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# Separating signal from combinatorial jets in a high background environment

Patrick Steffanic  Charles Hughes  Christine Nattrass  University of
Tennessee, Knoxville, TN, USA-37996.

###### Abstract

We study procedures for discriminating combinatorial jets in a high background
environment, such as a heavy ion collision, from signal jets arising from a
hard-scattering. We investigate a population of jets clustered from a combined
PYTHIA +TennGen event, focusing on jets which can unambiguously be classified
as signal or combinatorial jets. By selecting jets based on their kinematic
properties, we investigate whether it is possible to separate signal and
combinatorial jets without biasing the signal population significantly. We
find that, after a loose selection on the jet area, surviving combinatorial
jets are dominantly imposters, combinatorial jets with properties
indistinguishable from signal jets. We also find that, after a loose selection
on the leading hadron momentum, surviving combinatorial jets are still
dominantly imposters. We use rule extraction, a machine learning technique, to
extract an optimal kinematic selection from a random forest trained on our
population of jets. In general, this technique found a stricter kinematic
selection on the jet’s leading hadron momentum to be optimal. We find that it
is possible to suppress combinatorial jets significantly using this machine
learning based selection, but that some signal is removed as well. Due to this
stricter kinematic selection, we find that the surviving signal is biased
towards quark-like jets. Since similar selections are used in many
measurements, this indicates that those measurements are biased towards quark-
like jets as well. These studies should motivate an increased emphasis on
assumptions made when suppressing and subtracting combinatorial background and
the biases introduced by methods for doing so.

##  I Introduction

A hot, dense, strongly interacting liquid of quarks and gluons called the
Quark Gluon Plasma (QGP) is briefly created in high energy heavy ion
collisions [1, 2, 3, 4]. Two of the key signatures of the formation of the QGP
are jet quenching and hydrodynamical flow. There have been extensive
measurements of jets in a QGP, including single particle spectra, jet spectra,
fragmentation functions, and jet substructure [5]. While there have been some
constraints on the properties of the medium due from measurements of jets [6,
7], the era of quantitative measurements of jets is just beginning. A detailed
understanding of jet quenching requires a quantitative understanding of the
background.

The paradigm the field uses to separate signal and background assumes that
particles are either from jets or from background processes. While this
approach is commonly used in heavy ion collisions, we note that similar
approaches to a combinatorial background may be applicable to $p$+$p$
collisions in a high pile up environment. The signal is assumed to be a
cluster of particles from a hard process. The background includes particles
from all other processes, including other jets. Many background particles are
correlated, either due to resonances or flow. A jet finder will cluster all
particles into a jet, so the background impacts the signal both through
background particles clustered with signal jets and jets consisting
exclusively of background particles, called combinatorial jets.

In practice, there is some ambiguity in whether particles are from the signal
or the background. When partons interact with the medium, they may leave some
of their energy and momentum in medium particles, for instance through a wake
from movement of the parton through a fluid [8]. It is unclear in that case if
those particles should be considered signal or background. Furthermore, at low
momenta, the definition of a jet itself becomes ambiguous, as there is no
clear threshold for when a process is hard enough to result in a jet and a jet
finder will cluster particles with correlated momenta independent of their
production mechanism.

The assumption that particles are either from the signal or from the
background works well for describing combinatorial jets, jets composed
entirely of particles from the background. This can be seen by the agreement
between the sum of the energies of all particles found in a random cone in a
heavy ion collision and expectations for drawing random particles with momenta
matching that observed in the data [9]. While there are some deviations
between these observations and expectations from a random sample, there is
even good agreement with PYTHIA Angantyr, which includes correlations from
resonances and mini-jets [10]. The contribution from combinatorial jets is
typically managed by focusing on high momentum jets or suppressing the
background through kinematic selections such as requiring a minimum momentum
for the highest momentum particle [11]. Combinatorial jets have also been
described by mixed events and their contribution subtracted when their
contribution is limited by a coincidence with a high momentum hadron
$180^{\circ}$ away [12].

The contribution of background particles in jets has typically been subtracted
either through an iterative procedure to estimate background contributions
[13, 14], or by estimating the background per unit area [11, 12]. Recently a
shallow neural network was applied to estimate the background contribution to
jet measurements to extend these measurements to lower momenta and larger R
[15, 16].

Measurements of jets in heavy ion collisions are limited at low momenta both
because the number combinatorial jets becomes comparable to the number of
signal jets and because measurements have large uncertainties when
fluctuations in the background contributions to signal jets are comparable to
the jet momenta. In this study, we use a model with a randomly generated
background from TennGen [10], described in sec. II.1, and a signal from
PYTHIA, described in sec. II.2. We define unambiguous samples of signal and
combinatorial jets in sec. II.3, and characterize them by their properties,
summarized in sec. II.4. We introduce the silhouette value in sec. II.5 as an
alternate means to look at whether or not signal and combinatorial jets are
distinguishable. In sec. II.6 we describe a machine learning approach to
optimizing the separation of signal and combinatorial jets and in sec. II.7 we
describe the leading subjet fraction, which we use to look for bias introduced
by the kinematic selections used to separate signal and combinatorial jets. In
sec. III we describe the kinematic selections identified, discuss the
limitations in separating signal and combinatorial jets, and investigate
possible biases imposed by these kinematic selections.

##  II Method

We investigate ways to distinguish signal and combinatorial jets in heavy-ion
collisions. We use a model to unambiguously define signal and combinatorial
jets, which is not possible in experiment. We use machine learning to explore
promising observables, and their associated kinematic selections, that may
have been overlooked. We consider jet observables, described in sec. II.4,
whose interpretation is comparable in experiment and theory. We demonstrate
that the machine learning system reproduces the standard kinematic selections.
Furthermore, we show that any kinematic selection admits combinatorial jets
whose properties are indistinguishable from signal jets. To further reduce the
number of combinatorial jets, the number of signal jets is necessarily
reduced, introducing a bias.

We use TennGen [10, 17], briefly described in sec. II.1, for a realistic
background Pb+Pb event at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV with
correlations due to flow but no other physics correlations. We embed a $p$+$p$
collision produced with PYTHIA 6 [18] using the Perugia 2011c[19] tune at
$\sqrt{s}$ = 2.76 TeV, briefly described in sec. II.2, in the TennGen event to
generate a jet signal. We cluster the combined event with the anti-$k_{T}$ jet
finder, producing a population of jets with particles from both PYTHIA and
TennGen. We can then classify jets as combinatorial or signal by how much
momentum is from TennGen and PYTHIA particles, as described in sec. II.3.

We use a number of jet observables, discussed in sec. II.4, to characterize
our jet population and evaluate the effect of different kinematic selections
on signal and combinatorial jets. We introduce silhouette values, used to
quantify how similar an object is to other object in its cluster, in sec. II.5
and use the distribution of silhouette values to evaluate the similarity
between signal and combinatorial jets. We use a random forest, a type of
machine learning algorithm, coupled with a decision tree to search for optimal
selections that distinguish between signal and combinatorial jets. This
algorithm is described in sec. II.6. We study the momentum fraction carried by
the leading subjet, described in sec. II.7, to understand the bias towards
quark-like jets imposed by kinematic selections.

###  II.1 Background generation

TennGen emulates a realistic background for jet studies in heavy ion
collisions by throwing random particles which match the multiplicities [20],
momentum distributions [21], and azimuthal distributions [22] of single
particles. TennGen is described in greater detail in [10] and the source code
is publicly available [17].

The measured single particle double differential spectra for $\pi^{\pm}$, K±,
p and $\bar{p}$ from [21] are fit to a Boltzmann-Gibbs Blast Wave distribution
[23, 24]. This distribution is used to randomly select a momentum for each
particle. The single particle flow coefficients [22] are used to determine the
azimuthal distribution of particles with that momentum, and a random azimuthal
angle is determined from that distribution. The pseudorapidity $\eta$ of the
particle is randomly selected from a flat distribution in $-0.9<\eta<0.9$ to
match the $\eta$ acceptance of the ALICE detector. The multiplicity of each
particle species is determined from ratios [20] and is scaled up assuming a
constant charged particle multiplicity per unit pseudorapidity. We use 0–5%
central TennGen events, which have $\frac{dN}{d\eta}$ = 2217 and $\langle
p_{T}\rangle$ = 0.56 GeV/c. The multiplicities are determined from
measurements of the charged particle multiplicities in [25].

By construction, TennGen events contain no correlations other than those due
to flow. Previous studies indicate that the background can be described by
randomly selecting particles from the single particle distribution [9, 12,
10]. Some contributions from mini-jets and resonances could arguably be
considered signal and we aim to study the properties of jets which are
unambiguously combinatorial. The absence of these additional correlations in
TennGen is therefore a desirable feature for these studies. As such, all
particles in TennGen are considered background particles for measurements of
jets.

###  II.2 Signal generation

PYTHIA [18] is a general purpose Monte Carlo event generator. In this study we
generate proton-proton events at $\sqrt{s}$ = 2.76 TeV in PYTHIA using the
Perugia 2011c[19] tune and require a hard scattering with various
$p_{T}^{hardmin.}$. Other parameters are left at their defaults. Jets are
clustered from primary $\pi^{0}$, $\pi^{\pm}$, K±, p and $\bar{p}$ particles
with $|\eta|$ $<$ 0.9 using the anti-$k_{T}$ algorithm implemented in FastJet
v3.2.1 [26] with various jet resolution parameters $R$. We keep PYTHIA events
which have one jet with at least 80% of the $p_{T}^{hardmin.}$within the
acceptance in pseudorapidity and embed them in a TennGen event. This leads to
a slightly different distribution of jets than if we were to use minimum bias
PYTHIA events but does not qualitatively change the conclusions. Particles
from PYTHIA are considered to be signal particles. There is a small underlying
event in $p$+$p$, but we treat this as negligible compared to the jet signal.

###  II.3 Signal and combinatorial jets

We cluster all the particles from the combined TennGen and PYTHIA event with
the anti-$k_{T}$ jet finder. We calculate the fraction of each jet’s momentum
carried by PYTHIA particles. Jets which have less than $2\pi R^{2}$ GeV/$c$
from PYTHIA are classified as combinatorial jets. This allows up to the
average momentum in a random cone from the underlying event in PYTHIA assuming
an average momentum density of 2 GeV/$c$ per unit area. Jets which contain at
least 0.8 $p_{T}^{hardmin.}$GeV/$c$ from PYTHIA particles are classified as
signal jets. This ensures that only PYTHIA jets are classified as signal jets,
without any combinatorial jets classified incorrectly as signal jets. The
remainder are not classified. This allows us to identify unambiguous samples
of signal and combinatorial jets.

The results presented in sec. III focus on $R=0.5$ and $p_{T}^{hardmin.}$= 40
GeV/$c$ and results for additional resolution parameters ranging from R=0.2 to
0.6 for $p_{T}^{hardmin.}$ranging from 10 to 80 GeV/$c$ are given in the
Supplemental Material
[[SeeSupplementalMaterialat][forkinematicselectionsofothervaluesofR,
and$p_T^hardmin.$.]supp].

###  II.4 Observables

Our objective is to identify observables which may help discriminate between
signal and combinatorial jets, could realistically be used in data, and either
would lead to a negligible bias in the surviving population of signal jets or
whose bias could be reproduced well in model calculations. In particular, our
aim is to study low momentum jets to investigate approaches to decreasing the
lower threshold for jet measurements and decrease the systematic uncertainties
associated with background subtraction in this region. We started with
observables which could be measured on an individual jet basis and eliminated
observables using a combination of our knowledge of the strengths and
weaknesses of these observables and statistical techniques. We only used
observables which are reliably measurable in data and calculable in models
with reasonable uncertainties. This excludes the $n^{th}$ leading particle’s
momentum for n$>$1, for instance, because they would be difficult to model
accurately, and may make the model sensitive to fluctuations in data and
models. We used the scikit learn implementation of principle component
analysis [28] to better understand which observables are redundant, and
feature importance from our random forest [29] to remove observables which had
little discriminatory power. The observables we chose are summarized in tab.
1. The principle component analysis indicates that these observables explain
98% of the variance in our data. Of that, $p_{T}^{1}$ accounts for the
majority of the variance. While a similar approach may lead to a different set
of observables, we think that this is a realistic set of observables which
could be used to discriminate between signal and combinatorial jets.

Symbol | Name | Definition
---|---|---
$A_{jet}$ | Jet Area | Area covered by all jets constituents
$p_{T}^{1}$ | Leading Hadron Momentum | Momentum of leading jet constituent
$\lambda_{1}^{1}$ | Jet Width | $\sum_{i=1}^{N_{constit.}}z_{consit.,i}\cdot\Delta R_{constit.i,jet}$
$\langle p_{T}\rangle$ | Mean $p_{T}$ | $\frac{1}{N_{constit.}}\sum_{i=1}^{N_{constit.}}p_{T,i}$
Table 1: Observables used to characterize each jet population.

####  II.4.1 Area

To calculate the area of jet, we add many very soft particles(”ghosts”) to the
event, counting how many ghosts are clustered into our jet. The jet area is
given by

$A_{jet}=A_{g}\langle N_{g}\rangle$ (1)

where $A_{g}$ is the area of a single ghost and $\langle N_{g}\rangle$ is the
average number of ghosts clustered into our jet [30].

####  II.4.2 Leading hadron momentum

The leading hadron momentum, $p_{T}^{1}$, is the highest momentum jet
constituent. While there is some model dependence in calculating a leading
hadron momentum in theory calculations because hadronization is non-
perturbative, such calculations are fairly robust since single hadron
observables in $p$+$p$ collisions agree well with pQCD calculations [31]. We
opted not to include the subleading hadron momentum and beyond because they
would make model calculations more sensitive to details of hadronization.

####  II.4.3 Jet width

The jet width[32], $\lambda_{1}^{1}$, is given by

$\lambda_{1}^{1}=\sum_{i=1}^{N}z_{i}\cdot\frac{\Delta R_{i,jet}}{R}$ (2)

where $N$ is the number of constituents in the jet, $z_{i}$ is the momentum
fraction carried by constituent $i$, and $\Delta R_{i,jet}$ is the distance in
$\eta$-$\phi$ space between constituent $i$ and the jet axis. This provides a
measure of how far constituents are from the jet axis on average.

####  II.4.4 Mean constituent transverse momentum

Mean constituent transverse momentum including background, $\langle
p_{T}\rangle$, is the average $p_{T}$ of the jet’s constituents. TennGen is
expected to reproduce the $\langle p_{T}\rangle$ from data fairly accurately.

We investigated the use of higher order moments of the momentum distribution,
such as the standard deviation. These features provide useful information, but
reproducing them in a model would require getting the single particle spectrum
and the fragmentation functions correct to high precision. We concluded this
would add too much model dependence.

###  II.5 Silhouette values

We borrow a technique from data science to characterize the overlap between
our different populations. Our two populations are unambiguous signal, and
combinatorial jets. The silhouette value[33] describes, for each signal or
combinatorial jet, whether it shares more characteristics with its own cluster
or the other cluster. The silhouette value for the jet with index i is given
by

$S(i)=\frac{b(i)-a(i)}{max\\{a(i),b(i)\\}}$ (3)

$a(i)$ is the mean in-class distance,

$a(i)=\frac{1}{N_{I}-1}\sum_{j\neq i}^{N_{I}}d(i,j)$ (4)

where the sum runs over jets of the same class as jet i, and $N_{I}$ is the
number of jets in the same class as jet i; $b(i)$ is the mean out-of-class
distance,

$b(i)=\frac{1}{N_{J}}\sum_{j}^{N_{J}}d(i,j)$ (5)

where the sum here runs over jets of the opposite class from jet i, and
$N_{J}$ is the number of jets in the opposite class. The $d(i,j)$ in both
equations represents the distance between jet i and jet j. This is typically
the Euclidean distance computed in feature space. We standardize our data so
that each feature lies in the range [0,1], ensuring that each feature
contributes equally to the silhouette value, rather than features with larger
ranges having a larger effect.

$d(i,j)=\biggl{\\{}\bigg{(}\frac{A_{jet,j}-A_{jet,i}}{A_{jet}^{max}-A_{jet}^{min}}\bigg{)}^{2}+\bigg{(}\frac{p_{T,j}^{1}-p_{T,i}^{1}}{p_{T}^{1,max}-p_{T}^{1,min}}\bigg{)}^{2}\\\
+\bigg{(}\frac{\lambda_{1,j}^{1}-\lambda_{1,i}^{1}}{\lambda_{1}^{1,max}-\lambda_{1}^{1,min}}\bigg{)}^{2}+\bigg{(}\frac{\langle
p_{T}\rangle_{j}-\langle p_{T}\rangle_{i}}{\langle p_{T}\rangle^{max}-\langle
p_{T}\rangle^{min}}\bigg{)}^{2}\biggr{\\}}^{\frac{1}{2}}.$ (6)

Silhouette values have a range from -1 to 1. A jet with a positive silhouette
value is more similar to its own class than the other class. A negative
silhouette value indicates the opposite, the jet is more similar to jets from
the other class than to jets from its own class. While it would be possible to
extend the list of observables, we do not anticipate others would have any
significant distinguishing power. We rejected a number of interesting
observables that were either too complex to faithfully simulate or too
difficult to measure in data. Silhouette values could help determine the
effectiveness of any new observable to distinguish signal and combinatorial
jets.

###  II.6 Kinematic selection optimization

We train a machine learning system to learn about the relationship between a
jet’s features and whether it is a signal jet or a combinatorial jet using the
input features described in sec. II.4. We use a random forest, but a neural
network or any other algorithm capable of classification could be used. We
then train a decision tree on the predictions of the random forest. The
decision tree is a classification algorithm that uses a series of kinematic
selections to classify each jet. This technique is a type of rule extraction
called the oracle method[34]. We extract the top-level node of our trained
decision tree, the kinematic selection which best separates signal and
combinatorial jets. We then evaluate the biases and background reduction of
any such selection. Our goal is to extract the useful information from machine
learning while avoiding its downsides, namely over-fitting and model
dependence. The details of our specific machine learning system are mentioned
below.

####  II.6.1 Decision trees

We use the sci-kit learn implementation of the decision tree[35], which is
based on the Classification and Regression Trees algorithm described in [36].
A decision tree recursively partitions the feature space such that the samples
with the same labels are grouped together. Each candidate split, $\theta$,
consists of a feature and a threshold; in our case, a kinematic selection. The
selection is evaluated according to an impurity function H and its quality is
determined by

$G(Q_{m},\theta)=\frac{N_{m}^{left}}{N_{m}}H(Q_{m}^{left}(\theta))+\frac{N_{m}^{right}}{N_{m}}H(Q_{m}^{right}(\theta))$
(7)

where $Q_{m}$ are the data at node m, $N_{m}$ is the total number of samples
at node m, and the left (right) superscripts indicate that the data are below
(above) the threshold. The algorithm selects the split which minimizes G.
There are two primary choices for the impurity function H, Gini impurity

$\sum_{i=1}^{N_{c}}p_{i}(1-p_{i})$ (8)

and entropy

$-\sum_{i=1}^{N_{c}}p_{i}log_{2}p_{i}$ (9)

where $N_{c}$ is the number of classes and $p_{i}$ is the probability of
randomly picking an element of class i. We use Gini impurity in this study.

Decision trees can be prone to over-fitting the data, resulting in poor
generalization. Additionally, their accuracy is quite dependent on appropriate
hyper-parameter tuning [35]. We used scikit-learn v1.2.0 and the default
parameters of the DecisionTreeClassifier except for the max_depth parameter,
which was set to 3.

####  II.6.2 Random forests

In order to overcome the problem of over-fitting the random forest
algorithm[37] is used. This is an ensemble method involving training hundreds
of randomized decision trees and averaging their predictions for a more
robust, general prediction. There are two sources of randomness in the
algorithm: each decision tree sees only a random sample of the data, and at
each splitting the decision tree can use either all of the features or a
random subset of a chosen size. Each decision tree is trained independently
from the others. The variance of a random forest is smaller than that of a
single decision tree due to the injection of randomness and resulting average
over the decision trees. The prediction for each jet becomes the ground truth
for the ”oracle” decision tree. It should be noted that the scikit-learn
implementation is not exactly as in [37], as described in [38]. We used
scikit-learn v1.2.0 and the default parameters of the RandomForestClassifier
except as noted in tab. 2.

Parameter name | This study | Default
---|---|---
n_estimators | 200 | 100
max_depth | 3 | None
min_samples_leaf | 100 | 1
min_weight_fraction_leaf | 0.1 | 0.0
max_samples | 0.9 | 1.0
random_state | 42 | None
Table 2: Non-default parameters used for the RandomForestClassifier in this
study.

After the ”oracle” decision tree is trained, we extract a kinematic
selection–the top node of the tree–as well as the signal jet and combinatorial
jet rejection rates after applying the selection. We then apply these
selections to our data and study the potential biases that they introduce to
determine their usefulness in analyses.

###  II.7 Leading sub-jet momentum fraction

The concept of quark or gluon jets is only defined at leading order, so any
realistic distinction, even in a model calculation, is somewhat ad hoc.
However, models predict differences between quark-like and gluon-like jets.
Suppression of background by selecting on the kinematic properties of jets may
bias the population of surviving jets towards or away from quark-like or
gluon-like jets because quark-like jets fragment into fewer, harder particles
which are closer on average to the jet axis than gluon-like jets [39, 40]. The
observables in sec. II.4 are therefore expected to have different
distributions for quark-like and gluon-like jets.

We use the leading subjet momentum fraction to qualitatively evaluate whether
kinematic selections impose a substantial bias towards quark-like jets. The
jet constituents are reclustered with the anti-$k_{T}$ jet finder with a
smaller radius parameter, $R=0.1$. The leading subjet momentum fraction,
$z_{subjet}$, is the fraction of the jet’s total momentum in the leading
subjet [41]

$z_{subjet}=\frac{p_{T}^{subjet}}{p_{T}^{jet}}.$ (10)

Studies of this observable indicate that quark-like jets have a higher
$z_{subjet}$ while gluon-like jets have a lower $z_{subjet}$ [42, 43]. We use
only PYTHIA particles to determine $z_{subjet}$ in our sample. We note that
the connection between $z_{subjet}$ and the leading parton is more tenuous for
smaller $R$ and lower momenta, but nevertheless consider this a reasonable
observable to test for biases towards quark-like jets.

##  III Results

Figure 1: Distribution of $A_{jet}$ vs. $\lambda_{1}^{1}$ for signal and
combinatorial jets with $R=0.5$ and $p_{T}^{hardmin.}$$=40$ GeV/$c$ after each
kinematic selection. The z-axis has a log scale.

We successively apply four different kinematic selections. Here we present
results for $R=0.5$ and $p_{T}^{hardmin.}$$=40$ GeV/$c$. Results from other
selections can be found in the appendices. Figure 1(a) shows the inclusive
distribution of jet area versus $\lambda_{1}^{1}$ for both signal and
combinatorial jets. This shows the overlap between both jet populations. There
are few signal jets at small areas, indicating that the large area region can
be selected with little bias. We therefore apply the ALICE selection of
$A>0.6\pi R^{2}$. For jets with resolution parameters $R>0.3$ and
$p_{T}^{hardmin.}$$<30$ GeV/$c$ there may be some bias imposed due to more
signal jets in the low area region, shown in Supplemental Material. Figure 2
shows the distribution of $p_{T}^{1}$, $\lambda_{1}^{1}$, and $\langle
p_{T}\rangle$ for signal and combinatorial jets before and after this
selection normalized by the total number of jets before the selection. Changes
in the signal distributions are negligible except for resolution parameters
R=0.5, and 0.6 when $p_{T}^{hardmin.}$$<$ 20 GeV/$c$, shown in Supplemental
Material, while the surviving combinatorial jet distributions for
$\lambda_{1}^{1}$ and $\langle p_{T}\rangle$ become more like those of signal
jets. We call these combinatorial jets which look like signal jets ”imposter
jets.” The selection on area is so effective because many combinatorial jets
consist of a single particle; such jets have small areas with low
$\lambda_{1}^{1}$ and a $\langle p_{T}\rangle$ distribution closer to the
inclusive particle momentum distribution.

Figure 2:  Distributions of leading hadron momentum, jet width, and mean
constituent momentum for jets with $R=0.5$ and $p_{T}^{hardmin.}$$=40$ GeV/$c$
before and after excluding jets with $A<$ $0.6*\pi R^{2}$. The overall
reduction of combinatorial jets was 66.3%.

The jets remaining after applying a kinematic selection in fig. 2 indicate a
significant difference between $p_{T}^{1}$ distributions for signal and
combinatorial jets, while the $\lambda_{1}^{1}$ distributions overlap
significantly for signal and combinatorial jets. The differences for both
$p_{T}^{1}$ and $\lambda_{1}^{1}$ increase with $p_{T}^{hardmin.}$and decrease
with increasing resolution parameter. The $\langle p_{T}\rangle$ distributions
indicate a separation between signal and combinatorial jets. They follow the
same trends in $p_{T}^{hardmin.}$and R as in $p_{T}^{1}$ and
$\lambda_{1}^{1}$, but the differences are not as large as those in the
$p_{T}^{1}$ distributions. Furthermore, the $\langle p_{T}\rangle$
distribution would be difficult to recreate in simulation, meaning that any
biases would be difficult to reproduce for comparisons between models and
data. Figure 1(b) shows that after this selection, the distributions of signal
and background jets overlap significantly, so any further selection will
suppress signal jets as well.

Figure 3:  Distributions of jet area, jet width, and mean constituent momentum
for jets with $R=0.5$ and $p_{T}^{hardmin.}$$=40$ GeV/$c$ before and after
excluding jets with $p_{T}^{1}<$ 3 GeV/$c$. The overall reduction of
combinatorial jets was 81.6%.

We then investigate a selection of $p_{T}^{1}>3.0$ GeV/$c$. The distributions
of $A$, $\lambda_{1}^{1}$, and $\langle p_{T}\rangle$ for surviving signal and
combinatorial jets are shown in fig. 3. As for the selection on area, there is
no apparent difference in the distributions for surviving signal jets.
Surviving combinatorial jets are imposters. Figure 1(c) shows that the
properties of the surviving jets, indeed, still overlap significantly. A
selection on $p_{T}^{1}$ is effective at suppressing background, but it is not
collinear safe and may introduce biases. Biases may be unavoidable, and the
impact of a selection on $p_{T}^{1}$ is at least likely to be easier to
reproduce in model calculations than other observables, such as $\langle
p_{T}\rangle$.

Figure 4:  Distributions of jet area, leading hadron momentum, jet width, and
mean constituent momentum for jets with $R=0.5$ and $p_{T}^{hardmin.}$$=40$
GeV/$c$ before and after excluding jets with $A<$ $0.6*\pi R^{2}$, and
$p_{T}^{1}<5.036$ GeV/$c$. The overall reduction of combinatorial jets was
99.8%. This tighter selection rejects predominantly gluon-like signal jets, as
shown in Figure 6.

We then approach kinematic selections using rule extraction from a random
forest. The selection on area is efficient, cutting little or no signal while
eliminating significant background, but a tighter selection which eliminated
significant signal might be difficult to reproduce in models. We therefore
keep the area selection and use the random forest, as well as the decision
tree, both described in sec. II.6, to identify the best kinematic selection
among $p_{T}^{1}$, $\lambda_{1}^{1}$ and $\langle p_{T}\rangle$. The algorithm
found that the optimal selection was $p_{T}^{1}$ $>5.036$ GeV/$c$ for jets
with R=0.5, and $p_{T}^{hardmin.}$=40 GeV/$c$. For other values of resolution
parameter and $p_{T}^{hardmin.}$the trend is generally a tighter selection on
$p_{T}^{1}$ ranging from 3.5 GeV/$c$ to 5.2 GeV/$c$, given in tab. 4.. The
algorithm finds $\langle p_{T}\rangle$ to be the optimal selection for
$p_{T}^{hardmin.}$$>60$ GeV/$c$, but we do not explore it in this study for
the reasons mentioned above. The extracted selections reproduce the machine
learning systems predictions within 1% accuracy. We can see in fig. 1(d) that
the remaining combinatorial jets are imposters. Figure 4 shows the impact of
this selection on the distribution of $A$, $\lambda_{1}^{1}$, and $\langle
p_{T}\rangle$ for signal and combinatorial jets. The suppression of
combinatorial jets is much greater than that seen in fig. 2 or fig. 3.

Figure 5: Distributions of silhouette values for signal and combinatorial jets with R=0.5, $p_{T}^{hardmin.}$=40 GeV/$c$ after each kinematic selection. The silhouette values are recomputed for each new population of jets. Each population is normalized by the total inclusive number of jets. The silhouette value describes whether a jet is more similar to its own class, or to the opposite class as described in sec. II.5. Selection | Population | $\%>0$ | $\%<0$
---|---|---|---
Inclusive | Signal | 100% | 0%
Combinatorial | 63% | 37%
$A>0.6\pi R^{2}$ | Signal | 84% | 16%
Combinatorial | 84% | 16%
$p_{T}^{1}>3.0GeV/c$ | Signal | 84% | 16%
Combinatorial | 84% | 16%
$A>0.6\pi R^{2}$, | Signal | 84% | 16%
$p_{T}^{1}>5.036GeV/c$ | Combinatorial | 84% | 16%
Table 3: The percentage of R=0.5, $p_{T}^{hardmin.}$=40 GeV/$c$ jets which
have silhouette values above and below zero.

We have only considered rectilinear selections so far, but it is possible that
some combination of observables described in sec. II.4 may be more effective
at distinguishing signal and combinatorial jets. The silhouette values
described in sec. II.5 are designed to help determine whether two sets are
distinguishable or whether there is too much overlap. Figure 5 shows the
silhouette values for each of our selections. Table 3 lists the fraction of
signal and combinatorial jets above and below zero. The inclusive distribution
in fig. 5(a) shows that, before the area selection, there is a large
population of combinatorial jets with a positive silhouette value (63%). These
combinatorial jets are easier to distinguish from signal jets. However, there
is also a significant population of imposters, those with a negative
silhouette value (37%). Figure 5(b), (c), and (d) show the silhouette values
for signal and combinatorial jets after the area selection, $p_{T}^{1}$
selection, and the selection chosen by the random forest. In these cases, the
distributions of silhouette values for signal and combinatorial jets have
similar shapes, indicating that either is just as likely to look like its own
group or like the other group.

Figure 6: $z_{subjet}$ ratio of accepted signal jets to inclusive signal jets
with $R=0.5$ and $p_{T}^{hardmin.}$$=40$ GeV/$c$ after applying each
selection. Jets with lower values of $z_{subjet}$ have been suggested to be
more gluon-like.

The selection chosen by the machine learning algorithm suppresses
combinatorial jets much more effectively, removing 99.9% of combinatorial
jets. However, signal jets may be more susceptible to survivor bias, as this
selection removes 1.6% of signal jets. Figure 6 shows the distribution of
$z_{subjet}$ for each kinematic selection compared to the inclusive
distribution for signal jets. The selection on $A$ and $p_{T}^{1}$ $>3.0$
GeV/$c$ are consistent with one for all $z_{subjet}$. For the kinematic
selection chosen by the machine learning algorithm, low $z_{subjet}$ signal
jets are significantly suppressed. This suppression is more pronounced for
jets with larger resolution parameters and lower $p_{T}^{hardmin.}$, shown in
Supplemental Material
[[SeeSupplementalMaterialat][forkinematicselectionsofothervaluesofR,
and$p_T^hardmin.$.]supp].

##  IV Conclusions

We used the background generator TennGen combined with signal jets from PYTHIA
to investigate ways that signal and combinatorial jets can be distinguished in
heavy ion collisions. TennGen events only contain correlations due to flow,
providing an unambiguous definition of the combinatorial background. We use
properties which could be reproduced in data, $A$, $p_{T}^{1}$,
$\lambda_{1}^{1}$, and $\langle p_{T}\rangle$, to describe each jet. We find
that signal and combinatorial jets overlap inextricably. The silhouette values
show that they are indistinguishable using properties which could
realistically be used in data. Any kinematic selection to reduce the number of
combinatorial jets leaves a population of imposter jets which look like signal
jets.

Most kinematic selections to reduce combinatorial jets, aside from a loose cut
on the area, reduce the population of signal jets as well. While a loose
selection on $p_{T}^{1}$ does not appear to impose as much bias, the tighter
selection suggested by the machine learning system significantly biases the
surviving jet population towards quark-like jets. If such a selection were
applied in data, this indicates that the surviving signal jets are biased
towards quark-like jets. Measurements where corrections for kinematic
selections are made by an unmodified simulation, such as PYTHIA, could be
correcting for unmeasured gluon-like jets with measurements of quark-like
jets. Complicated methods for distinguishing signal and combinatorial jets,
such as black-box machine learning or correcting for imposter jets using
unfolding, may have model-dependent assumptions. The possibility of such
issues should be clearly elucidated in studies which use these methods. We
call for a greater focus on any assumptions made when subtracting
combinatorial background and biases introduced by methods for suppressing and
subtracting this background.

##  V Acknowledgements

We are grateful to Mateusz Ploskon, Raghav Elayavalli, and Hannah Bossi for
feedback on the manuscript. This work was supported in part by funding from
the Division of Nuclear Physics of the U.S. Department of Energy under Grant
No. DE-FG02-96ER40982. We also acknowledge support from the UTK and ORNL Joint
Institute for Computational Sciences Advanced Computing Facility.

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Appendix A: Figures for all $p_{T}^{hardmin.}$ and R

###  .1 R=0.2, $p_{T}^{hardmin.}$=10 GeV/c

Figure 7: Jet area vs. jet width for R=0.2 $p_{T}^{hardmin.}$=10 GeV/$c$.
Figure 8: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.2 $p_{T}^{hardmin.}$=10 GeV/$c$ after area selection. Figure
9: Jet a) area, b) width, and c) mean constituent momentum for R=0.2
$p_{T}^{hardmin.}$=10 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 10: Jet a) area, b) width, and c) mean
constituent momentum for R=0.2 $p_{T}^{hardmin.}$=10 GeV/$c$ after leading
hadron selection. Figure 11: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.2
$p_{T}^{hardmin.}$=10 GeV/$c$. Figure 12: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.2 $p_{T}^{hardmin.}$=10 GeV/$c$.

###  .2 R=0.2, $p_{T}^{hardmin.}$=20 GeV/c

Figure 13: Jet area vs. jet width for R=0.2 $p_{T}^{hardmin.}$=20 GeV/$c$.
Figure 14: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.2 $p_{T}^{hardmin.}$=20 GeV/$c$ after area selection. Figure
15: Jet a) area, b) width, and c) mean constituent momentum for R=0.2
$p_{T}^{hardmin.}$=20 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 16: Jet a) area, b) width, and c) mean
constituent momentum for R=0.2 $p_{T}^{hardmin.}$=20 GeV/$c$ after leading
hadron selection. Figure 17: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.2
$p_{T}^{hardmin.}$=20 GeV/$c$. Figure 18: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.2 $p_{T}^{hardmin.}$=20 GeV/$c$.

###  .3 R=0.2, $p_{T}^{hardmin.}$=30 GeV/c

Figure 19: Jet area vs. jet width for R=0.2 $p_{T}^{hardmin.}$=30 GeV/$c$.
Figure 20: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.2 $p_{T}^{hardmin.}$=30 GeV/$c$ after area selection. Figure
21: Jet a) area, b) width, and c) mean constituent momentum for R=0.2
$p_{T}^{hardmin.}$=30 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 22: Jet a) area, b) width, and c) mean
constituent momentum for R=0.2 $p_{T}^{hardmin.}$=30 GeV/$c$ after leading
hadron selection. Figure 23: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.2
$p_{T}^{hardmin.}$=30 GeV/$c$. Figure 24: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.2 $p_{T}^{hardmin.}$=30 GeV/$c$.

###  .4 R=0.2, $p_{T}^{hardmin.}$=40 GeV/c

Figure 25: Jet area vs. jet width for R=0.2 $p_{T}^{hardmin.}$=40 GeV/$c$.
Figure 26: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.2 $p_{T}^{hardmin.}$=40 GeV/$c$ after area selection. Figure
27: Jet a) area, b) width, and c) mean constituent momentum for R=0.2
$p_{T}^{hardmin.}$=40 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 28: Jet a) area, b) width, and c) mean
constituent momentum for R=0.2 $p_{T}^{hardmin.}$=40 GeV/$c$ after leading
hadron selection. Figure 29: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.2
$p_{T}^{hardmin.}$=40 GeV/$c$. Figure 30: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.2 $p_{T}^{hardmin.}$=40 GeV/$c$.

###  .5 R=0.2, $p_{T}^{hardmin.}$=60 GeV/c

Figure 31: Jet area vs. jet width for R=0.2 $p_{T}^{hardmin.}$=60 GeV/$c$.
Figure 32: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.2 $p_{T}^{hardmin.}$=60 GeV/$c$ after area selection. Figure
33: Jet a) area, b) width, and c) mean constituent momentum for R=0.2
$p_{T}^{hardmin.}$=60 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 34: Jet a) area, b) width, and c) mean
constituent momentum for R=0.2 $p_{T}^{hardmin.}$=60 GeV/$c$ after leading
hadron selection. Figure 35: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.2
$p_{T}^{hardmin.}$=60 GeV/$c$. Figure 36: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.2 $p_{T}^{hardmin.}$=60 GeV/$c$.

###  .6 R=0.2, $p_{T}^{hardmin.}$=80 GeV/c

Figure 37: Jet area vs. jet width for R=0.2 $p_{T}^{hardmin.}$=80 GeV/$c$.
Figure 38: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.2 $p_{T}^{hardmin.}$=80 GeV/$c$ after area selection. Figure
39: Jet a) area, b) width, and c) mean constituent momentum for R=0.2
$p_{T}^{hardmin.}$=80 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 40: Jet a) area, b) width, and c) mean
constituent momentum for R=0.2 $p_{T}^{hardmin.}$=80 GeV/$c$ after leading
hadron selection. Figure 41: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.2
$p_{T}^{hardmin.}$=80 GeV/$c$. Figure 42: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.2 $p_{T}^{hardmin.}$=80 GeV/$c$.

###  .7 R=0.3, $p_{T}^{hardmin.}$=10 GeV/c

Figure 43: Jet area vs. jet width for R=0.3 $p_{T}^{hardmin.}$=10 GeV/$c$.
Figure 44: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.3 $p_{T}^{hardmin.}$=10 GeV/$c$ after area selection. Figure
45: Jet a) area, b) width, and c) mean constituent momentum for R=0.3
$p_{T}^{hardmin.}$=10 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 46: Jet a) area, b) width, and c) mean
constituent momentum for R=0.3 $p_{T}^{hardmin.}$=10 GeV/$c$ after leading
hadron selection. Figure 47: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.3
$p_{T}^{hardmin.}$=10 GeV/$c$. Figure 48: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.3 $p_{T}^{hardmin.}$=10 GeV/$c$.

###  .8 R=0.3, $p_{T}^{hardmin.}$=20 GeV/c

Figure 49: Jet area vs. jet width for R=0.3 $p_{T}^{hardmin.}$=20 GeV/$c$.
Figure 50: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.3 $p_{T}^{hardmin.}$=20 GeV/$c$ after area selection. Figure
51: Jet a) area, b) width, and c) mean constituent momentum for R=0.3
$p_{T}^{hardmin.}$=20 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 52: Jet a) area, b) width, and c) mean
constituent momentum for R=0.3 $p_{T}^{hardmin.}$=20 GeV/$c$ after leading
hadron selection. Figure 53: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.3
$p_{T}^{hardmin.}$=20 GeV/$c$. Figure 54: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.3 $p_{T}^{hardmin.}$=20 GeV/$c$.

###  .9 R=0.3, $p_{T}^{hardmin.}$=30 GeV/c

Figure 55: Jet area vs. jet width for R=0.3 $p_{T}^{hardmin.}$=30 GeV/$c$.
Figure 56: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.3 $p_{T}^{hardmin.}$=30 GeV/$c$ after area selection. Figure
57: Jet a) area, b) width, and c) mean constituent momentum for R=0.3
$p_{T}^{hardmin.}$=30 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 58: Jet a) area, b) width, and c) mean
constituent momentum for R=0.3 $p_{T}^{hardmin.}$=30 GeV/$c$ after leading
hadron selection. Figure 59: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.3
$p_{T}^{hardmin.}$=30 GeV/$c$. Figure 60: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.3 $p_{T}^{hardmin.}$=30 GeV/$c$.

###  .10 R=0.3, $p_{T}^{hardmin.}$=40 GeV/c

Figure 61: Jet area vs. jet width for R=0.3 $p_{T}^{hardmin.}$=40 GeV/$c$.
Figure 62: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.3 $p_{T}^{hardmin.}$=40 GeV/$c$ after area selection. Figure
63: Jet a) area, b) width, and c) mean constituent momentum for R=0.3
$p_{T}^{hardmin.}$=40 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 64: Jet a) area, b) width, and c) mean
constituent momentum for R=0.3 $p_{T}^{hardmin.}$=40 GeV/$c$ after leading
hadron selection. Figure 65: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.3
$p_{T}^{hardmin.}$=40 GeV/$c$. Figure 66: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.3 $p_{T}^{hardmin.}$=40 GeV/$c$.

###  .11 R=0.3, $p_{T}^{hardmin.}$=60 GeV/c

Figure 67: Jet area vs. jet width for R=0.3 $p_{T}^{hardmin.}$=60 GeV/$c$.
Figure 68: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.3 $p_{T}^{hardmin.}$=60 GeV/$c$ after area selection. Figure
69: Jet a) area, b) width, and c) mean constituent momentum for R=0.3
$p_{T}^{hardmin.}$=60 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 70: Jet a) area, b) width, and c) mean
constituent momentum for R=0.3 $p_{T}^{hardmin.}$=60 GeV/$c$ after leading
hadron selection. Figure 71: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.3
$p_{T}^{hardmin.}$=60 GeV/$c$. Figure 72: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.3 $p_{T}^{hardmin.}$=60 GeV/$c$.

###  .12 R=0.3, $p_{T}^{hardmin.}$=80 GeV/c

Figure 73: Jet area vs. jet width for R=0.3 $p_{T}^{hardmin.}$=80 GeV/$c$.
Figure 74: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.3 $p_{T}^{hardmin.}$=80 GeV/$c$ after area selection. Figure
75: Jet a) area, b) width, and c) mean constituent momentum for R=0.3
$p_{T}^{hardmin.}$=80 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 76: Jet a) area, b) width, and c) mean
constituent momentum for R=0.3 $p_{T}^{hardmin.}$=80 GeV/$c$ after leading
hadron selection. Figure 77: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.3
$p_{T}^{hardmin.}$=80 GeV/$c$. Figure 78: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.3 $p_{T}^{hardmin.}$=80 GeV/$c$.

###  .13 R=0.4, $p_{T}^{hardmin.}$=10 GeV/c

Figure 79: Jet area vs. jet width for R=0.4 $p_{T}^{hardmin.}$=10 GeV/$c$.
Figure 80: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.4 $p_{T}^{hardmin.}$=10 GeV/$c$ after area selection. Figure
81: Jet a) area, b) width, and c) mean constituent momentum for R=0.4
$p_{T}^{hardmin.}$=10 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 82: Jet a) area, b) width, and c) mean
constituent momentum for R=0.4 $p_{T}^{hardmin.}$=10 GeV/$c$ after leading
hadron selection. Figure 83: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.4
$p_{T}^{hardmin.}$=10 GeV/$c$. Figure 84: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.4 $p_{T}^{hardmin.}$=10 GeV/$c$.

###  .14 R=0.4, $p_{T}^{hardmin.}$=20 GeV/c

Figure 85: Jet area vs. jet width for R=0.4 $p_{T}^{hardmin.}$=20 GeV/$c$.
Figure 86: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.4 $p_{T}^{hardmin.}$=20 GeV/$c$ after area selection. Figure
87: Jet a) area, b) width, and c) mean constituent momentum for R=0.4
$p_{T}^{hardmin.}$=20 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 88: Jet a) area, b) width, and c) mean
constituent momentum for R=0.4 $p_{T}^{hardmin.}$=20 GeV/$c$ after leading
hadron selection. Figure 89: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.4
$p_{T}^{hardmin.}$=20 GeV/$c$. Figure 90: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.4 $p_{T}^{hardmin.}$=20 GeV/$c$.

###  .15 R=0.4, $p_{T}^{hardmin.}$=30 GeV/c

Figure 91: Jet area vs. jet width for R=0.4 $p_{T}^{hardmin.}$=30 GeV/$c$.
Figure 92: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.4 $p_{T}^{hardmin.}$=30 GeV/$c$ after area selection. Figure
93: Jet a) area, b) width, and c) mean constituent momentum for R=0.4
$p_{T}^{hardmin.}$=30 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 94: Jet a) area, b) width, and c) mean
constituent momentum for R=0.4 $p_{T}^{hardmin.}$=30 GeV/$c$ after leading
hadron selection. Figure 95: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.4
$p_{T}^{hardmin.}$=30 GeV/$c$. Figure 96: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.4 $p_{T}^{hardmin.}$=30 GeV/$c$.

###  .16 R=0.4, $p_{T}^{hardmin.}$=40 GeV/c

Figure 97: Jet area vs. jet width for R=0.4 $p_{T}^{hardmin.}$=40 GeV/$c$.
Figure 98: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.4 $p_{T}^{hardmin.}$=40 GeV/$c$ after area selection. Figure
99: Jet a) area, b) width, and c) mean constituent momentum for R=0.4
$p_{T}^{hardmin.}$=40 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 100: Jet a) area, b) width, and c) mean
constituent momentum for R=0.4 $p_{T}^{hardmin.}$=40 GeV/$c$ after leading
hadron selection. Figure 101: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.4
$p_{T}^{hardmin.}$=40 GeV/$c$. Figure 102: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.4 $p_{T}^{hardmin.}$=40 GeV/$c$.

###  .17 R=0.4, $p_{T}^{hardmin.}$=60 GeV/c

Figure 103: Jet area vs. jet width for R=0.4 $p_{T}^{hardmin.}$=60 GeV/$c$.
Figure 104: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.4 $p_{T}^{hardmin.}$=60 GeV/$c$ after area selection. Figure
105: Jet a) area, b) width, and c) mean constituent momentum for R=0.4
$p_{T}^{hardmin.}$=60 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 106: Jet a) area, b) width, and c) mean
constituent momentum for R=0.4 $p_{T}^{hardmin.}$=60 GeV/$c$ after leading
hadron selection. Figure 107: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.4
$p_{T}^{hardmin.}$=60 GeV/$c$. Figure 108: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.4 $p_{T}^{hardmin.}$=60 GeV/$c$.

###  .18 R=0.4, $p_{T}^{hardmin.}$=80 GeV/c

Figure 109: Jet area vs. jet width for R=0.4 $p_{T}^{hardmin.}$=80 GeV/$c$.
Figure 110: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.4 $p_{T}^{hardmin.}$=80 GeV/$c$ after area selection. Figure
111: Jet a) area, b) width, and c) mean constituent momentum for R=0.4
$p_{T}^{hardmin.}$=80 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 112: Jet a) area, b) width, and c) mean
constituent momentum for R=0.4 $p_{T}^{hardmin.}$=80 GeV/$c$ after leading
hadron selection. Figure 113: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.4
$p_{T}^{hardmin.}$=80 GeV/$c$. Figure 114: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.4 $p_{T}^{hardmin.}$=80 GeV/$c$.

###  .19 R=0.5, $p_{T}^{hardmin.}$=10 GeV/c

Figure 115: Jet area vs. jet width for R=0.5 $p_{T}^{hardmin.}$=10 GeV/$c$.
Figure 116: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.5 $p_{T}^{hardmin.}$=10 GeV/$c$ after area selection. Figure
117: Jet a) area, b) width, and c) mean constituent momentum for R=0.5
$p_{T}^{hardmin.}$=10 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 118: Jet a) area, b) width, and c) mean
constituent momentum for R=0.5 $p_{T}^{hardmin.}$=10 GeV/$c$ after leading
hadron selection. Figure 119: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.5
$p_{T}^{hardmin.}$=10 GeV/$c$. Figure 120: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.5 $p_{T}^{hardmin.}$=10 GeV/$c$.

###  .20 R=0.5, $p_{T}^{hardmin.}$=20 GeV/c

Figure 121: Jet area vs. jet width for R=0.5 $p_{T}^{hardmin.}$=20 GeV/$c$.
Figure 122: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.5 $p_{T}^{hardmin.}$=20 GeV/$c$ after area selection. Figure
123: Jet a) area, b) width, and c) mean constituent momentum for R=0.5
$p_{T}^{hardmin.}$=20 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 124: Jet a) area, b) width, and c) mean
constituent momentum for R=0.5 $p_{T}^{hardmin.}$=20 GeV/$c$ after leading
hadron selection. Figure 125: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.5
$p_{T}^{hardmin.}$=20 GeV/$c$. Figure 126: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.5 $p_{T}^{hardmin.}$=20 GeV/$c$.

###  .21 R=0.5, $p_{T}^{hardmin.}$=30 GeV/c

Figure 127: Jet area vs. jet width for R=0.5 $p_{T}^{hardmin.}$=30 GeV/$c$.
Figure 128: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.5 $p_{T}^{hardmin.}$=30 GeV/$c$ after area selection. Figure
129: Jet a) area, b) width, and c) mean constituent momentum for R=0.5
$p_{T}^{hardmin.}$=30 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 130: Jet a) area, b) width, and c) mean
constituent momentum for R=0.5 $p_{T}^{hardmin.}$=30 GeV/$c$ after leading
hadron selection. Figure 131: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.5
$p_{T}^{hardmin.}$=30 GeV/$c$. Figure 132: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.5 $p_{T}^{hardmin.}$=30 GeV/$c$.

###  .22 R=0.5, $p_{T}^{hardmin.}$=40 GeV/c

Figure 133: Jet area vs. jet width for R=0.5 $p_{T}^{hardmin.}$=40 GeV/$c$.
Figure 134: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.5 $p_{T}^{hardmin.}$=40 GeV/$c$ after area selection. Figure
135: Jet a) area, b) width, and c) mean constituent momentum for R=0.5
$p_{T}^{hardmin.}$=40 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 136: Jet a) area, b) width, and c) mean
constituent momentum for R=0.5 $p_{T}^{hardmin.}$=40 GeV/$c$ after leading
hadron selection. Figure 137: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.5
$p_{T}^{hardmin.}$=40 GeV/$c$. Figure 138: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.5 $p_{T}^{hardmin.}$=40 GeV/$c$.

###  .23 R=0.5, $p_{T}^{hardmin.}$=60 GeV/c

Figure 139: Jet area vs. jet width for R=0.5 $p_{T}^{hardmin.}$=60 GeV/$c$.
Figure 140: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.5 $p_{T}^{hardmin.}$=60 GeV/$c$ after area selection. Figure
141: Jet a) area, b) width, and c) mean constituent momentum for R=0.5
$p_{T}^{hardmin.}$=60 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 142: Jet a) area, b) width, and c) mean
constituent momentum for R=0.5 $p_{T}^{hardmin.}$=60 GeV/$c$ after leading
hadron selection. Figure 143: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.5
$p_{T}^{hardmin.}$=60 GeV/$c$. Figure 144: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.5 $p_{T}^{hardmin.}$=60 GeV/$c$.

###  .24 R=0.5, $p_{T}^{hardmin.}$=80 GeV/c

Figure 145: Jet area vs. jet width for R=0.5 $p_{T}^{hardmin.}$=80 GeV/$c$.
Figure 146: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.5 $p_{T}^{hardmin.}$=80 GeV/$c$ after area selection. Figure
147: Jet a) area, b) width, and c) mean constituent momentum for R=0.5
$p_{T}^{hardmin.}$=80 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 148: Jet a) area, b) width, and c) mean
constituent momentum for R=0.5 $p_{T}^{hardmin.}$=80 GeV/$c$ after leading
hadron selection. Figure 149: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.5
$p_{T}^{hardmin.}$=80 GeV/$c$. Figure 150: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.5 $p_{T}^{hardmin.}$=80 GeV/$c$.

###  .25 R=0.6, $p_{T}^{hardmin.}$=10 GeV/c

Figure 151: Jet area vs. jet width for R=0.6 $p_{T}^{hardmin.}$=10 GeV/$c$.
Figure 152: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.6 $p_{T}^{hardmin.}$=10 GeV/$c$ after area selection. Figure
153: Jet a) area, b) width, and c) mean constituent momentum for R=0.6
$p_{T}^{hardmin.}$=10 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 154: Jet a) area, b) width, and c) mean
constituent momentum for R=0.6 $p_{T}^{hardmin.}$=10 GeV/$c$ after leading
hadron selection. Figure 155: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.6
$p_{T}^{hardmin.}$=10 GeV/$c$. Figure 156: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.6 $p_{T}^{hardmin.}$=10 GeV/$c$.

###  .26 R=0.6, $p_{T}^{hardmin.}$=20 GeV/c

Figure 157: Jet area vs. jet width for R=0.6 $p_{T}^{hardmin.}$=20 GeV/$c$.
Figure 158: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.6 $p_{T}^{hardmin.}$=20 GeV/$c$ after area selection. Figure
159: Jet a) area, b) width, and c) mean constituent momentum for R=0.6
$p_{T}^{hardmin.}$=20 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 160: Jet a) area, b) width, and c) mean
constituent momentum for R=0.6 $p_{T}^{hardmin.}$=20 GeV/$c$ after leading
hadron selection. Figure 161: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.6
$p_{T}^{hardmin.}$=20 GeV/$c$. Figure 162: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.6 $p_{T}^{hardmin.}$=20 GeV/$c$.

###  .27 R=0.6, $p_{T}^{hardmin.}$=30 GeV/c

Figure 163: Jet area vs. jet width for R=0.6 $p_{T}^{hardmin.}$=30 GeV/$c$.
Figure 164: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.6 $p_{T}^{hardmin.}$=30 GeV/$c$ after area selection. Figure
165: Jet a) area, b) width, and c) mean constituent momentum for R=0.6
$p_{T}^{hardmin.}$=30 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 166: Jet a) area, b) width, and c) mean
constituent momentum for R=0.6 $p_{T}^{hardmin.}$=30 GeV/$c$ after leading
hadron selection. Figure 167: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.6
$p_{T}^{hardmin.}$=30 GeV/$c$. Figure 168: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.6 $p_{T}^{hardmin.}$=30 GeV/$c$.

###  .28 R=0.6, $p_{T}^{hardmin.}$=40 GeV/c

Figure 169: Jet area vs. jet width for R=0.6 $p_{T}^{hardmin.}$=40 GeV/$c$.
Figure 170: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.6 $p_{T}^{hardmin.}$=40 GeV/$c$ after area selection. Figure
171: Jet a) area, b) width, and c) mean constituent momentum for R=0.6
$p_{T}^{hardmin.}$=40 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 172: Jet a) area, b) width, and c) mean
constituent momentum for R=0.6 $p_{T}^{hardmin.}$=40 GeV/$c$ after leading
hadron selection. Figure 173: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.6
$p_{T}^{hardmin.}$=40 GeV/$c$. Figure 174: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.6 $p_{T}^{hardmin.}$=40 GeV/$c$.

###  .29 R=0.6, $p_{T}^{hardmin.}$=60 GeV/c

Figure 175: Jet area vs. jet width for R=0.6 $p_{T}^{hardmin.}$=60 GeV/$c$.
Figure 176: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.6 $p_{T}^{hardmin.}$=60 GeV/$c$ after area selection. Figure
177: Jet a) area, b) width, and c) mean constituent momentum for R=0.6
$p_{T}^{hardmin.}$=60 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 178: Jet a) area, b) width, and c) mean
constituent momentum for R=0.6 $p_{T}^{hardmin.}$=60 GeV/$c$ after leading
hadron selection. Figure 179: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.6
$p_{T}^{hardmin.}$=60 GeV/$c$. Figure 180: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.6 $p_{T}^{hardmin.}$=60 GeV/$c$.

###  .30 R=0.6, $p_{T}^{hardmin.}$=80 GeV/c

Figure 181: Jet area vs. jet width for R=0.6 $p_{T}^{hardmin.}$=80 GeV/$c$.
Figure 182: Jet a) leading hadron momentum, b) width, and c) mean constituent
momentum for R=0.6 $p_{T}^{hardmin.}$=80 GeV/$c$ after area selection. Figure
183: Jet a) area, b) width, and c) mean constituent momentum for R=0.6
$p_{T}^{hardmin.}$=80 GeV/$c$ after area selection and ML suggested stricter
leading hadron selection. Figure 184: Jet a) area, b) width, and c) mean
constituent momentum for R=0.6 $p_{T}^{hardmin.}$=80 GeV/$c$ after leading
hadron selection. Figure 185: Silhouette values for each kinematic selection.
a) Inclusive, b) area selection, c) leading hadron momentum selection, d)
area+stricter leading hadron momentum selection for R=0.6
$p_{T}^{hardmin.}$=80 GeV/$c$. Figure 186: $z_{subjet}$ ratio of accepted
signal jets for each kinematic selection to the inclusive signal jet
population for R=0.6 $p_{T}^{hardmin.}$=80 GeV/$c$.

Appendix B: Kinematic selections extracted from machine learning system

R | $p_{T}^{hardmin.}$ | Feature | Selection Threshold |  % Comb. Jets Rejected for ML |  % Signal Jets Rejected for ML |  S/B Increase |  % Comb. Jets Rejected for ML + Area Selection |  % Signal Jets Rejected for ML + Area Selection |  S/B Increase |  % Comb. Jets Rejected for $p_{T}^{1}$ selection |  % Signal Jets Rejected for $p_{T}^{1}$ selection |  S/B Increase
---|---|---|---|---|---|---|---|---|---|---|---|---
0.2 | 10 GeV/$c$ | $p_{T}^{1}$ |  $>$3.349 GeV/$c$ |  98.01% |  5.89% |  47.3 |  98.11% |  6.03% |  49.7 |  95.73% |  2.64% |  22.8
| 20 GeV/$c$ | $p_{T}^{1}$ |  $>$4.021 GeV/$c$ |  99.50% |  1.03% |  197.9 |  99.52% |  1.04% |  206.2 |  95.66% |  0.04% |  23.0
| 40 GeV/$c$ | $\langle p_{T}\rangle$ |  $>$0.862 GeV/$c$ |  98.24% |  0.24% |  56.7 |  99.95% |  0.24% |  1995.2 |  95.69% |  0.00% |  23.2
| 80 GeV/$c$ | $\langle p_{T}\rangle$ |  $>$1.122 GeV/$c$ |  99.49% |  0.03% |  196.0 |  100% |  0.03% |  $\infty$ |  95.75% |  0.00% |  23.5
0.3 | 10 GeV/$c$ | $p_{T}^{1}$ |  $>$3.394 GeV/$c$ |  96.21% |  15.05% |  22.4 |  96.59% |  15.54% |  24.8 |  91.38% |  7.24% |  10.8
| 20 GeV/$c$ | $p_{T}^{1}$ |  $>$3.952 GeV/$c$ |  98.92% |  3.20% |  82.0 |  99.00% |  3.21% |  96.8 |  91.61% |  0.23% |  11.9
| 40 GeV/$c$ | $p_{T}^{1}$ |  $>$5.257 GeV/$c$ |  99.96% |  0.83% |  2479.3 |  99.96% |  0.83% |  2479.3 |  91.81% |  0.00% |  12.0
| 80 GeV/$c$ | $\langle p_{T}\rangle$ |  $>$0.825 GeV/$c$ |  97.94% |  0.08% |  48.5 |  99.99% |  0.08% |  9992.0 |  91.69% |  0.00% |  12.0
0.4 | 10 GeV/$c$ | $p_{T}^{1}$ |  $>$3.486 GeV/$c$ |  95.07% |  25.92% |  15.0 |  95.74% |  26.91% |  17.2 |  86.51% |  11.85% |  6.5
| 20 GeV/$c$ | $p_{T}^{1}$ |  $>$3.975 GeV/$c$ |  98.27% |  6.59% |  54.0 |  98.44% |  6.65% |  59.8 |  86.67% |  0.51% |  7.5
| 40 GeV/$c$ | $p_{T}^{1}$ |  $>$5.125 GeV/$c$ |  99.86% |  1.56% |  703.1 |  99.88% |  1.56% |  820.3 |  86.89% |  0.00% |  7.6
| 80 GeV/$c$ | $\langle p_{T}\rangle$ |  $>$0.706 GeV/$c$ |  96.59% |  0.25% |  29.3 |  99.98% |  0.25% |  4987.5 |  87.04% |  0.00% |  7.7
0.5 | 10 GeV/$c$ | $p_{T}^{1}$ |  $>$3.497 GeV/$c$ |  92.83% |  33.01% |  9.3 |  94.09% |  34.50% |  11.1 |  81.41% |  14.77% |  4.6
| 20 GeV/$c$ | $p_{T}^{1}$ |  $>$4.082 GeV/$c$ |  97.92% |  11.07% |  42.8 |  98.26% |  11.24% |  51.0 |  81.21% |  0.94% |  5.3
| 40 GeV/$c$ | $p_{T}^{1}$ |  $>$5.036 GeV/$c$ |  99.79% |  2.23% |  465.6 |  99.81% |  2.23% |  514.6 |  81.23% |  0.00% |  5.3
| 80 GeV/$c$ | $\langle p_{T}\rangle$ |  $>$0.647 GeV/$c$ |  95.04% |  0.79% |  20.0 |  99.96% |  0.79% |  2480.3 |  81.72% |  0.00% |  5.5
0.6 | 10 GeV/$c$ | $p_{T}^{1}$ |  $>$3.424 GeV/$c$ |  88.88% |  33.45% |  6.0 |  91.17% |  35.16% |  7.3 |  75.95% |  15.51% |  3.5
| 20 GeV/$c$ | $p_{T}^{1}$ |  $>$4.178 GeV/$c$ |  97.79% |  15.54% |  38.2 |  98.14% |  15.79% |  45.3 |  76.41% |  1.17% |  4.2
| 40 GeV/$c$ | $p_{T}^{1}$ |  $>$5.222 GeV/$c$ |  99.77% |  3.83% |  418.1 |  99.79% |  3.83% |  458.0 |  76.40% |  0.00% |  4.2
| 80 GeV/$c$ | $\langle p_{T}\rangle$ |  $>$0.612 GeV/$c$ |  93.24% |  1.40% |  14.6 |  99.87% |  1.40% |  758.5 |  76.62% |  0.00% |  4.3
Table 4: Kinematic selections determined by the machine learning algorithm
described in sec. II.6, along with the rejection rates for signal and
combinatorial jets.