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Eur. Phys. J. C (2015) 75:59

DOI 10.1140/epjc/s10052-015-3267-2

Regular Article - Theoretical Physics

SoftKiller, a particle-level pileup removal method

Matteo Cacciari

1,2,3,a

, Gavin P. Salam

4,b

, Gregory Soyez

Université Paris Diderot, Paris, France

Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, 75005 Paris, France

CNRS, UMR 7589, LPTHE, 75005 Paris, France

CERN, PH-TH, 1211 Geneva 23, Switzerland

IPhT, CEA Saclay, CNRS URA 2306, 91191 Gif-sur-Yvette Cedex, France

Received: 21 July 2014 / Accepted: 11 January 2015 / Published online: 6 February 2015

Abstract Existing widely used pileup removal approaches

correct the momenta of individual jets. In this article we intro-

duce an event-level, particle-based pileup correction proce-

dure, SoftKiller. It removes the softest particles in an event,

up to a transverse momentum threshold that is determined

dynamically on an event-by-event basis. In simulations, this

simple procedure appears to be reasonably robust and brings

superior jet resolution performance compared to existing jet-

based approaches. It is also nearly two orders of magnitude

faster than methods based on jet areas.

1 Introduction

At high-luminosity hadron colliders such as CERN’s Large

Hadron Collider (LHC), an issue that has an impact on many

analyses is pileup, the superposition of multiple proton–

proton collisions at each bunch crossing. Pileup affects a

range of observables, such as jet momenta and shapes, miss-

ing transverse energy and lepton and photon isolation. In the

speciﬁc case of jets, it can add tens of GeV to a jet’s trans-

verse momentum and signiﬁcantly worsens the resolution

for reconstructing the jet momentum. In the coming years

the LHC will move towards higher luminosity running, ulti-

mately increasing pileup by up to a factor of ten for the high-

luminosity LHC [1]. The experiments’ ability to mitigate

pileup’s adverse effects will therefore become increasingly

crucial to fully exploit the LHC data, especially at low and

moderate momentum scales, for example in studies of the

Higgs sector.

Some approaches to reducing the impact of pileup are

deeply rooted in experimental reconstruction procedures. For

e-mail: [email protected]

On leave from CNRS, UMR 7589, LPTHE, F-75005, Paris, France

example, charged hadron subtraction (CHS) in the context of

particle ﬂow [2] exploits detectors’ ability to identify whether

a given charged track is from a pileup vertex or not. Other

aspects of pileup mitigation are largely independent of the

experimental details: for example both ATLAS and CMS

[3,4] rely on the area–median approach [5,6], which makes

a global estimate for the transverse-momentum-ﬂow density,

ρ, and then applies a correction to each jet in proportion to

its area.

In this article, we introduce and study a new generic pileup

removal method. Instead of correcting individual jets, it cor-

rects for pileup at the level of particles. Such a method should

make a guess, for each particle in an event, as to whether it

comes from pileup or from the hard collision of interest. Par-

ticles deemed to be from pileup are simply discarded, while

the much smaller set of residual “hard-collision” particles are

passed to the jet clustering. Event-wide particle-level subtrac-

tion, if effective, would greatly simplify pileup mitigation in

advanced jet studies such as those that rely on jet substruc-

ture [7]. Even more importantly, as we shall see, it has the

potential to bring signiﬁcant improvements in jet resolution

and computational speed. This latter characteristic makes our

approach particularly appealing also for trigger-level appli-

cations.

The basis of our pileup suppression method, which we

dub “SoftKiller” (SK), is that the simplest characteristic

of a particle that affects whether it is likely to be from

pileup or not is its transverse momentum. In other words,

we will discard particles that fall below a certain transverse-

momentum threshold. The key feature of the method will

be its event-by-event determination of that threshold, cho-

sen as the lowest p

value that causes ρ, in the median–

area method, to be evaluated as zero. In a sense, this

can be seen as the extreme limit of ATLAS’s approach

of increasing the topoclustering noise threshold as pileup

increases [8].

123

59 Page 2 of 16 Eur. Phys. J. C (2015) 75 :59

Hard

Pileup

Original event

Pileup

Hard

After SoftKiller

cut

ytpmeytpmeytpmeytpmeytpme

Fig. 1 Illustration of the SoftKiller method. The left plot depicts par-

ticles in an event, with the hard-event particles shown in blue and the

pileup particles shown in red.Ontheright, the same event after apply-

ing the SoftKiller. The vertical dotted lines represent the edges of the

patches used to estimate the pileup density ρ

This approach might at ﬁrst sight seem excessively naïve

in its simplicity. We have also examined a range of other

methods. For example, one approach involved an all-orders

matrix-element analysis of events, similar in spirit to shower

deconstruction [9,10]; others involved event-wide extensions

of a recent intrajet particle-level subtraction method [11] and

subjet-level [12,13] approaches (see also [14]); we have also

been inspired by calorimeter [15–17] and particle-level [18]

methods developed for heavy-ion collisions. Such methods

and their extensions have signiﬁcant potential. However, we

repeatedly encountered additional complexity, for example

in the form of multiple free parameters that needed ﬁxing,

without a corresponding gain in performance. Perhaps with

further work those drawbacks can be alleviated, or perfor-

mance can be improved. For now, we believe that it is useful

to document one method that we have found to be both simple

and effective.

2 The SoftKiller method

The SoftKiller method involves eliminating particles below

some p

cutoff, p

cut

, chosen to be the minimal value that

ensures that ρ is zero. Here, ρ is the event-wide estimate

of transverse-momentum-ﬂow density in the area–median

approach [5,6]: the event is broken into patches and ρ is

taken as the median, across all patches, of the transverse-

momentum-ﬂow density per unit area in rapidity-azimuth:

ρ = median

i∈patches





, (1)

where p

and A

are, respectively, the transverse momen-

tum and area of patch i. In the original formulation of the

area–median method, the patches were those obtained by

running inclusive k

clustering [19,20], but subsequently it

was realised that it was much faster and equally effective to

use (almost) square patches of size a × a in the rapidity-

azimuth plane. That will be our choice here. The use of the

median ensures that hard jets do not overly bias the ρ estimate

(as quantiﬁed in Ref. [21]).

Choosing the minimal transverse-momentum threshold,

cut

, that results in ρ = 0 is equivalent to gradually rais-

ing the p

threshold until exactly half of the patches contain

no particles, which ensures that the median is zero. This is

illustrated in Fig. 1. Computationally, p

cut

is straightforward

to evaluate: one determines, for each patch i,thep

of the

hardest particle in that patch, p

max

and then p

cut

is given by

the median of p

max

values:

cut

= median

i∈patches



max



. (2)

With this choice, half the patches will contain only particles

that have p

< p

cut

. These patches will be empty after appli-

cation of the p

threshold, leading to a zero result for ρ as

deﬁned in Eq. (1).

The computational time to evaluate p

cut

as in Eq. (2) scales linearly in the number of particles and the

method should be amenable to parallel implementation.

Imposing a cut on particles’ transverse momenta elimi-

nates most of the pileup particles, and so might reduce the

ﬂuctuations in residual pileup contamination from one point

to the next within the event. However, as with other event-

wide noise-reducing pileup and underlying-event mitigation

approaches, notably the CMS heavy-ion method [15–17](cf.

the analysis in Appendix A.4 of Ref. [22]), the price that one

pays for noise reduction is the introduction of biases. Specif-

ically, some particles from pileup will be above p

cut

and so

remain to contaminate the jets, inducing a net positive bias in

the jet momenta. Furthermore some particles in genuine hard

jets will be lost, because they are below the p

cut

, inducing a

negative bias in the jet momenta. The jet energy scale will

One practically important aspect of the area–median method is the

signiﬁcant rapidity dependence of the pileup, most easily accounted for

through a manually determined rapidity-dependent rescaling. This is

discussed in detail in Appendix B.

Applying a p

threshold to individual particles is not collinear safe;

in the speciﬁc context of pileup removal, we believe that this is not a

signiﬁcant issue, as we discuss in more detail in Appendix A.

123

Eur. Phys. J. C (2015) 75 :59 Page 3 of 16 59

0.5

1.5

2.5

0 20 40 60 80 100 120 140 160 180 200

SoftKiller p

cut

[GeV]

√s=14 TeV, Pythia8(4C), SoftKiller(a=0.4)

t,gen

>20 GeV

t,gen

>1 TeV

-20

-10

0 0.5 1 1.5 2 2.5 3

loss [GeV]

cut

[GeV]

loss from hard

20 < p

t,jet

< 50 GeV

100 < p

t,jet

< 200 GeV

1000 < p

t,jet

< 2000 GeV

gain [GeV]

√s=14 TeV, Pythia8(4C)

gain from pileup

μ=140

μ=60

μ=20

Fig. 2 Left Val ue o f t he p

cut applied by the SoftKiller, displayed

as a function of the number of pileup events. We show results for two

different values of the generator minimal p

for the hard event, p

t,gen

The solid line is the average p

cut

value, while the dashed lines indicate

the one-standard-deviation band. Right Plot of the p

that is lost when

applying a given p

cut (the x axis) to the constituents of jets clustered

(anti-k

, R = 0.4) from the hard event (solid lines) and the residual

pileup p

that remains after applying that same cut to the constituents

of circular patches of radius 0.4 in pure-pileup events (dashed lines)

only be correctly reproduced if these two kinds of bias are

of similar size,

so that they largely cancel. There will be an

improvement in the jet resolution if the ﬂuctuations in these

biases are modest.

Figure 2 shows, on the left, the average p

cut

value, together

with its standard deviation (dashed lines), as a function of the

number of pileup interactions, n

. The event sample con-

sists of a superposition of n

zero bias on one hard dijet

event, in 14 TeV proton–proton collisions, all simulated with

Pythia 8 (tune 4C) [23]. The 4C tune gives reasonable agree-

ment with a wide range of minimum-bias data, as can be seen

by consulting MCPlots [24].

The underlying event in the

hard event has been switched off, and all particles have been

made massless, maintaining their p

, rapidity and azimuth.

These are our default choices throughout this paper. The

grid used to determine p

cut

has a spacing of a  0.4 and

extends up to |y| < 5. One sees that p

cut

remains moder-

ate, below 2 GeV, even for pileup at the level foreseen for

the high-luminosity upgrade of the LHC (HL-LHC), which

For patch areas that are similar to the typical jet area, this can be

expected to happen because half the patches will contain residual pileup

of order p

cut

, and since jets tend to have only a few low-p

particles

from the hard scatter, the loss will also be order of p

cut

In Appendix C we also brieﬂy examine the Pythia 6 [25] Z2 tune [26],

and ﬁnd very similar results.

If one keeps the underlying event in the hard event, much of it

(about 1 GeV for both the area–median approach and the SoftKiller)

is subtracted together with the pileup correction, affecting slightly the

observed shifts. Keeping massive particles does not affect the SK perfor-

mance but requires an extra correction for the area–median subtraction

[27]. We therefore use massless particles for simplicity.

is expected to reach an average (Poisson-distributed) num-

ber of pileup interactions of μ  140. The right-hand plot

shows the two sources of bias: the lower (solid) curves, illus-

trate the bias on the hard jets induced by the loss of genuine

hard-event particles below p

cut

. Jet clustering is performed

with the anti-k

jet algorithm [28] with R = 0.4, as imple-

mented in a development version of FastJet 3.1 [29,30].

The three line colours correspond to different jet p

ranges.

The loss has some dependence on the jet p

itself, notably for

higher values of p

cut

In particular it grows in absolute terms

for larger jet p

’s, though it decreases relative to the jet p

The positive bias from residual pileup particles (in circular

patches of radius 0.4 at rapidity y = 0) is shown as dashed

curves, for three different pileup levels. To estimate the net

bias, one should choose a value for n

, read the average p

cut

from the left-hand plot, and for that p

cut

compare the solid

curve with the dashed curve that corresponds to the given

. Performing this exercise reveals that there is indeed a

reasonable degree of cancellation between the positive and

negative biases. Based on this observation, we can move for-

ward with a more detailed study of the performance of the

method.

For our purposes here, the version that we used is equivalent to the

most recent public release, FastJet 3.0.6.

In a local parton–hadron duality type approach to calculate hadron

spectra, the spectrum of very low p

particles in a jet of a given ﬂavour

is actually independent of the jet’s p

[31].

A study of ﬁxed p

cutoffs, rather than dynamically determined ones,

is performed in Appendix D.

123

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