Particle-level pileup subtraction for jets and jet shapes

Abstract

We present an extension to the jet area-based pileup subtraction for both jet kinematics and jet shapes. A particle-level approach is explored whereby the jet constituents are corrected or removed using an extension of the methods currently being employed by the LHC experiments. Several jet shapes and nominal jet radii are used to assess the performance in simulated events with pileup levels equivalent to approximately 30 and 100 interactions per bunch crossing, which are characteristic of both the LHC Run I and Run II conditions. An improved performance in removing the pileup contributions is found when using the new subtraction method. The performance of the new procedure is also compared to other existing methods.

Published for SISSA by Springer

Received: March 26, 2014

Accepted: May 29, 2014 Published: June 16, 2014

Particle-level pileup subtraction for jets and jet shapes

Peter Berta,a Martin Spousta,a David W. Miller,b and Rupert Leitnera

aFaculty of Mathematics and Physics, Charles University in Prague, V Holeovikch 2, Prague, Czech Republic

bEnrico Fermi Institute, University of Chicago,

Chicago, IL, U.S.A.

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: We present an extension to the jet area-based pileup subtraction for both jet kinematics and jet shapes. A particle-level approach is explored whereby the jet constituents are corrected or removed using an extension of the methods currently being employed by the LHC experiments. Several jet shapes and nominal jet radii are used to assess the performance in simulated events with pileup levels equivalent to approximately 30 and 100 interactions per bunch crossing, which are characteristic of both the LHC Run I and Run II conditions. An improved performance in removing the pileup contributions is found when using the new subtraction method. The performance of the new procedure is also compared to other existing methods.

Keywords: Jet substructure, Jets, Hadron-Hadron Scattering, Event-by-event uctuation

ArXiv ePrint: 1403.3108

Open Access, c

[circlecopyrt] The Authors.

Article funded by SCOAP3. doi:http://dx.doi.org/10.1007/JHEP06(2014)092

Web End =10.1007/JHEP06(2014)092

JHEP06(2014)092

Contents

1 Introduction 1

2 Subtraction algorithm 2

3 Performance of the subtraction 53.1 Jet kinematics 63.2 Jet shape denitions 83.3 Jet shape subtraction 9

4 Conclusions 12

1 Introduction

The intense environment created by the high luminosity of the Large Hadron Collider (LHC) necessitates novel methods for isolating, mitigating, and, where possible, correcting for the contributions of multiple uncorrelated proton-proton interactions (pileup) to the measured hadronic nal state. Pileup has a substantial impact on both jet kinematics and substructure, thereby degrading critical tools for identifying new physics via highly boosted hadronic decays of W , Z, and Higgs bosons, or top quarks.

The last few years has seen the development of several e ective tools for pileup mitigation and removal. Simple subtraction techniques remove a constant o set from the measured transverse momentum that is proportional to the number of observed pileup events [1]. So-called grooming techniques such as ltering [2], pruning [3], and trimming [4], actively remove potential pileup constituents from jets. Other approaches, such as the jet cleansing method [5] or charged hadron subtraction [6], use tracking information to identify a given hadronic energy deposition with charged particles originating in pileup interactions.

Techniques that utilize event-by-event and jet-by-jet information to determine the extent of contamination from pileup provide a new approach to perform jet physics at very high luminosities. The area-based subtraction procedure [7] corrects the jet 4-momentum and it is extended to account for hadron masses in ref. [8]. The shape-expansion method [8] provides general approach to correct jet shapes.

The extension of the area-based subtraction procedure that we propose here allows for a particle-by-particle approach to this concept. We nd improved performance in removing the contributions due to pileup using this new procedure even for previously intractable jet shape observables (such as planar ow). Furthermore, this approach provides the possibility to perform pileup subtraction without explicit consideration of a specic jet algorithm, reducing the constraints and increasing the exibility of the jet area-based subtraction procedure overall. Therefore, this method may be used also in heavy ion physics where the jet reconstruction is challenging due to sizable underlying event [911].

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2 Subtraction algorithm

The novel feature of the approach described here is the local subtraction of pileup at the level of individual jet constituents. In contrast to the area-based subtraction and the shape-expansion method, the constituent-level subtraction is performed particle-by-particle, thereby correcting both the 4-momentum of the jet and its substructure, simultaneously. This is achieved by combining the kinematics of particles within a specic jet with the kinematics of soft negative particles that are added to balance the pileup contribution.

The basic ingredient of the particle-level subtraction is the pileup energy density estimation which is identical to that used in the shape-expansion method proposed in ref. [8]. The contamination due to pileup is described in terms of the transverse momentum density and mass density m. The expected pileup deposition in a small region of y is expressed by the 4-momentum

ppileup = [ cos , sin , ( + m) sinh y, ( + m) cosh y] [notdef] y , (2.1)

where the pileup pT and mass densities, and m, are assumed to be weakly dependent on rapidity y and azimuth . In the shape-expansion method, all particles (or e ective particles such as calorimeter towers [13] or clusters [14]) in the event are grouped into patches in order to estimate the densities used in eq. (2.1). The patches are dened by jets reconstructed using the kt algorithm [15, 16]. The transverse momentum, pTpatch, and mass, m patch, of each patch is determined by summing over all particles within that patch:

pTpatch =

Xi2patchpTi, m patch = Xi2patch

[parenleftbigg][radicalBig]

m2i + p2Ti pTi[parenrightbigg]

JHEP06(2014)092

, (2.2)

where pTi and mi are the transverse momentum and mass of particle i, respectively. Each patch covers certain area Apatch in the (y ) plane. The overall background pT and mass densities are estimated as

= medianpatches

pTpatch Apatch

, (2.3)

although several modications exist, including y-dependent and m [17]. The estimation of the background densities is the rst step which needs to be followed by a scheme by which to subtract a specied amount of those densities.

In our approach, massless particles with very low momentum are incorporated into the event such that they uniformly cover the y plane with high density. These soft particles

are referred to as ghosts and they are most commonly used to dene the area of a jet [12] or to perform the shape-expansion correction. Each ghost covers a certain xed area, Ag,

in the y plane which is dened by the ghost number density (Ag is its inverse). The

4-momentum of each particle or ghost is expressed as

p = [pT cos , pT sin , (pT + m ) sinh y, (pT + m ) cosh y], (2.4)

2

, m = medianpatches

m patch Apatch

where m =

qm2 + p2T pT (in what follows, we will use superscript g to denote the kinematic variables of ghosts). After adding ghosts into the event, the jet clustering algorithm runs over all particles and ghosts delivering the same jets as in the case without the ghosts. Now, the jets contain except the real particles also ghosts which can be used to correct for the pileup contribution within each jet. Eq. (2.1) is translated into the 4-momentum of each ghost by identifying the transverse momentum pgT and mass mg with the amount of pileup within area Ag:

pgT = Ag [notdef] , mg = Ag [notdef] m.

(2.5)

An iterative procedure is used to dene the scheme for calculating the specied amount of transverse momentum and mass m to subtract from each jet constituent. For each pair of particle i and ghost k, a matching scheme is implemented using the distance measure, Ri,k, dened as

Ri,k = p Ti [notdef] [radicalBig]

2. (2.6)

For complete generality, is allowed to be any real number, but is taken to be zero in the studies performed here. The list of all distance measures, [notdef] Ri,k[notdef], is sorted from the lowest to the highest values. The pileup removal proceeds iteratively, starting from the particle-ghost pair with the lowest Ri,k. At each step, the momentum pT and mass m

of each particle i and ghost k are modied as follows.

If pTi pgTk : pTi ! pTi pgTk, pgTk ! 0;

otherwise: pTi ! 0,

pgTk ! pgTk pTi.

yi ygk

If m i mg k : m i ! m i mg k, mg k ! 0;

otherwise: m i ! 0,mg k ! mg k m i.(2.7)

The azimuth and rapidity of the particles and ghosts remain unchanged. The iterative process is terminated when the end of the sorted list is reached. Alternatively, a threshold Rmax can be introduced to stop the iterations when Ri,k > Rmax. In principle, introducing the Rmax threshold also guarantees that only ghosts neighbouring a given particle are used to correct the kinematics of that particle. Particles with zero transverse momentum after the iterative process are discarded and the 4-momentum of a given jet is recalculated following a desired recombination scheme (commonly, the 4-momentum recombination scheme is used [18]). It can happen that after the subtraction no real particle remains. This may be a signal that such a jet originates from pileup.

The scalar subtraction in eq. (2.7) is chosen instead of 4-momentum subtraction since it allows to reduce the local di erences between the actual background deposit and its estimate from eq. (2.1).1 The scalar subtraction also eliminates the occurrence of unphysical

1An alternative form of eq. (2.7) with subtracting the 4-momenta would lead to a corrected jet with the same 4-momentum as if the area-based subtraction from ref. [8] was applied which follows from the additiveness of 4-momenta. The performance of such particle-level correction will be explored in an upcoming study.

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2 +

i gk

[vextendsingle][vextendsingle][vextendsingle][vextendsingle][vextendsingle]

negative squared masses which may be present when subtracting 4-momenta. Furthermore, the scalar summation is also used in the calculation of the transverse momentum of patches in eq. (2.2) and thereby it avoids the dependence of background densities in eq. (2.3) on the shape and size of the patches.

The above described subtraction procedure referred to as constituent subtraction corrects both the 4-momentum of a jet as well as its substructure. The constituent subtraction works equally well when applied directly to Monte Carlo truth particles from simulation as when applied to a coarse pseudo-detector grid over which the energy from the truth particles is distributed (see section 3.3). An important feature of the algorithm is that it preserves longitudinal invariance an arbitrary jet after the correction and a subsequent boost in the direction of colliding beams has the same constituents as the same jet which is rst boosted and then corrected. The algorithm can be easily extended to account for rapidity dependence of background densities and m in eq. (2.5).

It is also straightforward to extend the method further to the whole event instead of correcting just particles within a jet. Jet nding can then be performed using the subtracted event. Global event shapes can also benet from the correction in addition to individual jet observables. The performance and resolution of missing transverse energy calculated from calorimeter energy deposits may also improve, thereby enhancing several searches for physics beyond the Standard Model. Studies of whole-event constituent subtraction are left to future work, as well as testing directly within the experimental communities.

An important advantage of the constituent subtraction is the speed it can be as much as twenty times faster compared to the shape-expansion method, depending on the type of the jet shape and the nominal jet radius. Furthermore, the shape-expansion correction must be determined for each jet shape in consideration, whereas the constituent subtraction approach provides a corrected set of constituents, from which any shape may be determined. Corrected constituents may also then be used as inputs to jet grooming and tagging algorithms, e.g. the top-quark tagging using the shower deconstruction method [19]. In comparison to the jet cleansing method or charged hadron subtraction used by the CMS experiment, the constituent subtraction does not require any knowledge about the connection of each charged particle with the signal vertex or pileup vertices, though such a knowledge might in principle be used to further enhance capabilities of the algorithm.

The constituent subtraction procedure has following free parameters: Ag, Rmax, and

. The basic recommended settings are: Ag = 0.01, Rmax ! 1, and = 0. These

settings were used in the performance studies presented in section 3. The subtraction is stable with respect to varying Ag. The variation of Ag by a factor of two does not lead to a change in any of the studied quantities that would be signicant with respect to the statistical uncertainty shown on plots in section 3. Introducing a nite Rmax may improve

the performance of the correction and the speed of the algorithm when running over the full event. The conguration with > 0 prefers to subtract the lower pT constituents which more often originate from background. This conguration will not be discussed in this paper but it appears to lead to an improvement in the correction of some of the jet shapes.

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The software for the constituent subtraction is implemented as a part of the FastJet Contrib project [20].

3 Performance of the subtraction

The constituent subtraction algorithm corrects both the jet kinematics (pT and mass) and the jet shapes. Studies of the algorithm performance for pT are discussed in section 3.1 along with comparisons to the area-based subtraction which follows ref. [8] where the pileup 4-momentum (2.1) is subtracted using the jet area 4-vector A as

pcorr = [px Ax, py Ay, pz ( + m)Ay, E ( + m)AE]. (3.1)

The performance of the subtraction applied to both the jet mass and several jet shapes is presented in section 3.3. Comparisons of the constituent subtraction approach with the shape-expansion method [8] are also presented.

The studies presented are performed using events generated with PYTHIA 8.180, tune 4C [21, 22] but without any detector simulation. The e ect of additional proton-proton collisions is emulated by using inclusive events (often referred to as minimum bias events) overlaid with the hard scattering interaction, which are also generated with PYTHIA 8.180. The CTEQ 5L, LO parton density functions [23], congured to simulate the LHC conditions at ps = 8 TeV, are used for all event generation. Two processes are simulated without underlying event: di-jet events covering the pT range of 10-800 GeV and events with boosted top quarks from decay Z[prime] ! tt of hypothetical boson Z[prime] with mass of 1.5 TeV. The

performance of the subtraction is tested using jets clustered with the anti-kt algorithm [24] with the distance parameter R = 0.7 or R = 1.0 and jets clustered with Cambridge-Aachen (C/A) algorithm [25] with R = 1.2. These are representative jet denitions for both the ATLAS [26] and CMS [27] experimental collaborations. The number of pileup events, nPU , has a Poisson distribution with a mean [angbracketleft]nPU [angbracketright]. Two pileup conditions are simulated, hnPU [angbracketright] = 30 and [angbracketleft]nPU [angbracketright] = 100. These pileup congurations represent realistic conditions for

LHC Run I and upcoming LHC Run II2 as well as for the high luminosity LHC running [28]. On average, the pileup contribution to the hard-scatter event can be described through mean value of transverse momentum densities, [angbracketleft][notdef], and pileup uctuations characterized

by standard deviation, []. For the used conguration [angbracketleft]nPU [angbracketright] = 100, these quantities are h[notdef] 75 GeV and [] 13 GeV.

All jet nding and background estimation is performed using FastJet 3.0.6 [17, 29]. The shape-expansion correction is performed using FastJet Contrib 1.003 [20]. The patches in eq. (2.3) are obtained by clustering particles with the kt algorithm [15, 16] with distance parameter R = 0.4. The non-negligible dependence of the background densities and m on rapidity impacts each of the corrections methods discussed below. Consequently,

2For LHC Run II, collisions at ps = 14 TeV are planed. MC studies predict [angbracketleft]nPU[angbracketright] of 120 and no

signicant increase in the size of pileup densities and inter-event uctuations for this centre-of-mass energy.

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in order to focus the comparisons and performance evaluations, only patches with rapidity

|y[notdef] < 2.0 are used in eq. (2.3) and jets are required to be fairly central, with [notdef] [notdef] < 2.0.33.1 Jet kinematics

The ability of the subtraction to correctly recover the kinematics of the jet can be characterized in terms of following quantities: jet momentum response, jet momentum resolution, jet position resolution, and jet nding e ciency. These quantities are commonly used to evaluate the performance of the jet reconstruction, see e.g. refs. [3033]. In this section we evaluate these quantities both for the constituent subtraction and area-based subtraction.

The rst quantity characterizing the basic performance of the subtraction is the jet momentum response. It can be dened as [angbracketleft] pT[angbracketright]/porigT = [angbracketleft]pT porigT[angbracketright]/porigT where porigT is the original jet momentum with no pileup and pT is either the pileup corrected jet momentum or the momentum of uncorrected jet that is jet clustered in the presence of pileup with no subtraction. This quantity is also often referred to as the jet energy scale. In the optimal situation, the jet momentum response should be zero which means that, on average, the algorithm can reconstruct the same pT as with no pileup. Left panel of gure 1 shows the jet momentum response as a function of the number of pileup collisions, nPU , that is the size of the pileup. The jet momentum response of subtracted jets di ers from zero by less then a 1%. The jet momentum response of subtracted jets is stable with respect to the pileup which is a crucial condition for the jet reconstruction. Without satisfying this condition any cut applied on the jet pT would lead to a choice of di erent subset of jets depending on the size of the pileup. Small deviation from zero of the jet momentum response is resulting from ignoring the rapidity dependence of the pileup density and m and from a small average bias of pileup densities by a presence of the hard-scatter event. Such small deviation can be easily corrected after the jet reconstruction by multiplying the jet momentum by a correction factor. The constituent subtraction performs equally well as the area-based subtraction.

The small deviation of jet momentum response from zero for corrected jets can be contrasted with the jet momentum response of uncorrected jets in the case of low pileup scenario the momentum response is 10-20%, in the case of high pileup scenario the jet momentum response is around 40%. This means that in the high pileup case, there is on average approximately 40 GeV of the pileup background underneath each jet leading to a reconstruction of a typical 100 GeV jet as a 140 GeV jet if performing no subtraction.

The second quantity characterizing the basic performance of the subtraction is the jet momentum resolution dened as [ pT]/porigT = [pT porigT]/porigT where [. . .] denotes the standard deviation. The jet momentum resolution is dictated by the presence of uctuations in the underlying pileup background leading to dependence [ pT]/porigT = c/porigT where c is a constant. The jet momentum resolution is shown in the upper middle panel of gure 1. The t of the jet momentum resolution of uncorrected jets by c/porigT leads to c 25 GeV which results from the magnitude of [] and pileup uctuations in plane

3This pseudorapidity requirement limits the rate of top quarks originating from Z[prime] boson decaying at rest. Thus, in this study, a signicant fraction of top quarks originate from decays of Z[prime] carrying a non-zero momentum in the direction of colliding beams.

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Figure 1: Jet momentum response (left). Jet momentum resolution (upper middle) and jet nding e ciency (lower middle). Jet position resolution (right). Jets prior the subtraction denoted as pileup (square markers) are compared to jets corrected by the constituent subtraction (full circles) and jets corrected by the area-based subtraction (open circles). The dashed line in the left panel shows a constant at 0.8% to guide the eye.

Curve in the upper middle panel represents a t of the jet momentum resolution by c/pT resulting c 25 GeV.

within each particular event. The constituent subtraction and area-based subtraction have similar jet momentum resolution while both methods signicantly improve it.

The jet nding e ciency is dened as the number of original jets having a matching corrected (or uncorrected) jet divided by the number of original jets. The matching criterion is the distance in the plane between the original jet and corrected (or uncorrected)

jet satisfying the condition R =

p 2 + 2 < 0.2. This quantity is plotted in the lower middle panel of gure 1. It shows that in the case of high pileup events it is di cult in principle to reconstruct the jets with porigT < 50 GeV due to the presence of sizable uctuating background. The jet e ciency is better for the constituent subtraction than for the area-based subtraction.

The last quantity evaluated is the jet position resolution which characterizes the ability to recover the original jet axis in pseudorapidity, , or azimuth, . The jet position resolution in and are similar. The jet position resolution in , [ ], is dened as the standard deviation of the di erence between the original jet position and position of the corrected (or uncorrected) jet. The [ ] is plotted in the right panel of gure 1 where a clear di erence between jets with pileup contribution and corrected jets is present. Jets corrected by the area-based subtraction have slightly worse jet position resolution than jets corrected by the constituent subtraction.

Based on the analysis of the basic performance, we can conclude the constituent subtraction has a good ability to correct for the pileup background and to recover the original jet kinematics even in the presence of a sizable pileup. The constituent subtraction has

7

generally similar performance as the area-based subtraction. A slightly better performance in terms of jet position resolution and jet e ciency may be attributed to the correction of the jet internal structure which is done by the constituent subtraction. The ability of the constituent subtraction to correct the jet internal structure is discussed in section 3.3.

3.2 Jet shape denitions

The ability of the constituent subtraction method to recover the internal structure of jet has been tested by evaluating four jet shape variables that are discussed in the literature to be useful for analyzing the boosted objects or to perform jet tagging [34, 35]. Here we briey introduce these four jet shapes:

The jet mass which can also be used to identify the hadronic decays of boosted heavy

particles [38, 39].

The N-subjettiness, N, dened as [36] N = 1d0

XkpTk [notdef] min( R1k, R2k, . . . , RNk) , with, d0 XkpTk [notdef] R (3.2)

where R is the distance parameter of the jet algorithm, pTk is the transverse momentum of constituent k and Rik is the distance between a subjet i and a constituent k. The N subjets are dened by re-clustering the constituents of the jet with exclusive version of the kt algorithm [16] and requiring that exactly N subjets are found. Beside the N-subjettiness also the subjettiness ratio, MN = M/N, can be used to characterize the jet substructure. Typically, the three-to-two ratio, 32 = 3/2, is used

which provides a good discrimination between standard QCD jets and jets formed e.g. by boosted top quarks.

The kt splitting scale, pd12, dened as [37]

pd12 = min(p1T, p2T) [notdef] R12, (3.3) where p1T and p2T are the transverse momenta of two subjets and R12 is the distance between these two subjets. The two subjets are found by going back one step in the clustering history of the kt algorithm. The variable pd12 can be used to distinguish heavy-particle decays, which tend to be reasonably symmetric when the decay is to like-mass particles, from the largely asymmetric splittings that originate from QCD radiation in light-quark or gluon jets.

The longitudinally invariant version of the planar ow, Pf, dened as [8]: Pf = 4 1 2

( 1 + 2)2 , (3.4)

where 1 and 2 are the eigenvalues of 2 [notdef] 2 matrix: M =

XipTi [notdef] ( i jet) [notdef] ( i jet), (3.5)

where and correspond to rapidity or azimuth.

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Figure 2: Performance of the constituent subtraction for jets clustered with the anti-kt algorithm. Red triangles show distribution without pileup, blue squares show the uncorrected distribution with pileup, open and closed circles show distributions corrected by the shape-expansion and constituent subtraction method, respectively. The nPU dependence of mean [angbracketleft] x[angbracketright] and standard deviation [ x] are shown in the lower panel for each jet shape.

3.3 Jet shape subtraction

The constituent subtraction method is tested on various combinations of signal samples, pileup conditions, clustering algorithms, and jet shapes dened in section 3.2. The details of the conguration are provided at the beginning of section 3. The constituent subtraction can recover the original jet shape with a good accuracy in all evaluated combinations.

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Figure 3: Performance of the constituent subtraction for jets clustered with the C/A algorithm. Red triangles show distribution without pileup, blue squares show the uncorrected distribution with pileup, open and closed circles show distributions corrected by the shape-expansion and constituent subtraction method, respectively. The nPU dependence of mean

h x[angbracketright] and standard deviation [ x] are shown in the lower panel for each jet shape.

A representative subset of performance plots for the anti-kt algorithm is shown in gure 2 for various jet pT intervals.4 Four distributions of jet shapes are plotted for each presented plot: the original distribution (that is the distribution without pileup), the distribution with pileup, the distributions corrected by the constituent subtraction and the shape-expansion5 methods. To quantify precisely the performance of the correction, two quantities have been evaluated for the di erences between jet shape x and its original value without pileup xorig: the mean value of these di erences [angbracketleft] x[angbracketright] = [angbracketleft]x xorig[angbracketright] and the

standard deviation of these di erences [ x] = [xxorig] which represents the resolution.

For each combination of congurations, the uncorrected distributions di er signicantly from the corresponding original distribution, and have a signicant dependence on nPU . A

substantial improvement is achieved by the constituent subtraction. The mean di erence

h x[angbracketright] does not exhibit the nPU dependence and it is always centered near zero after the

subtraction. The resolution [ x] is improved as well. The constituent subtraction method performs similarly or mostly better when compared to the shape-expansion method.

For any of the studied jet shapes, the shape-expansion method can lead to negative corrected jet shapes that are unphysical. To better visualize the contribution of such

4The pT of the jets without pileup is used to dene the pT intervals. The jets with pileup and the corrected jets are matched to the original jets without pileup. In some cases, additional cut is applied on mass or subjettiness ratio 21 again on jets without pileup.

5For the jet mass, the area-based method using eq. (3.1) is used which is identical to the shape-expansion method.

10

a. u.

anti-k dijets < 600 GeV

p

500

R=1.0

no PU

= 100

a. u.

no PU

= 100

a. u.

0.15

0.3

R=1.0

anti-k Z' < 800 GeV

p

600m > 50 GeV

C/A R=1.2 dijets < 300 GeV

p

200

no PU

= 100

n

0.3

area-based constituent

expansion constituent

expansion constituent

n

n

0.2

0.1

0.2

0.1

0.1

0.05

0 0 200 400

0 0 0.5 1 1.5

0 0 0.2 0.4

m [GeV]

t

21

t

1

[GeV] m D

300

t

D

1

t

D

21 0.2

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100

0.1

0.1

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0

50

80 100 120

] 21 0.15

0 80 100 120

80 100 120

m] [GeV] D [ s

30

D

n

D

n

n

PU

[

s

PU

[

s

PU

40

0.1

0.1

0.05

0.05

80 100 120

80 100 120

80 100 120

n

n

n

PU

PU

PU

Figure 4: Performance of the constituent subtraction in events simulating a segmented detector. Red triangles show distribution without pileup, blue squares show the uncorrected distribution with pileup, open and closed circles show distributions corrected by the shape-expansion and constituent subtraction method, respectively. The nPU dependence of mean

h x[angbracketright] and standard deviation [ x] are shown in the lower panel for each jet shape.

values, the rst bin with negative jet shape in plots of gures 24 is set to the fraction of negatively corrected jet shapes.6 Unphysical values can also occur in the case of the area-based correction of the jet mass when the corrected energy is smaller than the magnitude of corrected momentum. Again, the negative bin represents the fraction of such jets. The fraction of unphysical jet shapes obtained from the shape-expansion method reaches up to

12% depending on the pT interval and the type of the jet shape.

The constituent subtraction method has been tested also on the jets clustered with C/A algorithm which is often employed in various studies of the jet substructure and boosted objects [34]. The clustering in the C/A algorithm is based purely on the geometry and thus it leads to jet with a di erent jet area compared to the anti-kt algorithm [12].

The performance of the constituent subtraction method for C/A algorithm with distance parameter R = 1.2 is shown in gure 3. For this conguration, the impact of the pileup on jet shapes is much stronger compared to the conguration with the anti-kt algorithm. The constituent subtraction can recover the original distributions and it exhibits signicantly better ability to subtract the pileup compared to the shape-expansion method.

Further, the constituent subtraction method has been tested on jets reconstructed in events run through a simple simulation of a segmented detector. In this simulation, the plane is divided into cells of size 0.1 [notdef] 0.1. Particles pointing to the same cell are

6For the shape-expansion correction of ratios 21 or 32, the numerator and denominator are corrected individually. When at least one of these corrected variables is negative, the corrected 21 or 32 is counted as

negative. For the calculation of the mean and resolution of 21 or 32, the negative values are not used. For any other jet shapes, the negative values are set to zero so that they do not bias the mean and resolution.

11

tagging efficiency

0.5

tagging efficiency

R=1.0

1.2

R=1.0

500

anti-k dijets

< 600 GeV

T

p

no PU with PU expansion constituent

anti-k Z'

< 600 GeV

T

p

t

500

no PU with PU expansion constituent

t

1

1

0.8

80 100 120

80 100 120

n

n

PU

PU

Figure 5: Tagging e ciencies for background (left) and signal (right) samples using tagging cut pd12 > 50 GeV in events simulating a segmented detector. Red triangles show the tagging e ciency for jets without pileup. Blue squares show the tagging e ciency for jets with pileup, open and closed circles show tagging e ciency for jets corrected by the shape-expansion method and constituent subtraction method, respectively.

combined into one new e ective particle by summing their energies. The mass of the cell is set to zero and its position is set to the center of the cell. These new e ective particles

have the same properties as the calorimeter clusters or towers used in real experiments and they are a combination of the pileup and signal. The jet nding algorithm runs over these events delivering jets that are corrected in the same way as for events composed of standard particles. A typical example of the performance of the subtraction methods in case of this simulation is shown in gure 4. The constituent subtraction exhibits very similar performance as without the detector simulation which also applies for the shape-expansion method while the constituent subtraction again outperforms the shape-expansion method. Degradation of the performance of jet mass reconstruction is seen for all methods in the conguration of jet reconstruction with large distance parameter. This is a consequence of a sensitivity of jet mass to variations in the constituent transverse momenta of constituents that are at large angles with respect to the jet axis. While other variables are less sensitive to such variations, the jet mass can change signicantly by adding a soft particle to the jet periphery.

An important test is to evaluate the jet tagging performance. The splitting scale, pd12, is used to tag the boosted top quarks from the Z[prime] decay and tagging e ciencies have been evaluated. The signal sample can be compared with the di-jet sample which in this case provides a reasonable estimate of the background for the Z[prime] ! tt decay. The result is

shown on gure 5. One can see that both the constituent subtraction and shape-expansion can achieve the same tagging e ciency as in the case of no pileup.

The above presented results demonstrate the stability and good performance of the constituent subtraction method.

4 Conclusions

We have introduced a new tool to correct for the pileup in high-luminosity LHC running that represents an extension and a simplication of the current state of the art. The

12

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constituent subtraction method operates at the level of the jet constituents and provides both a performance improvement and a simplication compared to existing methods: the precision of the reconstruction of jet shapes is improved as well as the speed of the correction itself.

The constituent subtraction method is tested by evaluating the pileup dependence, and other key metrics, of several jet shapes and jet kinematics using multiple jet denitions. Improvements are demonstrated in both the reduction of uctuations in the resulting jet shapes as a function of pileup and the ability to remove the pileup dependence of the corrected quantities. It also provides a better jet position resolution and jet nding e ciency for reconstructing jets from boosted objects, which directly impacts the experimental sensitivity to new physics.

Since the correction proceeds without knowledge of a jet algorithm, a novel application of this approach would be to correct the whole event prior to jet nding. Not only would this have implications for the technical performance and computational resources currently devoted to evaluation the pileup subtraction for each jet individually, but it also has the potential to improve the determination of the missing transverse energy. Furthermore, the constituent subtraction approach can be used to correct for the underlying event in heavy ion collisions.

It is very important that these studies be veried by the experiments using both fully simulated data samples of signal and background events, as well as in situ studies using data. Given the excellent correspondence between the similar preliminary studies of earlier pileup correction methods and the experimental reality, we expect that the performance observed here is quantitatively representative of what can be achieved by the experimental collaborations. Nonetheless, any new approach must be vetted and tested thoroughly.

Acknowledgments

The authors would like to thank Gregory Soyez and Gavin Salam for their feedback and assistance in understanding and using the shape-expansion tools. The work is supported by Charles University in Prague, projects PRVOUK P45, UNCE 204020/2012, and GA UK No 320813. DWM is supported in part by the Neubauer Family Foundation Fellows Program for Assistant Professors.

Open Access. This article is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/

Web End =CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

[1] ATLAS collaboration, Pile-up corrections for jets from proton-proton collisions at ps = 7 TeV in ATLAS in 2011, http://cds.cern.ch/record/1459529

Web End =ATLAS-CONF-2012-064 (2012).

[2] J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new Higgs search channel at the LHC, http://dx.doi.org/10.1103/PhysRevLett.100.242001

Web End =Phys. Rev. Lett. 100 (2008) 242001 [http://arxiv.org/abs/0802.2470

Web End =arXiv:0802.2470 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,100,242001

Web End =INSPIRE ].

13

JHEP06(2014)092

[3] S.D. Ellis, C.K. Vermilion and J.R. Walsh, Techniques for improved heavy particle searches with jet substructure, http://dx.doi.org/10.1103/PhysRevD.80.051501

Web End =Phys. Rev. D 80 (2009) 051501 [http://arxiv.org/abs/0903.5081

Web End =arXiv:0903.5081 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D80,051501

Web End =INSPIRE ].

[4] D. Krohn, J. Thaler and L.-T. Wang, Jet Trimming, http://dx.doi.org/10.1007/JHEP02(2010)084

Web End =JHEP 02 (2010) 084 [http://arxiv.org/abs/0912.1342

Web End =arXiv:0912.1342 ] [http://inspirehep.net/search?p=find+J+JHEP,1002,084

Web End =INSPIRE ].

[5] D. Krohn, M.D. Schwartz, M. Low and L.-T. Wang, Jet Cleansing: Pileup Removal at High Luminosity, http://arxiv.org/abs/1309.4777

Web End =arXiv:1309.4777 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1309.4777

Web End =INSPIRE ].

[6] CMS collaboration, Jet performance in CMS, https://cds.cern.ch/record/1627818

Web End =CERN-CMS-CR-2013-325 (2013).

[7] M. Cacciari and G.P. Salam, Pileup subtraction using jet areas, http://dx.doi.org/10.1016/j.physletb.2007.09.077

Web End =Phys. Lett. B 659 (2008) 119 [http://arxiv.org/abs/0707.1378

Web End =arXiv:0707.1378 ] [http://inspirehep.net/search?p=find+J+Phys.Lett.,B659,119

Web End =INSPIRE ].

[8] G. Soyez, G.P. Salam, J. Kim, S. Dutta and M. Cacciari, Pileup subtraction for jet shapes, http://dx.doi.org/10.1103/PhysRevLett.110.162001

Web End =Phys. Rev. Lett. 110 (2013) 162001 [http://arxiv.org/abs/1211.2811

Web End =arXiv:1211.2811 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,110,162001

Web End =INSPIRE ].

[9] L. Apolinario, N. Armesto and L. Cunqueiro, An analysis of the inuence of background subtraction and quenching on jet observables in heavy-ion collisions, http://dx.doi.org/10.1007/JHEP02(2013)022

Web End =JHEP 02 (2013) 022 [http://arxiv.org/abs/1211.1161

Web End =arXiv:1211.1161 ] [http://inspirehep.net/search?p=find+J+JHEP,1302,022

Web End =INSPIRE ].

[10] M. Spousta, Jet Quenching at LHC, http://dx.doi.org/10.1142/S0217732313300176

Web End =Mod. Phys. Lett. A 28 (2013) 1330017 .

[11] CMS collaboration, Underlying-Event Subtraction for Particle Flow, http://cms.cern.ch/iCMS/jsp/db_notes/noteInfo.jsp?cmsnoteid=CMS%20DP-2013/018

Web End =CMS DP-2013/018 .

[12] M. Cacciari, G.P. Salam and G. Soyez, The Catchment Area of Jets, http://dx.doi.org/10.1088/1126-6708/2008/04/005

Web End =JHEP 04 (2008) 005 [http://arxiv.org/abs/0802.1188

Web End =arXiv:0802.1188 ] [http://inspirehep.net/search?p=find+J+JHEP,0804,005

Web End =INSPIRE ].

[13] G. Bellettini, R. Bertani, C. Bradaschia, R. Del Fabbro, A. Scribano et al., Hadron calorimeter towers with a high space resolution, http://dx.doi.org/10.1016/0167-5087(82)90080-1

Web End =Nucl. Instrum. Meth. 204 (1982) 73 [ http://inspirehep.net/search?p=find+J+Nucl.Instrum.Meth.,204,73

Web End =INSPIRE ].

[14] ATLAS collaboration, Calorimeter Clustering Algorithms : Description and Performance, http://cds.cern.ch/record/1099735

Web End =ATL-LARG-PUB-2008-002 (2008).

[15] S.D. Ellis and D.E. Soper, Successive combination jet algorithm for hadron collisions, http://dx.doi.org/10.1103/PhysRevD.48.3160

Web End =Phys. http://dx.doi.org/10.1103/PhysRevD.48.3160

Web End =Rev. D 48 (1993) 3160 [http://arxiv.org/abs/hep-ph/9305266

Web End =hep-ph/9305266 ] [http://inspirehep.net/search?p=find+Phys.Rev.D48,D48,3160

Web End =INSPIRE ].

[16] S. Catani, Y.L. Dokshitzer, M.H. Seymour and B.R. Webber, Longitudinally invariant Kt clustering algorithms for hadron hadron collisions, http://dx.doi.org/10.1016/0550-3213(93)90166-M

Web End =Nucl. Phys. B 406 (1993) 187 [http://inspirehep.net/search?p=find+J+Nucl.Phys.,B406,187

Web End =INSPIRE ].

[17] M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, http://dx.doi.org/10.1140/epjc/s10052-012-1896-2

Web End =Eur. Phys. J. C 72 (2012) http://dx.doi.org/10.1140/epjc/s10052-012-1896-2

Web End =1896 [http://arxiv.org/abs/1111.6097

Web End =arXiv:1111.6097 ] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1111.6097

Web End =INSPIRE ].

[18] G.C. Blazey, J.R. Dittmann, S.D. Ellis, V.D. Elvira, K. Frame et al., Run II jet physics, FERMILAB-CONF-00-092-E [http://arxiv.org/abs/hep-ex/0005012

Web End =hep-ex/0005012 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ex/0005012

Web End =INSPIRE ].

[19] D.E. Soper and M. Spannowsky, Finding top quarks with shower deconstruction, http://dx.doi.org/10.1103/PhysRevD.87.054012

Web End =Phys. Rev. http://dx.doi.org/10.1103/PhysRevD.87.054012

Web End =D 87 (2013) 054012 [http://arxiv.org/abs/1211.3140

Web End =arXiv:1211.3140 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D87,054012

Web End =INSPIRE ].

[20] http://fastjet.hepforge.org/contrib

Web End =http://fastjet.hepforge.org/contrib .

[21] T. Sjstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, http://dx.doi.org/10.1088/1126-6708/2006/05/026

Web End =JHEP 05 http://dx.doi.org/10.1088/1126-6708/2006/05/026

Web End =(2006) 026 [http://arxiv.org/abs/hep-ph/0603175

Web End =hep-ph/0603175 ] [http://inspirehep.net/search?p=find+J+JHEP,0605,026

Web End =INSPIRE ].

[22] T. Sjstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, http://dx.doi.org/10.1016/j.cpc.2008.01.036

Web End =Comput. http://dx.doi.org/10.1016/j.cpc.2008.01.036

Web End =Phys. Commun. 178 (2008) 852 [http://arxiv.org/abs/0710.3820

Web End =arXiv:0710.3820 ] [http://inspirehep.net/search?p=find+J+Comput.Phys.Commun.,178,852

Web End =INSPIRE ].

[23] CTEQ collaboration, H.L. Lai et al., Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions, http://dx.doi.org/10.1007/s100529900196

Web End =Eur. Phys. J. C 12 (2000) 375 [http://arxiv.org/abs/hep-ph/9903282

Web End =hep-ph/9903282 ] [http://inspirehep.net/search?p=find+J+Eur.Phys.J.,C12,375

Web End =INSPIRE ].

14

JHEP06(2014)092

[24] M. Cacciari, G.P. Salam and G. Soyez, The Anti-k(t) jet clustering algorithm, http://dx.doi.org/10.1088/1126-6708/2008/04/063

Web End =JHEP 04 http://dx.doi.org/10.1088/1126-6708/2008/04/063

Web End =(2008) 063 [http://arxiv.org/abs/0802.1189

Web End =arXiv:0802.1189 ] [http://inspirehep.net/search?p=find+J+JHEP,0804,063

Web End =INSPIRE ].

[25] Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, http://dx.doi.org/10.1088/1126-6708/1997/08/001

Web End =JHEP 08 (1997) 001 [http://arxiv.org/abs/hep-ph/9707323

Web End =hep-ph/9707323 ] [http://inspirehep.net/search?p=find+J+JHEP,9708,001

Web End =INSPIRE ].

[26] ATLAS collaboration, Performance of jet substructure techniques for large-R jets in proton-proton collisions at ps = 7 TeV using the ATLAS detector, http://dx.doi.org/10.1007/JHEP09(2013)076

Web End =JHEP 09 (2013) 076 [http://arxiv.org/abs/1306.4945

Web End =arXiv:1306.4945 ] [http://inspirehep.net/search?p=find+J+JHEP,1309,076

Web End =INSPIRE ].

[27] CMS Collaboration, Jet Performance in pp Collisions at 7 TeV, http://cds.cern.ch/record/1279362

Web End =CMS-PAS-JME-10-003 (2010).

[28] O.S. Bruning, HL-LHC Parameter Space and Scenarios, Proc. Chamonix 2012 workshop on LHC Performance (2012).

[29] M. Cacciari and G.P. Salam, Dispelling the N3 myth for the kt jet-nder, http://dx.doi.org/10.1016/j.physletb.2006.08.037

Web End =Phys. Lett. B 641 http://dx.doi.org/10.1016/j.physletb.2006.08.037

Web End =(2006) 57 [http://arxiv.org/abs/hep-ph/0512210

Web End =hep-ph/0512210 ] [http://inspirehep.net/search?p=find+J+Phys.Lett.,B641,57

Web End =INSPIRE ].

[30] ATLAS collaboration, Jet energy measurement with the ATLAS detector in proton-proton collisions at ps = 7 TeV, http://dx.doi.org/10.1140/epjc/s10052-013-2304-2

Web End =Eur. Phys. J. C 73 (2013) 2304 [http://arxiv.org/abs/1112.6426

Web End =arXiv:1112.6426 ] [http://inspirehep.net/search?p=find+J+Eur.Phys.J.,C73,2304

Web End =INSPIRE ].

[31] CMS collaboration, Determination of jet energy calibration and transverse momentum resolution in CMS, http://dx.doi.org/10.1088/1748-0221/6/11/P11002

Web End =2011 JINST 6 P11002 .

[32] CDF collaboration, A. Bhatti et al., Determination of the jet energy scale at the collider detector at Fermilab, http://dx.doi.org/10.1016/j.nima.2006.05.269

Web End =Nucl. Instrum. Meth. A 566 (2006) 375 [http://arxiv.org/abs/hep-ex/0510047

Web End =hep-ex/0510047 ] [http://inspirehep.net/search?p=find+J+Nucl.Instrum.Meth.,A566,375

Web End =INSPIRE ].

[33] D0 collaboration, Jet energy scale determination in the D0 experiment, http://cds.cern.ch/record/1640111

Web End =FERMILAB-PUB-13-577 (2013).

[34] A. Altheimer et al., Jet Substructure at the Tevatron and LHC: New results, new tools, new benchmarks, http://dx.doi.org/10.1088/0954-3899/39/6/063001

Web End =J. Phys. G39 (2012) 063011 .

[35] J. Gallicchio and M.D. Schwartz, Quark and Gluon Tagging at the LHC, http://dx.doi.org/10.1103/PhysRevLett.107.172001

Web End =Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.107.172001

Web End =107 (2011) 172001 [http://arxiv.org/abs/1106.3076

Web End =arXiv:1106.3076 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,107,172001

Web End =INSPIRE ].

[36] J. Thaler and K. Van Tilburg, Identifying Boosted Objects with N-subjettiness, http://dx.doi.org/10.1007/JHEP03(2011)015

Web End =JHEP 03 http://dx.doi.org/10.1007/JHEP03(2011)015

Web End =(2011) 015 [http://arxiv.org/abs/1011.2268

Web End =arXiv:1011.2268 ] [http://inspirehep.net/search?p=find+J+JHEP,1103,015

Web End =INSPIRE ].

[37] J.M. Butterworth, B.E. Cox and J.R. Forshaw, W W scattering at the CERN LHC, http://dx.doi.org/10.1103/PhysRevD.65.096014

Web End =Phys. http://dx.doi.org/10.1103/PhysRevD.65.096014

Web End =Rev. D 65 (2002) 096014 [http://arxiv.org/abs/hep-ph/0201098

Web End =hep-ph/0201098 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D65,096014

Web End =INSPIRE ].

[38] A. Abdesselam, E.B. Kuutmann, U. Bitenc, G. Brooijmans, J. Butterworth et al., Boosted objects: A Probe of beyond the Standard Model physics, http://dx.doi.org/10.1140/epjc/s10052-011-1661-y

Web End =Eur. Phys. J. C 71 (2011) 1661 [http://arxiv.org/abs/1012.5412

Web End =arXiv:1012.5412 ] [http://inspirehep.net/search?p=find+J+Eur.Phys.J.,C71,1661

Web End =INSPIRE ].

[39] CMS collaboration, Studies of jet mass in dijet and W/Z+jet events, http://dx.doi.org/10.1007/JHEP05(2013)090

Web End =JHEP 05 (2013) 090 [http://arxiv.org/abs/1303.4811

Web End =arXiv:1303.4811 ] [http://inspirehep.net/search?p=find+J+JHEP,1305,090

Web End =INSPIRE ].

15

JHEP06(2014)092