberof neutral soft QCD particles across the ( η, p T ) space, superimposed with a heatmap correspond-ing to ∆ p T ( η, p T ) in MeV/c. A comparison withfigure 4 (b) shows that those bins that exhibit alower relative uncertainty on the estimated num-ber of soft QCD particles, σ ˆ n b / ˆ n b , also correspondto lower ∆ p T , as expected. It is worth noticingthat σ ˆ n b / ˆ n b = p (1 − w ) /nw does not dependon Monte Carlo truth information and can be esti-mated directly from the data. This makes it pos-sible to restrict the use of this technique to ( η, p T ) bins that are associated with a value of σ ˆ n b / ˆ n b lower than a predefined threshold.The quantity ∆ p T ( η, p T ) provides an estimateof the contribution of individual particles in theevent to the /E T resolution with reference to pileupcontamination. A preliminary estimate of the im-pact of ∆ w on the /E T resolution can be given interms of σ P U/E T ≃ √ N < σ ∆ pT > , where N is the to-tal number of particles in the event and < σ ∆ pT > is the standard deviation of ∆ p T ( η, p T ) averagedover the ( η, p T ) space. For the sake of an approxi-mate calculation, we assume < σ ∆ p T > ≃ σ < ∆ p T > .Figure 8 (b) shows the distribution of h ∆ p T ( η, p T ) i over the Monte Carlo events anal-ysed in this study. In each event, the average in h ∆ p T ( η, p T ) i is weighted with the number of par-ticles in the data, n ( η, p T ) , and is taken over the ( η, p T ) space. Assuming a total number of particlesin the event N ≃ , , the RMS of h ∆ p T ( η, p T ) i in figure 8 (b) leads to σ P U/E T ≃ . GeV/c. This is anotable improvement when compared to the stateof the art [17], and is in line with the results ob-tained using other particle weighting methods [2].It should be emphasised that the above remarksrelate to a generator-level study and exclusivelyconcentrate on the effect of pileup. While the lat-ter is a major source of concern in the upcominghigher-luminosity regimes at the LHC, a proper in-vestigation will also have to take into account otherfactors, such as detector effects, mis-reconstrution,beam-related events, and contamination from cos-mic muons. Moreover, a full investigation of thistechnique in a proper analysis framework will needto be performed.
We have presented a proof of concept of a newapproach to the use of particle weights at high-luminosity hadron collider experiments, a distinc-tive feature of which is the idea of employingthe weights to reshape the particle-level kinematicdistributions in the data. We have applied thismethod to the task of estimating the number ofneutral particles associated with pileup, i.e. withlow-energy strong interactions from other proton-proton collisions, in different kinematic regions in-side collision events. Pileup is a major source ofcontamination at the Large Hadron Collider, andits impact on physics analysis is expected to be-come even more significant in the upcoming higher-luminosity regimes.We build on a view of collision events as mix-tures of particles originating from different physicsprocesses, whereby the use of particle weights helpsresolve the conceptual issues associated with colourconnection.Because of the quantum nature of the under-lying physics processes, the kinematic patterns ofpileup particles are typically different in differentevents, i.e. individual events can be associatedwith distinctive pileup kinematic “fingerprints” atthe particle level. We have shown that our ap- Both charged and neutral EFERENCES REFERENCES proach makes it possible to estimate the numberof neutral pileup particles in different kinematicregions inside events with reasonable accuracy, re-gardless of whether or not particles originatingfrom the signal hard scattering are present. Sincethe estimates do not correspond to average num-bers of particles, but rather to the actual num-bers in each event, our approach takes into accountthe inherent variability across collisions due to thepresence of statistical fluctuations in the data.With regard to the reconstruction pipelinesof the experiments, we concentrate on a stagewhereby individual particles have not yet been as-signed to jets, i.e. to collections of final-state parti-cles originating from the same scattered hard par-ton.We expect the combined use of this tech-nique with existing methods to result in further-improved performance in terms of pileup subtrac-tion in higher-luminosity scenarios at the LargeHadron Collider, particularly with reference tothe contamination from low-energy neutral parti-cles. From a broader perspective, as more parti-cle weighting methods are proposed, we envisagethe possibility of combining the different weights,e.g. using multivariate techniques, with a viewto making use of all the information available inthe data with regard to which process individualparticles originated from. It is also our opinionthat the simplicity and parallelisation potentialof this algorithm make it a promising candidatefor inclusion in particle-level event filtering pro-cedures upstream of jet reconstruction at futurehigh-luminosity hadron collider experiments.We intend to investigate possible ways of im-proving on the performance of this method, as wellas to study more in detail the relation betweenthis algorithm and the Markov Chain Monte Carlotechnique that we used in a previous study wherewe proposed the idea of filtering individual colli-sion events on a particle-by-particle basis at high-luminosity hadron colliders.
Acknowledgments
The author wishes to thank the High EnergyPhysics Group at Brunel University London fora stimulating environment, and particularly Prof. Akram Khan, Prof. Peter Hobson and Dr. PaulKyberd for fruitful conversations, as well as Dr.Ivan Reid for help with technical issues. Particu-lar gratitude also goes to the High Energy PhysicsGroup at University College London, especially toProf. Jonathan Butterworth for his valuable com-ments. The author also wishes to thank Prof.Trevor Sweeting at the UCL Department of Statis-tical Science, as well as Dr. Alexandros Beskos atthe same department for fruitful discussions. Fi-nally, particular gratitude goes to Prof. CarstenPeterson and to Prof. Leif Lönnblad at the De-partment of Theoretical Physics, Lund University.
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