# JEWEL on a (2+1)D background

Isobel Kolbé  Email<EMAIL_ADDRESS>Instituto Galego de Fisica de Altas
Enerxias (IGFAE), Universidade de Santiago de Compostela, E-15782 Galicia,
Spain

# JEWEL on a (2+1)D background with applications to small systems and
substructure

Isobel Kolbé  Email<EMAIL_ADDRESS>Instituto Galego de Fisica de Altas
Enerxias (IGFAE), Universidade de Santiago de Compostela, E-15782 Galicia,
Spain

###### Abstract

High-$p_{T}$ jets are an important tool for characterizing the quark-gluon
plasma (QGP) created in heavy-ion collisions. However, a precise understanding
of the jet-medium interaction is still lacking, and the development of more
sophisticated observables is needed. This work presents a tool that allows for
the exploration of alternative high-$p_{T}$ observables in a variety of
collision systems. The tool builds on the publicly available JEWEL Monte Carlo
code, and allows for the evolution of a jet on any given (2+1)-dimensional
background. Proof-of-concept observables are also presented, studied using the
latest version of JEWEL, JEWEL-2.4.0. The simplicity of the separation of the
physics of the jet from the physics of the medium (while still allowing for
the usual JEWEL medium-response), allows for easy interpretation without the
need for complex parameterization. Results are produced using the RIVET
toolkit, which allows for transparent preservation and development of analyses
that are compatible with experimental methods. The code and analysis used to
produce the plots presented here are made publicly available on a Github
repository, with up-to-date usage instructions. This tool is expected to be
useful to the broad jet-physics community for the study of precision
observables for jets.

††preprint: APS/123-QED

##  I Introduction

The modification of high-$p_{T}$ jets in heavy-ion collisions is a critical
signature of the hot and dense matter created in heavy-ion collisions. In
central heavy-ion collisions, the main channel for the modification of
high-$p_{T}$ jets is known as “jet suppression”, which has enjoyed both
theoretical and experimental success (see [1] for a recent review). However,
while the theoretical understanding of the jet-medium interaction has become
very sophisticated, a need has arisen for more precise observables.

This paper presents a tool that may be used to expolore alternative
high-$p_{T}$ observables, specifically in a variety of collision systems. This
work builds on an existing jet Monte Carlo (MC) code, the publicly available
Jewel [2, 3, 4], providing Jewel with the ability to evolve a jet on any given
(2+1)-dimensional background. Presented here are also proof-of-concept
observables studied using the latest version of Jewel ,Jewel-2.4.0. Although
more sophisticated jet event generators exist and are often publicly
available, the value of the present interface lies in its simplicity. The
conceptual separation of the physics of the jet, handled by Jewel , and the
physics of the medium, allows for simple interpretation that remains unclouded
by the subtle interplay between various model parameters and effects.

The results presented here are produced using version 3 of the RIVET toolkit
[5]. Within RIVET, jets are clustered using the FASTJET package [6, 7], as
well as the LundPlane extension based on [8]. Additionally, the Jewel-2.4.0
release is accompanied by a RIVET projection for the constituent subtraction
method. The public availability of RIVET and its design philosophy of
transparent preservation and development of analyses that are compatable with
experimental methods means it is useful to develop observables with RIVET
analyses.

Since it is hoped that this tool will be useful to the broad jet-physics
community, the code is made publicly available, along with the RIVET analysis
used to produce the plots presented here. The code is hosted on a Github
repository https://github.com/isobelkolbe/jewel-2.4.0-2D.git, along with upt-
to-date usage instructions.

This paper is organised as follows: In section II, the medium interface for
Jewel is presented with a brief discussion of its features and validation. In
section III, the problem of small systems is explored by computing
illustrative substructure examples using the (2+1)D medium interface.

##  II Software

###  II.1 Basic features

Of particular importance is the new subtraction method (constituent
subtraction)[9], which improves Jewel’s reproduction of the jet mass and will
be particularly important for other jet substructure observables.

In the standard release, Jewel-2.4.0 can be run in two modes: in vacuum
(hereinafter “vac”), and with a simple medium model (hereinafter “medium”).
The simple medium is a radially symmetric, longitudinally expanding
temperature profile whose initial state is determined by a Glauber overlap of
Woods-Saxon thickness functions and a given initial temperature. Jewel-2.4.0
has also been upgraded to use LHAPDF 6 [10] and therefore has access to a wide
range of nuclear Parton Distribution Functions (nPDFs).

In order to study jets in a variety of collision systems, it is useful to be
able to evolve the jet on a changing background. A natural choice for the
determination of the properties of such a background is a hydrodynamic
simulation, but it is also useful to be able to use any arbitrary background.
Jewel has been used before in conjunction with a hydrodynamic background,
particularly to study the effect of jets on the source terms in hydrodynamic
simulations [11, 12]. In addition to these studies, hydrodynamic plugins for
Jewel have also been developed to study the sensitive interplay between
elliptic flow and $R_{AA}$ [13, 14, 15]. However, to the author’s knowledge,
such plugins have not yet been used to study jet substructure in small
systems, nor are they public.

The present work is built heavily on an interface originally implemented by
Korinna Zapp, one of the authors of [11, 12], which is in turn similar in
spirit to the medium-simple.f medium interface that is part of the standard
Jewel release. The plugin presented here, named simply ‘medium-2D‘ so that,
when built with Jewel will result in an executable jewel-2.4.0-2D, has the
following features: The interface

  1. 1.

reads in temperature and velocity contours for up to 90 time steps.

  2. 2.

can optionally read the locations of the binary collisions that source the
background generation. This is used to sample the location of the initial hard
scattering (the default is to sample Woods-Saxon overlap functions).

  3. 3.

correctly boosts into the rest frame of the fluid cell in order to determine
the fluid density.

  4. 4.

interfaces with the main Jewel code.

  5. 5.

(as with the standard Jewel release), is not able to use two different parton
distribution functions (PDFs) in an assymmetric system. Care must be taken to
ensure that observables are either not sensitive to the PDF, or that the
sensitivity to the PDF is carefully taken into account.

  6. 6.

does not output the hadronized products of the medium to the Jewel event
record: as in the standard Jewel release, the event record is a superposition
of the Jewel-evolved jet and a PYTHIA-produced event.

The medium interface can be passed a parameter file by passing the name of the
parameter file to the MEDIUMPARAMS parameter in the Jewel. The interface can
take many of the same parameters as Jewel’s simple medium since it must still
create an initial condition from which to sample the location of the initial
hard scattering if the user does not provide an $N_{coll}$ probability
density.

Updated instructions for use are maintained on the code repository.

###  II.2 Testing and Validation

Figure 1: The jet yield as a function of $p_{T}$ for jets evolved in Jewel,
either without a medium (green, “vac”), or with the same simple medium using
either Jewel’s own “simple” mode (cyan, “simple”), or using the 2D interface
presented here with medium profiles generated with Jewel’s simple medium code
(blue, “simple-2D”) . Monte Carlo errors are smaller than the thickness of the
line.

In order to test the interface, a set of temperature contours were produced
using the code from Jewel’s own medium-simple.f with no modifications. Jewel
was then run using the 2D interface presented here with these contours (along
with null velocity contours) as input, and the resulting distributions
compared. As an illustrative example, the jet yield as a function of
transverse momentum is shown in fig. 1 for ‘simple-2D’, ‘simple’, and ‘vac’,
corresponding to running Jewel with the present 2D interface on medium
profiles produced using Jewel’s internal simple medium code, with the standard
simple medium, and in vacuum, respectively. As expected, the vacuum case
deviates significantly from the two medium cases. The systematic differences
between “simple” and “simple-2D” are very sensitive to the granularity of the
temperature grid. While this can be improved significantly, the memory cost is
high.

##  III Jet Substructure and Small Systems

The medium interface presented here has broad applicability with in the study
of jets in heavy-ion collisions. A particular concern within the community at
present is related to small colliding systems such as proton-lead and (proton,
deuteron, helium)-gold. In this section, the problem of small systems is
explored. An argument is made for the need to develop substructure observables
that are independent of the yield but sensitive to the colliding system, a
task which will be greatly aided by the availability of the medium interface
presented in this work.

###  III.1 Small systems - a motivation

Decades of ultra-relativistic heavy ion collisions at colliders across the
world have led to a successful program of creating and beginning to
characterize the hot deconfined state of matter known as the quark-gluon
plasma (QGP) [16]. The study of the QGP falls largely into two categories: (1)
phenomena governing low-momentum particles, and (2) phenomena governing high-
momentum particles.

It is critical that the two categories of phenomena are described by a self-
consistent “standard model of the QGP” [17]. In very central $Pb-Pb$ or $Au-
Au$ collisions, this seems to be the case, but it has been known for several
years now that the framework is inconsistent in small colliding systems such
as $p-Pb$ or $d-Au$ : Low-momentum signatures of the QGP in small colliding
systems are characterized by several observables that are both measured
experimentally with a high degree of precision and described exceptionally
well theoretically (see [18] for a paedegocial review); On the other hand, the
high-momentum, or high-$p_{T}$ , signatures are not only absent, but their
absence remains unexplained.

This last statement needs to be refined: While other observables exist, the
gold standard for the observation of the modification of high-$p_{T}$ partons
by the QGP has been the nuclear modification factor, $R_{AA}$  (see [19] for
a review of jet measurements in heavy-ion collisions). $R_{AA}$ compares the
yield in a nucleus-nucleus ($AA$ ) collision, with that in $pp$ and attempts
to scale this ratio such that $R_{AA}\sim 1$ in the absence of the QGP. The
observable $R_{pA}$ (and related observables) does the same for a proton-
nucleus collision. Experimental measurements all but rule out the possibility
that $R_{pA}\nsim 1$ (see [1] and citations therein).

There can be several explanations for this inconsistency: It may be that the
model description of low-$p_{T}$ phenomena using the fluid mechanics
reminiscent of the QGP in $AA$ are going beyond their range of applicability
and should not be interpreted as evidence for collective behaviour. This
scenario has been studied extensively [20, 21]. The correlations may be due to
non-flow effects such as momentum anisotropies that exist already in the
initial state [22]. It seems clear that, even within hydrodynamic models that
are able to describe the low-$p_{T}$ phenomena, the nature of the medium in a
small system must necessarily be hotter and denser in order to produce
multiplicities that are comparable to peripheral $AA$ collisions [23].

However, the interpretation of the apparent absence of the modification of
high-$p_{T}$ partons in small systems is not as sophisticated. Theoretically,
it may be that the distance a hard parton travels through the medium is too
short to see any modification. If this were the case, then the perturbative
calculations that lead to this intuition would bear it out. As it turns out,
some studies have been done that show either that the modification should be
observable [24], or that the array of simplifying assumptions made in the
standard pQCD calculations are completely inconsistent with small systems,
rendering them unreliable [25]. It may be that the modification of
high-$p_{T}$ partons occurs on a time-scale that is much larger than the
lifetime of the QGP in small systems, i.e. that the mean free path is smaller
than the system size. This is a prediction that should easily be verifiable in
Monte Carlo (MC) simulations, and is partly the motivation for the present
work.

But there is a larger phenomenological obstacle to our understanding of the
modification of high-$p_{T}$ partons in small systems: $R_{AA}$ (or its
equivalent in a small system such as $R_{pA}$ ) is a wholly unsuitable
observable. The bulk of the problem lies in $R_{AA}$ ’s reliance on yields
that are sensitive to a host of biases that are accentuated in small systems.
These include the immense experimental difficulty of determining the number of
binary collisions [26], uncertainties in the fragmentation of jets, and the
initial production spectrum through the nuclear parton distribution functions
(nPDFs). In addition to these biases, the steeply falling production spectrum
means that the necessarily small amount of energy loss rapidly becomes
undetectable, even if it was present 111Some alternatives exist [27, 28] that
attempt to reduce the biases introduced by the steeply falling spectrum..
$R_{AA}$ is not able to falsify the claim that a medium of deconfined QCD
matter is produced in very central small systems.

It is clear that, whatever the physics of the modification of high-$p_{T}$
partons in small systems is, a much more sophisticated understanding of
sensitive, differential observables is needed. It is also crucial that such an
understanding is developed in the context of experimentally achievable goals.

###  III.2 Jet substructure

Jet substructure observables suffer from far fewer of the biases that plague
$R_{AA}$ . Jet substructure has been studied extensively in high-energy
particle physics [29, 30, 31], enjoying enormous success. There have also been
many theoretical advances in the study of jet substructure in heavy-ion
physics [32, 33, 34], along with several promising experamental measurements
[35, 36, 37] It is hoped that the present work will serve as a useful tool to
aid the community to develop new substructure observables that characterize
the modification of high-$p_{T}$ partons in heavy-ion collisions in a more
precise manner than $R_{AA}$ . It is not unreasonable to presume that such
precision observables will shed significant light on the modification of
high-$p_{T}$ partons in small systems as well.

Of particular importance in the study of jet substrcture in hadronic
collisions has been the development of appropriate grooming techniques.
Careful consideration of grooming techniques in studies involving Jewel are
particularly important 222This statement is independent of the need to
include an appropriate subtraction technique when using MC data generated by
Jewel when keeping track of recoils. See [9] for details on the constituent
subtraction method employed in this work. Once a Jewel event has been
appropriately subtracted, the further use of jet grooming is phenomenological.
since the soft particles in a Jewel event record are produced by PYTHIA and
are independent of the jets evolved by Jewel (except when including recoils in
Jewel).

The most widely used grooming technique in heavy-ions is the SoftDrop [38]
technique. A newer grooming technique is that of Dynamical Grooming [39],
which avoids the absolute scale cut-off employed by SoftDrop by using instead
the hardest branch in a Cambridge/Aachen (C/A) re-clustering sequence to
determine how to groom a jet. The only parameter used in Dynamical Grooming is
called $a$, and sets the definition of the term “hardest branch”. That is, the
hardest splitting in an angular ordered shower is defined as

$\kappa^{a}=\frac{1}{p_{T}}\max_{i\in\text{C/A
seq.}}\left[z_{i}(1-z_{i})p_{T,i}\left(\frac{\theta_{i}}{R}\right)^{a},\right]$
(1)

where $p_{T}$ is the transverse momentum of an entire jet with radius $R$, for
$z_{i}$, $p_{T,i}$, and $\theta_{i}$ the momentum sharing fraction, the energy
of the parent, and the relative splitting angle of the $i^{th}$ splitting in
the C/A [40] re-clustering sequence respectively. By choosing (potentially
continuous) values for $a$, one varies the definition of the “hardest branch”.
Through $a$, the hardest branch is defined as

  * •

$a=0$: the branch with the most symmetric momentum sharing (use $a=0.1$ to
avoid colliniear sensitivity);

  * •

$a=1$: the branch with the largest relative transverse momentum;

  * •

$a=2$: the branch with the shortest formation time.

The dynamical grooming procedure can then be used either to tag a particular
hard splitting in order to study its kinematics, or to groom the jet by
discarding all emissions that occur prior to the hard splitting in the C/A
sequence. Of course, this grooming procedure still assumes angular ordering of
emissions, which is not guaranteed in a heavy-ion collision.

In addition to the dynamically groomed jet momentum sharing fraction $z_{G}$,
three other observables are also presented in this section: the invariant jet
mass $M_{jet}$ (of a groomed jet, not the groomed jet mass), the number of
subjets, and the lund plane. The number of subjets is obtained by first
clustering $R=0.4$ jets in an event before, for each $R=0.4$ jet, reclustering
the constituents into $R=0.2$ jets. The lund plane is computed using the
FASTJET contrib package “LundPlane” [8].

(a)

(b)

Figure 2: (a) The jet yield and (b) the dynamically groomed ($a=0.1$) jet
momentum sharing fraction for $R=0.4$ anti-$k_{T}$ jets in the $0-5\%$ most
central bin of $He-Au$ collisions at $\sqrt{s_{NN}}=0.2$ TeV. Gold histograms
show simulated results using a gold nuclear PDF, while purple histograms show
simulated results run on Jewel’s default proton PDF setting.

In order to illustrate the use of the 2D medium interface presented here,
simulations were performed using publicly available (2+1)D MUSIC [41] profiles
with IP-Glasma initial conditions of the $0-5\%$ most central $He-Au$ at
$\sqrt{s_{NN}}=200$GeV and $Pb-Pb$ at $\sqrt{s_{NN}}=2.76$TeV collisions. Note
that the $0-5\%$ most central $He-Au$ bin is precisely the centrality bin in
which PHENIX measured the hierarchy of $v_{2,3}$ [42]. For both $Pb-Pb$ and
$He-Au$ , event-by-event fluctuations were simulated by running 2000 events on
each of 100 (200) simulation profiles for $Pb-Pb$ ($He-Au$ ).

Consider first the effect of the choice of PDF in fig. 2. Figure 2 shows two
different observables for dynamically groomed ($a=0.1$) anti-$k_{T}$, $R=0.4$
jets, simulated using the 2D medium interface with MUSIC profiles for $He-Au$
collisions at $\sqrt{s_{NN}}=200$ GeV. Each panel shows two histograms: The
dark purple histogram is obtained running with Jewel’s default proton PDF
(CT14nlo [43]), while the light gold histogram was obtained running with a
gold nuclear PDF (EPPS21 + CT18ANLO [44, 45]). Even for observables that are
expected to be sensitive to the PDF, like the jet spectrum, the simulation
agrees within Monte Carlo errors.

(a)

(b)

Figure 3: The (a) Lund Plane and (b) number of subjets of dynamically groomed
($a=0.1$), $R=0.4$ anti-$k_{T}$ jets in the $0-5\%$ most central bins of $He-
Au$ collisions at $\sqrt{s_{NN}}=0.2$ TeV and $Pb-Pb$ collisions at
$\sqrt{s_{NN}}=2.76$ TeV. Gold histograms show simulated results for $He-Au$
using a gold nuclear PDF, purple histograms for $He-Au$ using Jewel’s default
proton PDF setting, and blue histograms for $Pb-Pb$ .

As an illustrative example of standard substructure observables, consider fig.
3, showing the Lund Plane in the left panel and the number of subjets with
radius $R=0.2$ in the right panel, for dynamically groomed ($a=0.1$),
anti-$k_{T}$ jets with radius of $R=0.4$. Dark purple histograms are obtained
running with Jewel’s default proton PDF (CT14nlo [43]), light gold histograms
were obtained running with a gold nuclear PDF (EPPS21 + CT18ANLO [44, 45]), on
MUSIC $He-Au$ profiles, blue histograms were obtained running Jewel (default
proton PDF) on MUSIC $Pb-Pb$ profiles.

Figure 4: The jet mass for dynamically groomed, $R=0.4$ anti-$k_{T}$ jets in
the $0-5\%$ most central bins of $He-Au$ collisions at $\sqrt{s_{NN}}=0.2$ TeV
and $Pb-Pb$ collisions at $\sqrt{s_{NN}}=2.76$ TeV. Gold histograms show
simulated results for $He-Au$ using a gold nuclear PDF, purple histograms for
$He-Au$ using Jewel’s default proton PDF setting, and blue histograms for $Pb-
Pb$ . From left to right the panels use a grooming parameter of $a=0.1$,
$a=1$, and $a=2$ respectively, corresponding to different definitions of the
“hardest branch”.

The constituent subtraction method has been validated using the jet mass,
improving the interpretability of the shape of the jet mass distribution [9].
Consider therefore the variation in the shape due to the choice of grooming
parameter $a$ in fig. 4.

Figure 5: The groomed momentum sharing fraction for dynamically groomed,
$R=0.4$ anti-$k_{T}$ jets in the $0-5\%$ most central bins of $He-Au$
collisions at $\sqrt{s_{NN}}=0.2$ TeV and $Pb-Pb$ collisions at
$\sqrt{s_{NN}}=2.76$ TeV. Gold histograms show simulated results for $He-Au$
using a gold nuclear PDF, purple histograms for $He-Au$ using Jewel’s default
proton PDF setting, and blue histograms for $Pb-Pb$ . From left to right the
panels use a grooming parameter of $a=0.1$, $a=1$, and $a=2$ respectively,
corresponding to different definitions of the “hardest branch”.

Lastly, the groomed momentum sharing fraction is shown in fig. 5 for
dynamically groomed anti-$k_{T}$ jets with radius of $R=0.4$, for the three
standard choices of $a$. It is curious to note the peak in the $He-Au$ samples
in the $a=1$ and $a=2$ panels of fig. 5 which is absent for the $Pb-Pb$
samples. An exploration of the origins of this feature is left for later work
as it will involve the higher statistics needed to perform studies that are
differential in the jet energy.

##  IV Conclusion and Outlook

The purpose of this letter is to present a medium interface for Jewel that
allows Jewel to sample a given set of temperature and velocity profiles of a
(2+1)D medium. The interface is made publicly available. It is hoped that this
tool will be of use to the broader heavy-ion jet community to aid in the
exploration of jets in a variety of collision systems.

There is an important aspect of heavy-ion collisions that is not yet taken
into account by this interface - the underlying event. In its current form,
this medium interface relies, in precisely the same way as the standard Jewel
medium model, on a completely uncorrelated underlying event produced by
PYTHIA. Although one may gain some access to the part of the event that is
correlated with the jet by keeping track of recoiling partons, it would still
be desirable to have, in the Jewel event record, the underlying event that is
the result of the medium upon which the jet was evolved. It is worth noting
that, without the information from the underlying event, it is not possible to
study any observable that relies on the soft constituents of the event, such
as high-$p_{T}$ -$v_{2}$. Such a modification of the main Jewel code is a much
larger undertaking and is left for future work.

Although much focus has been places here on the use of this interface to study
small systems, its usefulness extends to any precision study of the jet-medium
interaction. There is particular scope to vary the nature of the medium using
this interface, which allows for a cleanly interpretable exploration of
aspects of jet evolution that are sensitive to the nature of the medium, not
simply the existence thereof.

##  V Acknowledgments

I gratefully acknowledge the major contribution to the original implementation
of the medium interface by Korinna Zapp. Thank you to Alba Soto-Ontoso for
providing a C++ class that implements the dynamical grooming procedure, and to
Liliana Apolinário for help implementing the constituent subtraction. Thank
you to Chun Shen for support in accessing the MUSIC profiles.

I would like to express gratitude to Urs Wiedemann, Guilherme Milhano and
Korinna Zapp for early discussions that lead to this project being started, as
well as to the CERN TH department for their hospitality during the start of
this project, and the SA-CERN collaboration for funding to visit CERN.

I am grateful for many fruitful discussions with, and helpful suggestions
from, Leonardo Barreto, Fabio Canedo and Marcelo Munhoz at the University of
Sao Paulo. This project has further benefited greatly from insights garnered
through conversations with Liliana Apolinário, Jasmine Brewer, Raghav
Kunnawalkam Elayavalli, Mawande Lushozi, Anna McCoy, Titus Mombächer,
Christine Nattrass, Dmytro Oliinychenko, and Carlos Salgado.

Lastly, the development of this project relied heavily on access to resources
at both the Institute for Nuclear Theory at the University of Washington (and
was therefore partially supported by the U.S. DOE under Grant No. DE-
FG02-00ER41132) and the Galician Institute for High Energy Physics at the
University of Santiago de Compostela; I would like to express particular
gratitude to the general and computing administrative staff at both
institutions.

This work is supported by European Research Council project
ERC-2018-ADG-835105 YoctoLHC; by Maria de Maetzu excellence program under
project CEX2020-001035-M; by Spanish Research State Agency under project
PID2020-119632GB- I00; and by Xunta de Galicia (Centro singular de
investigacion de Galicia accreditation 2019-2022), by European Union ERDF.)

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