The JETSCAPE Collaboration

# Multi-scale evolution of charmed particles in a nuclear medium

W. Fan<EMAIL_ADDRESS>Department of Physics, Duke University, Durham NC
27708.  G. Vujanovic<EMAIL_ADDRESS>Department of Physics and
Astronomy, Wayne State University, Detroit MI 48201.  Department of Physics,
University of Regina, Regina, SK S4S 0A2, Canada.  S. A. Bass  Department of
Physics, Duke University, Durham NC 27708.  A. Majumder  Department of Physics
and Astronomy, Wayne State University, Detroit MI 48201.  A. Angerami
Lawrence Livermore National Laboratory, Livermore CA 94550.  R. Arora
Research Computing Group, University Technology Solutions, The University of
Texas at San Antonio, San Antonio TX 78249.  S. Cao  Institute of Frontier and
Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237,
China  Department of Physics and Astronomy, Wayne State University, Detroit MI
48201.  Y. Chen  Laboratory for Nuclear Science, Massachusetts Institute of
Technology, Cambridge MA 02139.  Department of Physics, Massachusetts
Institute of Technology, Cambridge MA 02139.  T. Dai  Department of Physics,
Duke University, Durham NC 27708.  L. Du  Department of Physics, McGill
University, Montréal QC H3A 2T8, Canada.  R. Ehlers  Department of Physics and
Astronomy, University of Tennessee, Knoxville TN 37996.  Physics Division, Oak
Ridge National Laboratory, Oak Ridge TN 37830.  H. Elfner  GSI
Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany.
Institute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main,
Germany.  Frankfurt Institute for Advanced Studies, 60438 Frankfurt am Main,
Germany.  R. J. Fries  Cyclotron Institute, Texas A&M University, College
Station TX 77843.  Department of Physics and Astronomy, Texas A&M University,
College Station TX 77843.  C. Gale  Department of Physics, McGill University,
Montréal QC H3A 2T8, Canada.  Y. He  Guangdong Provincial Key Laboratory of
Nuclear Science, Institute of Quantum Matter, South China Normal University,
Guangzhou 510006, China.  Guangdong-Hong Kong Joint Laboratory of Quantum
Matter, Southern Nuclear Science Computing Center, South China Normal
University, Guangzhou 510006, China.  M. Heffernan  Department of Physics,
McGill University, Montréal QC H3A 2T8, Canada.  U. Heinz  Department of
Physics, The Ohio State University, Columbus OH 43210.  B. V. Jacak
Department of Physics, University of California, Berkeley CA 94270.  Nuclear
Science Division, Lawrence Berkeley National Laboratory, Berkeley CA 94270.
P. M. Jacobs  Department of Physics, University of California, Berkeley CA
94270.  Nuclear Science Division, Lawrence Berkeley National Laboratory,
Berkeley CA 94270.  S. Jeon  Department of Physics, McGill University,
Montréal QC H3A 2T8, Canada.  Y. Ji  Department of Statistical Science, Duke
University, Durham NC 27708.  K. Kauder  Department of Physics, Brookhaven
National Laboratory, Upton NY 11973.  L. Kasper  Department of Physics and
Astronomy, Vanderbilt University, Nashville TN 37235.  W. Ke  Los Alamos
National Laboratory, Theoretical Division, Los Alamos, NM 87545.  M. Kelsey
Department of Physics and Astronomy, Wayne State University, Detroit MI 48201.
M. Kordell II  Cyclotron Institute, Texas A&M University, College Station TX
77843.  Department of Physics and Astronomy, Texas A&M University, College
Station TX 77843.  A. Kumar  Department of Physics, McGill University,
Montréal QC H3A 2T8, Canada.  Department of Physics and Astronomy, Wayne State
University, Detroit MI 48201.  J. Latessa  Department of Computer Science,
Wayne State University, Detroit MI 48202.  Y.-J. Lee  Laboratory for Nuclear
Science, Massachusetts Institute of Technology, Cambridge MA 02139.
Department of Physics, Massachusetts Institute of Technology, Cambridge MA
02139.  D. Liyanage  Department of Physics, The Ohio State University,
Columbus OH 43210.  A. Lopez  Instituto de Fìsica, Universidade de São Paulo,
C.P. 66318, 05315-970 São Paulo, SP, Brazil.  M. Luzum  Instituto de Fìsica,
Universidade de São Paulo, C.P. 66318, 05315-970 São Paulo, SP, Brazil.  S.
Mak  Department of Statistical Science, Duke University, Durham NC 27708.  A.
Mankolli  Department of Physics and Astronomy, Vanderbilt University,
Nashville TN 37235.  C. Martin  Department of Physics and Astronomy,
University of Tennessee, Knoxville TN 37996.  H. Mehryar  Department of
Computer Science, Wayne State University, Detroit MI 48202.  T. Mengel
Department of Physics and Astronomy, University of Tennessee, Knoxville TN
37996.  J. Mulligan  Department of Physics, University of California, Berkeley
CA 94270.  Nuclear Science Division, Lawrence Berkeley National Laboratory,
Berkeley CA 94270.  C. Nattrass  Department of Physics and Astronomy,
University of Tennessee, Knoxville TN 37996.  D. Oliinychenko  Nuclear Science
Division, Lawrence Berkeley National Laboratory, Berkeley CA 94270.  Institute
for Nuclear Theory, University of Washington, Seattle WA, 98195.  J.-F. Paquet
Department of Physics, Duke University, Durham NC 27708.  J. H. Putschke
Department of Physics and Astronomy, Wayne State University, Detroit MI 48201.
G. Roland  Laboratory for Nuclear Science, Massachusetts Institute of
Technology, Cambridge MA 02139.  Department of Physics, Massachusetts
Institute of Technology, Cambridge MA 02139.  B. Schenke  Physics Department,
Brookhaven National Laboratory, Upton NY 11973.  L. Schwiebert  Department of
Computer Science, Wayne State University, Detroit MI 48202.  A. Sengupta
Cyclotron Institute, Texas A&M University, College Station TX 77843.
Department of Physics and Astronomy, Texas A&M University, College Station TX
77843.  C. Shen  Department of Physics and Astronomy, Wayne State University,
Detroit MI 48201.  RIKEN BNL Research Center, Brookhaven National Laboratory,
Upton NY 11973.  A. Silva  Department of Physics and Astronomy, University of
Tennessee, Knoxville TN 37996.  C. Sirimanna  Department of Physics and
Astronomy, Wayne State University, Detroit MI 48201.  D. Soeder  Department of
Physics, Duke University, Durham NC 27708.  R. A. Soltz  Department of Physics
and Astronomy, Wayne State University, Detroit MI 48201.  Lawrence Livermore
National Laboratory, Livermore CA 94550.  I. Soudi  Department of Physics and
Astronomy, Wayne State University, Detroit MI 48201.  J. Staudenmaier
Institute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main,
Germany.  M. Strickland  Department of Physics, Kent State University, Kent,
OH 44242.  Y. Tachibana  Akita International University, Yuwa, Akita-city
010-1292, Japan.  Department of Physics and Astronomy, Wayne State University,
Detroit MI 48201.  J. Velkovska  Department of Physics and Astronomy,
Vanderbilt University, Nashville TN 37235.  X.-N. Wang  Key Laboratory of
Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central
China Normal University, Wuhan 430079, China.  Department of Physics,
University of California, Berkeley CA 94270.  Nuclear Science Division,
Lawrence Berkeley National Laboratory, Berkeley CA 94270.  R. L. Wolpert
Department of Statistical Science, Duke University, Durham NC 27708.  W. Zhao
Department of Physics and Astronomy, Wayne State University, Detroit MI 48201.

###### Abstract

Parton energy-momentum exchange with the quark gluon plasma (QGP) is a multi-
scale problem. In this work, we calculate the interaction of charm quarks with
the QGP within the higher twist formalism at high virtuality and high energy
using the MATTER model, while the low virtuality and high energy portion is
treated via a Linearized Boltzmann Transport (LBT) formalism. Coherence effect
that reduces the medium-induced emission rate in the MATTER model is also
taken into account through a virtuality-dependent $\hat{q}$, leaving the
simultaneous dependence of $\hat{q}$ on heavy quark mass and virtuality for
future studies. The interplay between these two formalisms is studied
phenomenologically and used to produce a first description of the D-meson and
charged hadron nuclear modification factor $R_{AA}$ across multiple
centralities. All calculations were carried out utilizing the JETSCAPE
framework.

##  I Introduction

Understanding the properties of the quark gluon plasma (QGP) at various energy
scales is at the core of the ongoing relativistic heavy-ion program at the
Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC)
[1]. Soft hadronic observables (e.g. the multiplicity of various hadronic
species or their anisotropic flow) probe transport properties of the QGP such
as its shear and bulk viscosity and can thus be used to constrain the latter
[2]. On the other hand, penetrating probes such as electromagnetic radiation
(see e.g. [3, 4, 5] and references therein) or high energy phenomena, such as
jets and heavy flavor production, give access to properties of the medium at
high temperatures (see e.g. [6, 7, 8] and reference therein). Jets and heavy
flavor production in the vacuum are well understood and calculable using
perturbative QCD techniques [9] as well as Monte Carlo generators of parton
showers such as PYTHIA [10, 11]. This provides a baseline against which the
nuclear medium modifications of these quantities give insight into the QGP
properties.

Medium-induced modifications of parton showers are encapsulated in QGP
transport coefficients [12, 13, 14]. Transverse momentum broadening
($\hat{q}$) of parton showers in the QGP is a notable example of such medium-
induced interactions. More formally,

$\hat{q}=\frac{\langle p^{2}_{T}\rangle_{L}}{L},$ (1)

where $\langle p^{2}_{T}\rangle_{L}$ corresponds to the squared transverse
momentum change of a parton as it traverses a distance $L$ through the QGP
medium before splitting, and thus $\hat{q}$ is the average transverse momentum
change per unit length.

As parton interactions change at different energy and virtuality scales, a
framework that allows for a systematic investigation of their medium-induced
interactions is needed [15], such as that provided by the Jet Energy-loss
Tomography with a Statistically and Computationally Advanced Program Envelope
(JETSCAPE) Collaboration. The holistic approach taken by JETSCAPE has improved
both, our understanding of the bulk transport coefficients of the QGP, such as
the shear and bulk viscosity [Paquet:2020rxl, 16, 17], as well as the jet
energy-loss transport coefficient $\hat{q}$ [18, 19]. Our goal in this work is
to describe the evolution of heavy quarks, specifically charm quarks, within
the QGP using the JETSCAPE framework, and to explore how the multi-scale
physics included in the JETSCAPE framework affect the leading D-meson as well
as the charged hadron nuclear modification factor $R_{AA}$. While, JETSCAPE
version 3.1 is used in our simulation, the current public version (i.e. v3.5)
of JETSCAPE [20] contains the same physics as explored herein and can be used
instead.

The multi-scale problem of parton interactions with the QGP, often called
parton “energy loss” for brevity, can be loosely separated into three regimes:
one of high energy ($E$) and high virtuality ($t$), followed by a high-$E$ and
low-$t$ regime both described via perturbation theory, ultimately ending up in
the low-$E$ and low-$t$ phase space where non-perturbative phenomena take
place. 111Past efforts [21] focused more on developing the theoretical
formalisms and/or numerical approaches to describe these kinematic regimes,
and thus often a single formalism was used throughout the entire evolution
history of the parton shower. The JETSCAPE framework provides the opportunity
to investigate multiple regimes in a consistent fashion. All three sectors are
incorporated inside the JETSCAPE framework, with the first two being the focus
of this study.

Starting in the high-$E$ and high-$t$ region of phase space, any virtual
particle will undergo multiple radiations and thereby reduce its virtuality.
Such processes are already described in the vacuum using Monte Carlo shower
generators, such as PYTHIA, which we here use solely to sample the hard
process giving rise to a parton shower. The subsequent virtuality-ordered
evolution of the shower profile, both in position and momentum spaces, will be
simulated using medium-modified interactions between hard partons and the QGP
following the in-medium Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP)
evolution [22, 23] based on the higher-twist formalism [24, 25, 26] valid when
$t^{2}\gg\hat{q}E$. The medium-modified DGLAP evolution is typically stopped
once the virtuality reaches $t\sim\sqrt{\hat{q}E}$.

When the virtuality scale is close to that of the medium, rate equations [27,
28, 29] become an apt description of parton evolution in the QGP. Formalisms
based on Baier-Dokshitzer-Mueller-Peigne-Schiff- (BDMPS) [30, 31], including
Zakharov’s [32] contribution (BDMPS-Z), or the Arnold-Moore-Yaffe (AMY) [33,
34, 35] approach, the Djordjevic-Gyulassy-Levai-Vitev [36, 37] prescription,
as well as those inspired from higher twist [38, 39, 40, 41] have all be used
in the past. In this work, we follow the higher twist-inspired rate equations
approach. Finally, once partons reach the low-$E$ low-$t$ region, they will be
handed off to PYTHIA for hadronization.

This work is organized as follows: In Sec. II we present details about the
hydrodynamical simulation of the QGP through which partons will interact, Sec.
III describes the multi-stage energy loss models used in this JETSCAPE
calculation, Sec. IV presents the results of this calculation, while Sec. V is
reserved for concluding remarks.

##  II Evolution of the QCD medium

The evolution of the QCD medium used throughout this study is performed using
a Bayesian tuned boost-invariant 2+1-dimensional hydrodynamic-inspired model
which involves three stages: a pre-hydrodynamic, hydrodynamic, and a hadronic
transport stage [2, 42, 43, 44]. The pre-hydrodynamic stage is composed of the
TRENTo (initial condition for Pb-Pb collisions) [45], followed by free-
streaming for a proper time of $\tau_{FS}=1.2$ fm/$c$. This generates a non-
trivial initial condition for the hydrodynamical simulation to follow. We have
generated in total 400 TRENTo initial Pb-Pb configurations in the 0-10%
centrality class at $\sqrt{s_{NN}}=5.02$ TeV. The relevant parameters used for
simulating the evolution of the QCD medium are extracted from a Bayesian
model-to-data comparison, explained in [2, 46].

The hydrodynamical simulation [47, 42] is performed until the the cross-over
temperature of $T_{c}=154$ MeV is reached [48], at which point fluid fields
are converted into particles [46, 49] whose subsequent evolution is governed
by hadronic Boltzmann transport [43, 44].

All parotns, including charm quarks, do not interact during the pre-
hydrodynamical evolution as it is given by free streaming. Since we shall
focus on charm quarks and D-mesons at momenta above $7$ GeV, hadronic final
state interactions are negligible as well. Thus, all parton (and charm quarks
in particular) only interact during the hydrodynamical portion of the
evolution, which is given by second-order Israel-Stewart theory [50, 51].
Other than conservation of energy and momentum, second-order hydrodynamical
equations also include relaxation-type equation for six independent viscous
degrees of freedom, namely five in the shear tensor $\pi^{\mu\nu}$ and one for
bulk pressure $\Pi$. The energy-momentum conservation equation reads:

$\displaystyle\partial_{\mu}T^{\mu\nu}$ $\displaystyle=$ $\displaystyle 0,$
$\displaystyle T^{\mu\nu}$ $\displaystyle=$ $\displaystyle\epsilon
u^{\mu}u^{\nu}-(P+\Pi)\Delta^{\mu\nu}+\pi^{\mu\nu}$ (2)

where $\epsilon$ is the energy density, $u^{\mu}$ is the flow four-velocity,
$P$ is the thermodynamic pressure related to $\epsilon$ by the equation of
state $P(\epsilon)$ [48, 46], $\Delta^{\mu\nu}=g^{\mu\nu}-u^{\mu}u^{\nu}$
projects on the spatial directions in the local fluid rest frame, and
$g^{\mu\nu}={\rm diag}(1,-1,-1,-1)$ is the metric tensor. The dissipative
degrees of freedom satisfy:

$\displaystyle\tau_{\Pi}\dot{\Pi}+\Pi$ $\displaystyle=$
$\displaystyle-\zeta\theta-\delta_{\Pi\Pi}\Pi\theta+\lambda_{\Pi\pi}\pi^{\alpha\beta}\sigma_{\alpha\beta},$
(3) $\displaystyle\tau_{\pi}\dot{\pi}^{\langle\mu\nu\rangle}+\pi^{\mu\nu}$
$\displaystyle=$ $\displaystyle
2\eta\sigma^{\mu\nu}-\delta_{\pi\pi}\pi^{\mu\nu}\theta+\lambda_{\pi\Pi}\Pi\sigma^{\mu\nu}-\tau_{\pi\pi}\pi^{\langle\mu}_{\alpha}\sigma^{\nu\rangle\alpha}+\phi_{7}\pi^{\langle\mu}_{\alpha}\pi^{\nu\rangle\alpha},$
(4)

where $\dot{\Pi}\equiv u^{\alpha}\partial_{\alpha}\Pi$,
$\dot{\pi}^{\langle\mu\nu\rangle}\equiv\Delta^{\mu\nu}_{\alpha\beta}u^{\lambda}\partial_{\lambda}\pi^{\alpha\beta}$,
$\Delta_{\alpha\beta}^{\mu\nu}\equiv\left(\Delta_{\alpha}^{\mu}\Delta_{\beta}^{\nu}+\Delta_{\beta}^{\mu}\Delta_{\alpha}^{\nu}\right)/2-\left(\Delta_{\alpha\beta}\Delta^{\mu\nu}\right)/3$,
$\theta\equiv\partial_{\alpha}u^{\alpha}$,
$\sigma^{\mu\nu}\equiv\partial^{\langle\mu}u^{\nu\rangle}$, with
$A^{\langle\mu\nu\rangle}\equiv\Delta^{\mu\nu}_{\alpha\beta}A^{\alpha\beta}$.
Other than $\zeta$ and $\eta$, which will be discussed in a moment, the
various transport coefficients present in Eqs. (3) and (4) were computed
assuming a single component gas of constituent particles in the limit $m/T\ll
1$ [52, 53], where $m$ is their mass and $T$ the temperature, respectively.
These are summarized in Table 1, where $c^{2}_{s}=\partial P/\partial\epsilon$
is the speed of sound squared.

Table 1: Transport coefficients in Eqs. (3) and (4). Bulk |  | $\tau_{\Pi}=\zeta\left[15(\epsilon+P)\left(\frac{1}{3}-c^{2}_{s}\right)^{2}\right]^{-1}$ | $\delta_{\Pi\Pi}=\frac{2}{3}\tau_{\Pi}$ |  | $\lambda_{\Pi\pi}=\frac{8}{5}\left(\frac{1}{3}-c^{2}_{s}\right)\tau_{\Pi}$ |  |  |  |
---|---|---|---|---|---|---|---|---|---
Shear |  | $\tau_{\pi}=5\eta\left(\epsilon+P\right)^{-1}$ | $\delta_{\pi\pi}=\frac{4}{3}\tau_{\pi}$ |  | $\lambda_{\pi\Pi}=\frac{6}{5}\tau_{\pi}$ |  | $\tau_{\pi\pi}=\frac{10}{7}\tau_{\pi}$ |  | $\phi_{7}=\frac{18}{175}\frac{\tau_{\pi}}{\eta}$

The specific shear viscosity ($\eta/s$) — where $s$ is the entropy density —
and the specific bulk viscosity ($\zeta/s$) are both taken from a recent
Bayesian model-to-data comparison [2].

##  III Parton interactions with the QGP

Following initial parton momentum production in PYTHIA and transverse
positions sampled from the binary collision profile in TRENTo , the evolution
of high-energy and high-virtuality partons is calculated in Modular All Twist
Transverse-scattering Elastic-drag and Radiation (MATTER) [54] (Modular All
Twist Transverse-scattering Elastic-drag and Radiation), which describes their
interactions with the QGP using the higher twist formalism [24, 25, 26]. The
latter develops a virtuality ordered shower, which this study extends by
including heavy quarks in MATTER according to the soft collinear effective
theory (SCET) devised by Ref. [55]. Once partons in the shower reach the low
virtuality (and high energy) regime, further evolution proceeds via the
Linearized Boltzmann Transport (LBT) model [56]. In the LBT formalism, the
interactions between the partons and the QGP preserve the virtuality of the
partons, while modifying their energy and three-momentum. Partons with
virtuality $t>t_{s}$, $t_{s}$ being the switching virtuality, are evolved by
MATTER, while those with $t\leq t_{s}$ are evolved using LBT.

Following the LBT evolution, the JETSCAPE framework determines whether the
partons undergo further evolution in MATTER (this can happen if a parton
quickly exits the medium and continues to shower in the vacuum, for example)
or whether they hadronize (hadronization is handled via fragmentation in
PYTHIA).

###  III.1 The higher-twist formalism in MATTER

This section summarizes the physical mechanisms involving heavy flavor. In the
higher twist approach, the radiation of a gluon off a heavy quark was first
theoretically devised using SCET in Ref. [55], while solely the light flavor
higher-twist calculations were explored in Refs. [24, 25, 26, 54]. The
radiation process $Q\to Q+g$, where $Q$ is a heavy quark, is [55]:

$\displaystyle\frac{dN^{\rm vac}}{dzdt}+\frac{dN^{\rm med}}{dzdt}$
$\displaystyle=$ $\displaystyle\frac{\alpha_{s}(t)}{2\pi}\frac{P_{g\leftarrow
Q}(z)}{t}\left\\{1+\int^{\tau^{+}_{Q}}_{0}d\tau^{+}\frac{1}{z(1-z)t(1+\chi)^{2}}\left[2-2\cos\left(\frac{\tau^{+}}{\tau^{+}_{Q}}\right)\right]\right.\times$
$\displaystyle\times$
$\displaystyle\left.\left[\left(\frac{1+z}{2}\right)-\chi+\left(\frac{1+z}{2}\right)\chi^{2}\right]\hat{q}\right\\}.$

where $z$ is the momentum fraction of the daughter heavy quark, $M$ is the
mass of the heavy quark, $\chi=(1-z)^{2}M^{2}/l^{2}_{\perp}$, with
$l^{2}_{\perp}$ being the relative transverse momentum square between the
outgoing daughter partons, determined via $z(1-z)t=l^{2}_{\perp}(1+\chi)$,
while $t$ is the virtuality of the heavy quark and $P_{g\leftarrow
Q}(z)=C_{F}\left(\frac{1+z^{2}}{1-z^{\,\,\,}}\right)$ is the splitting
function. The integral over light-cone time $\tau^{+}$ in Eq. (LABEL:eq:hq_ht)
assumes the medium is in its rest frame, with the upper bound
$\tau^{+}_{Q}=2q^{+}/t$ being given by the ratio of forward light-cone
momentum $q^{+}=\left(q^{0}+{\bf q}\cdot\hat{n}\right)/\sqrt{2}$ (with
$\hat{n}={\bf q}/|{\bf q}|$), and the virtuality $t$.

####  III.1.1 Transverse momentum broadening of partons in the QGP

The transverse momentum broadening ($\hat{q}$) acquired by the quark as it
traverses the QGP is the only quantity that explicitly depends on $\tau^{+}$
via its temperature dependence $\hat{q}(T)$. Following the the Hard Thermal
Loop (HTL) approximation as presented in Ref. [57], $\hat{q}$ is

$\displaystyle\hat{q}^{HTL}=C_{a}\frac{42\zeta(3)}{\pi}\alpha_{s}^{2}T^{3}\ln\left(\frac{cET}{4m^{2}_{D}}\right)$
(6)

where $C_{a}=N_{c}=3$ the number of colors, $\zeta(3)\approx 1.20205$ is
Apéry’s constant, $E$ is the incoming hard parton’s energy, while the Debye
mass is
$m^{2}_{D}=\frac{4\pi\alpha_{s}T^{2}}{3}\left(N_{c}+\frac{N_{f}}{2}\right)$,
with the number of flavors $N_{f}=3$, the temperature $T$, and $c\approx 5.7$
[58]. Using a calibration to light flavor experimental observables, an
effective value of $\alpha_{s}$ namely $\alpha^{(\rm eff)}_{s}=0.3$ was
obtained [59]. This formulation of $\hat{q}$ will also be used to study heavy
flavor energy loss in this work. The $R_{AA}$ study done in Ref. [59] also
revealed that a constant effective $\alpha^{(\rm eff)}_{s}$ can be improved by
allowing the coupling to run with the scale $\mu^{2}=2ET$ via

$\displaystyle\hat{q}^{HTL}=C_{a}\frac{42\zeta(3)}{\pi}\alpha_{s}\left(\mu^{2}\right)\alpha^{(\rm
eff)}_{s}T^{3}\ln\left(\frac{cET}{4m^{2}_{D}}\right)$ (7)

where

$\displaystyle m^{2}_{D}$ $\displaystyle=$
$\displaystyle\frac{4\pi\alpha^{(\rm
eff)}_{s}T^{2}}{3}\left(N_{c}+\frac{N_{f}}{2}\right)=6\pi\alpha^{(\rm
eff)}_{s}T^{2}$ $\displaystyle\alpha_{s}\left(\mu^{2}\right)$ $\displaystyle=$
$\displaystyle\begin{cases}\alpha^{(\rm eff)}_{s}&\mu^{2}<\mu^{2}_{0},\\\
\frac{4\pi}{11-2N_{f}/3}\frac{1}{\ln\left(\frac{\mu^{2}}{\Lambda^{2}}\right)}&\mu^{2}>\mu^{2}_{0}.\end{cases}$
(8)

with $E$ being the energy of the incoming hard parton participating in a
scattering or radiation process, and $\Lambda$ being chosen such that
$\alpha_{s}(\mu^{2})=\alpha^{(\rm eff)}_{s}$ at $\mu^{2}_{0}=1$ GeV2 [60].
Thus, in our simulation the incoming hard parton (with energy $E$) has a
different coupling (i.e., $\alpha_{s}(\mu^{2})$) than the QGP parton
$\left({\rm i.e.,}\,\,\alpha_{s}^{(\rm eff)}\right)$.

Furthermore, Ref. [60] suggests that $\hat{q}$ changes with the virtuality
scale — beyond the running of $\alpha_{s}(\mu^{2})$ — which offers an
alternative explanation of the puzzle where the extracted $\hat{q}/T^{3}$ is
around 50% smaller at the LHC compared to the RHIC [21]. As the virtuality of
the partons increases with energy, the transverse size of the dipole formed by
the parton and the emitted gluon decreases, and as a result, can only sample
gluons from the medium that have wavelengths comparable to this size. This
causes a suppression of $\hat{q}$ with higher parton virtuality. In Ref. [60]
an integrated form of $\hat{q}$ was adopted, whereas in this study an
effective parametrization of that virtuality dependence [59] is used

$\displaystyle\hat{q}(t)$ $\displaystyle=$
$\displaystyle\hat{q}^{HTL}\frac{c_{0}}{1+c_{1}\ln^{2}(t)+c_{2}\ln^{4}(t)}$
(9) $\displaystyle=$ $\displaystyle
C_{a}\frac{42\zeta(3)}{\pi}\alpha_{s}\left(\mu^{2}\right)\alpha^{(\rm
eff)}_{s}T^{3}\ln\left(\frac{cET}{4m^{2}_{D}}\right)\frac{c_{0}}{1+c_{1}\ln^{2}(t)+c_{2}\ln^{4}(t)},$

where $c_{1}$ and $c_{2}$ are tunable parameters, $t$ is the virtuality of the
parton, and $c_{0}=1+c_{1}\ln^{2}(t_{s})+c_{2}\ln^{4}(t_{s})$ is an overall
normalization ensuring that the $t$-dependent contribution — given by
$\hat{q}(t)/\hat{q}^{HTL}$ — is unitless and lies within 0 and 1 as $t$ does
not go below $t_{s}$. Also note that the virtuality dependence of $\hat{q}$ is
the same regardless of the mass of the quark. Other transport coefficients,
namely the longitudinal drag $\hat{e}$, and the longitudinal diffusion
$\hat{e}_{2}$, though present in MATTER, are not explored here, as their
virtuality dependence is currently unknown.

Given the importance of having a virtuality-dependent $\hat{q}(t)$ for light
flavor observables, the main aim of this study is to investigate whether a
virtuality-dependent $\hat{q}(t)$ can also affect heavy flavors. As no
calculations of $\hat{q}$ simultaneously include its virtuality and heavy
quark mass dependence — i.e., there is no $\hat{q}(t,M)$ available in the
literature — the light-flavor $\hat{q}(t)$ is used herein for both light and
heavy flavor to estimate of the magnitude of $\hat{q}$. At very large
virtualities $t\gg M^{2}$, we expect the heavy quark mass to play less of a
role, and the following approximation

$\displaystyle\hat{q}(t,M)\overset{t\gg M^{2}}{\simeq}\hat{q}(t)$ (10)

is taken throughout this study. To obtain $\hat{q}(t,M)$ in the future, the
SCET scheme [55] should be combined with the virtuality-dependent approach
[60].

####  III.1.2 Kinematic limits of the Sudakov form factor integral

In order to determine the virtuality $t$ of the parent particle, as well as
the momentum fraction of the $z$ of its decay products, we use the kinematics
of the reaction $Q\to Q+g$ to first determine the minimum/maximum momentum
fraction allowed for this process. Up to linear order in $t_{0}/t$ the $z$
limits are:

$\displaystyle z_{\rm min}$ $\displaystyle=$
$\displaystyle\frac{t_{0}}{t}+\frac{M^{2}}{M^{2}+t}+\mathcal{O}\left(\left(\frac{t_{0}}{t}\right)^{2}\right)$
$\displaystyle z_{\rm max}$ $\displaystyle=$ $\displaystyle
1-\frac{t_{0}}{t}+\mathcal{O}\left(\left(\frac{t_{0}}{t}\right)^{2}\right),$
(11)

where $t_{0}$ is the lowest scale below which MATTER evolution for light
flavor partons is physically applicable and is taken to be $t_{0}=1$ GeV2.
Requiring further that $z_{\rm max}>z_{\rm min}$ implies that $t$ has a lower
bond $t_{\rm min}$ which is $t_{\rm
min}=t_{0}\left(1+\sqrt{1+2M^{2}/t_{0}}\right)$. With these limits at hand,
determination of the virtuality $t$ is done by sampling the Sudakov form
factor, which gives a probability for no decay:

$\displaystyle\Delta_{Q\to Q+g}\left(t,t_{\rm
min}\right)=\exp\left[-\int^{t}_{t_{\rm min}}dt^{\prime}\int^{z_{\rm
max}}_{z_{\rm min}}dz\left(\frac{dN^{\rm vac}}{dzdt^{\prime}}+\frac{dN^{\rm
med}}{dzdt^{\prime}}\right)\right].$ (12)

Once the virtuality of the parent parton is determined the momentum fraction
$z$ can be determined by sampling $\int^{z_{\rm high}}_{z_{\rm
low}}dz\left(\frac{dN^{\rm vac}}{dzdt^{\prime}}+\frac{dN^{\rm
med}}{dzdt^{\prime}}\right)$ between $z_{\rm low}\geq z_{\rm min}$ and $z_{\rm
high}\leq z_{\rm max}$.

Heavy quarks can be produced in the medium via $g\to Q+\bar{Q}$, though such a
production is kinematically suppressed compared to light quark production via
gluon decay. Unlike the case of $Q\to Q+g$, the medium modifications to the
process of $g\to Q+\bar{Q}$ have not yet been derived using SCET. Thus, this
production process is approximated as follows [54, 61]:

$\displaystyle\frac{dN^{\rm vac}}{dzdt}+\frac{dN^{\rm med}}{dzdt}$
$\displaystyle=$ $\displaystyle\frac{\alpha_{s}(t)}{2\pi}\frac{P_{Q\leftarrow
g}(z)}{t}\left\\{1+\int^{\tau^{+}_{Q}}_{0}d\tau^{+}\frac{\hat{q}}{z(1-z)t}\left[2-2\cos\left(\frac{\tau^{+}}{\tau^{+}_{Q}}\right)\right]\right\\},$

where $P_{Q\leftarrow g}(z)=T_{R}\left[z^{2}+(1-z)^{2}\right]$, while heavy
quark mass corrections are neglected. Using Eq. (LABEL:eq:g_QQ), the
probability for the gluon not to split into $Q+\bar{Q}$ can be determined.
However, there are other channels contributing to the decay of the gluon and
hence the total probability for gluon not to split is the product of the
probabilities of gluon not splitting into pairs of gluons as well as heavy and
light flavor quarks. Though not explicitly presented here, those channels are
all accounted for in MATTER.

The kinematics of the $g\to Q+\bar{Q}$ decay limit the available phase space
of this process. Indeed, assuming $M^{2}/t\ll 1$ and $t_{0}/t\ll 1$:

$\displaystyle z_{\rm min}$ $\displaystyle=$
$\displaystyle\frac{t_{0}+M^{2}}{t}+\mathcal{O}\left(\left(\frac{t_{0}+M^{2}}{t}\right)^{2}\right)$
$\displaystyle z_{\rm max}$ $\displaystyle=$ $\displaystyle
1-\frac{t_{0}+M^{2}}{t}+\mathcal{O}\left(\left(\frac{t_{0}+M^{2}}{t}\right)^{2}\right).$
(14)

Requiring again that $z_{\rm max}>z_{\rm min}$ as well as $t>t_{\rm min}$,
implies a $t_{\rm min}=2(M^{2}+t_{0})$. The determination of $t$ and $z$
proceeds in the same way as for $Q\to Q+g$.

Once MATTER determines that a splitting has happened, additional
contributions, stemming from further $2\to 2$ scatterings, are calculated
using LBT scattering rates, whose principles are described in Sec. III.2.
Though these medium-induced $2\to 2$ scatterings are not energetic enough to
significantly alter the $t$ and $z$ of the parent/daughter partons in the
shower, they may involve enough energy/momentum exchange to promote medium
partons to become part of the jet shower, thus leaving dynamical sinks
affecting the hydrodynamical equations of motion. Partons leaving the
hydrodynamical descriptions are called “recoil” partons, whose back-reaction
onto the hydrodynamical fields is currently being studied within the JETSCAPE
Collaboration, but not herein.

###  III.2 The linearized Boltzmann transport formalism

The linearized Boltzmann transport (LBT) simulation assumes that a small
virtuality (see e.g. [6] and references therein) has been reached before
further interaction between partons and the QGP occurs. In that limit, LBT
neglects the virtuality of the parton, using on-shell energy and momentum
while calculating parton interactions with the medium, and restores it once a
parton exits the LBT evolution. The main focus of this study is to inspect how
energy-momentum exchange with the QGP affects the charm quark evolution. The
description of light-flavor parton interactions with the QGP is found in Ref.
[59]. The LBT formalism relies on solving the Boltzmann equation taking into
account $2\to 2$ and $2\to 3$ processes. Specifically, the evolution of the
momentum and position distribution of a hard quark $Q$ with momentum $p_{1}$
is given by [62, 39, 40]:

$\displaystyle p^{\mu}_{1}\partial_{\mu}f_{1}\left(x_{1},p_{1}\right)$
$\displaystyle=$ $\displaystyle\mathcal{C}_{\rm el}[f_{1}]+\mathcal{C}_{\rm
inel}[f_{1}]$ (15) $\displaystyle\mathcal{C}_{\rm el}[f_{1}]$ $\displaystyle=$
$\displaystyle\frac{d_{2}}{2}\int dP_{2}\int dP_{3}\int
dP_{3}(2\pi)^{4}\delta^{(4)}\left(p_{1}+p_{2}-p_{3}-p_{4}\right)\left|\mathcal{M}_{1,2\to
3,4}\right|^{2}\lambda_{2}\left(s,t,u\right)$ (16) $\displaystyle\times$
$\displaystyle\left\\{f_{3}\left({\bf p}_{3}\right)f_{4}\left({\bf
p}_{4}\right)\left[1\pm f_{1}\left({\bf p}_{1}\right)\right]\left[1\pm
f_{2}\left({\bf p}_{2}\right)\right]-f_{1}\left({\bf
p}_{1}\right)f_{2}\left({\bf p}_{2}\right)\left[1\pm f_{3}\left({\bf
p}_{3}\right)\right]\left[1\pm f_{4}\left({\bf p}_{4}\right)\right]\right\\}$

where $C_{\rm el}$ is the $2\to 2$ collision rate of the leading order (LO)
perturbative QCD (pQCD) $1+2\to 3+4$ process, $d_{2}$ is the spin-color
degeneracy of the incoming parton “2”, $\int
dP_{i}\equiv\int\frac{d^{3}p_{i}}{(2\pi)^{3}2p^{0}_{i}}$ with $i=2,3,4$; while
$\lambda_{2}\left(s,t,u\right)=\theta\left(s-2m^{2}_{D}\right)\theta\left(s+t-m^{2}_{D}\right)\theta\left(-t-m^{2}_{D}\right)$.
Finally, the procedure to calculate LO pQCD matrix element can be found in
Chapter 17.4 of Ref. [63], for instance, with matrix elements given in [64].

The medium-induced gluon radiation responsible for describing $2\to 3$
processes in $\mathcal{C}_{\rm inel}[f_{1}]$ uses the same higher twist
formulation as that employed in MATTER presented in Eq. (LABEL:eq:hq_ht).
Using the latter, the average number of gluons emitted from a hard heavy
quark, between time $t$ and $t+\Delta t$, is [24, 65, 25]:

$\displaystyle\bar{N}^{\rm med}(t\to t+\Delta t)$ $\displaystyle\approx$
$\displaystyle\Delta t\int dzdk_{\perp}^{2}\frac{dN^{\rm
med}}{dzdk_{\perp}^{2}dt}$ (17) $\displaystyle\frac{dN^{\rm
med}}{dzdk_{\perp}^{2}dt}$ $\displaystyle=$
$\displaystyle\frac{2\alpha_{s}P(z)}{\pi
k_{\perp}^{4}}\hat{q}\left(\frac{k_{\perp}^{2}}{k_{\perp}^{2}+z^{2}M^{2}}\right)^{4}\sin^{2}\left(\frac{t-t_{i}}{2\tau_{f}}\right).$
(18)

As different successive emissions are independent, a Poisson distribution
probability is employed, whereby the probability of emitting $n$ gluons is

$\mathcal{P}(n)=\frac{\left(\bar{N}^{\rm med}\right)^{n}}{n!}e^{-\bar{N}^{\rm
med}},$ (19)

while the probability of a total inelastic process is $\mathcal{P}_{\rm
inel.}=1-e^{-\bar{N}^{\rm med}}$. The procedure to determine whether (and how
many) elastic vs inelastic scatterings inside the QGP have occurred is
explored in detail in Ref. [59]. The only undetermined coefficient in LBT is
the strong coupling $\alpha_{s}$, which can be fixed to $\alpha^{({\rm
eff})}_{s}=0.3$ as mentioned before, or implemented as running coupling
$\alpha_{s}(\mu^{2})$. Both of cases are explored below. The LBT framework
also generates recoil partons in the same way as in MATTER described above.

##  IV Results

This work focuses on studying the interplay between the higher twist and the
Boltzmann transport energy loss mechanisms of charm quarks in the QGP, with an
emphasis on higher twist contribution since it is included for the first time
for open heavy flavor in a multi-stage calculation. Since the current JETSCAPE
computational setup doesn’t have multiple jets propagating through the same
medium simultaneously, the calculation of the nuclear modification factor
$R_{AA}$ simplifies to:

$\displaystyle
R^{D}_{AA}=\frac{\frac{d\sigma^{D}_{AA}}{dp_{T}}}{\frac{d\sigma^{D}_{pp}}{dp_{T}}}=\frac{\sum_{\ell}\frac{dN^{D}_{AA,\ell}}{dp_{T}}\hat{\sigma}_{\ell}}{\sum_{\ell}\frac{dN^{D}_{pp,\ell}}{dp_{T}}\hat{\sigma}_{\ell}}$
(20)

where $\frac{dN^{D}_{AA}}{dp_{T}}$ and $\frac{dN^{D}_{pp}}{dp_{T}}$ are the
multiplicity of D-mesons originating from A-A and p-p collisions in the
experimentally given $p_{T}$ bin, respectively. The spectrum
$\frac{dN^{D}_{AA,\ell}}{dp_{T}}$ is calculated utilizing our multi-stage
model with PYTHIA generating the original hard scattering, MATTER accounting
for virtuality ordered vacuum and in-medium splitting (see Sec. III.1), and
LBT providing the medium-induced shower modification at low virtuality and
high energy (see Sec. III.2). The cross-section for producing the hard
scattering process of the given range $\ell$ in transverse momentum
$\hat{p}_{T}$ is $\hat{\sigma}_{\ell}$ ($\hat{p}_{T}$ is the transverse
momentum of the exchanged parton in the hard scattering sampled by PYTHIA).
Many $\hat{\sigma}_{\ell}$ are sampled, spanning a large kinematic range of
the collision. The connection between the PYTHIA shower and the energy loss
models is chosen to be $0.6$ fm/$c$ but the dependence of $R_{AA}$ on this
quantity is found to be weak [59]. Roughly 10 million events are generated for
one simulation and are evenly distributed among 400 fluid dynamical events
giving rise to about 25000 events per fluid dynamical event. Hadronization is
handled by the Colorless string hadronization routine [11]. Note that bottom
quark energy loss is not accounted for in this study.

|
---|---
Figure 1: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) at the $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the
LHC in the 0-10% centrality. We set $c_{1}=10,\ c_{2}=100$ within the
$\hat{q}(t)$ parametrization [see in Eq. (9)] for the MATTER alone and the
MATTER+LBT curve. The other parameters for the MATTER+LBT curve is
$t_{s}=4$GeV2 found to best describe the $R_{AA}$ data. The p-p baseline for
the LBT curve is calculated using PYTHIA whereas the p-p baseline for the
MATTER and MATTER+LBT cases are calculated using MATTER vacuum [11]. Data
taken from Ref. [66, 67, 68].

Combining all the features of our calculation presented in Sec. III, namely a
multi-stage simulation, a virtuality ($t$)-dependent $\hat{q}$, i.e.
$\hat{q}(t)$, and a running $\alpha_{s}(\mu^{2})$, results in the behavior
seen in Fig. 1. On the left is the D-meson $R_{AA}$, while charged hadron
$R_{AA}$ is on the right. Given the experimental uncertainties, an in-medium
LBT or MATTER calculation alone has difficulty describing simultaneously
charged hadrons and D-meson $R_{AA}$ over a wide $p_{T}$ range. A multi-stage
calculation significantly improves the agreement to data, due to multiple
contributing factors. In the following sections, MATTER and LBT simulations
will first be studied in isolation. This allows a deeper understanding of how
each physical simulations affects $R_{AA}$, thus leading to an appreciation of
how the improvement in Fig. 1 is achieved within the combined simulation.

###  IV.1 $R_{AA}$ from LBT

To obtain $R_{AA}$ using LBT as the sole energy loss mechanism, an initial
parton distribution needs to be provided. One way to obtain this distribution
is by using the PYTHIA vacuum shower. The latter is also used to provide the
proton-proton baseline needed to calculate $R_{AA}$. Combining PYTHIA and LBT,
two simulations were performed: one $\alpha^{\rm(eff)}_{s}=0.3$ serves as
reference $R_{AA}$ calculation, while the other, using $\alpha_{s}(\mu^{2})$,
studies the effects of a running $\alpha_{s}$ on $R_{AA}$.

|
---|---
Figure 2: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
0-10% centrality. The p-p baseline is calculated using PYTHIA.

The results of these calculations are found in Fig. 2. Since these
calculations rely on perturbation theory, solely results above $p_{T}\approx
7$ GeV/$c$ are shown. The calculations with constant
$\alpha^{\rm(eff)}_{s}=0.3$ (dashed lines) generate significant energy loss at
high $p_{T}$, producing an $R_{AA}$ slope that is inconsistent with data, for
both charged hadrons and D-mesons. Including the effects of a running coupling
$\alpha_{s}(\mu^{2})$ (dotted lines) reduces the amount of parton interactions
at high $p_{T}$, which improves the overall $R_{AA}$ slope to better mimic
what is seen in experimental data.

Note that past standalone LBT calculations can describe well experimental data
on $R_{AA}$ and $v_{2}$ for both light and heavy quark hadrons, see Refs. [40,
69, 70, 6] for example. These LBT calculations have a different treatment of
initial spectra, bulk evolution, and hadronization procedures, compared the
one shown here. Furthermore, different values of $\alpha_{s}$ for the
interaction vertex connecting to thermal partons and jet partons were
employed. However, Refs. [40, 70] have not considered how a medium-modified
DGLAP showering mechanism (such as MATTER) can affect the subsequent Boltzmann
transport evolution. The JETSCAPE framework is designed to connect different
energy-loss schemes, such the medium-modified DGLAP evolution in MATTER and
on-shell transport in LBT, thus going beyond studying them in isolation.
Results from the standalone LBT as implemented in the JETSCAPE framework are
shown here to illustrate the importance of a multi-stage in-medium jet shower
evolution.

Except for $D^{0}$-meson $R_{AA}$ at high $p_{T}$, assuming that no energy
loss occurs during the high virtuality showering of partons in a jet is an
approximation that doesn’t provide a good description of the data. Thus, the
goal of the next section is to investigate how energy loss affects the high-
virtuality portion of the shower simulated via the higher twist formalism in
MATTER.

###  IV.2 $R_{AA}$ from MATTER

|
---|---
Figure 3: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
0-10% centrality. HTL denotes a Hard Thermal Loop calculation using
$\hat{q}^{HTL}$, while no recoil refers to scattering processes being
deactivated in MATTER.

As MATTER is being used throughout the entire virtuality evolution herein, the
higher twist formalism upon which it is based is employed until $t_{s}=1$
GeV2. MATTER simulates the energy-momentum exchange between the partons of the
medium and jet partons via two types of interactions. The first type of
interaction is medium-induced inelastic radiation encapsulated in $\hat{q}$, a
non-stochastic transport coefficient accounting for deviations from vacuum
splittings. Elastic $2\to 2$ scatterings between jet and medium partons are
treated stochastically. For each parton in the shower, the $2\to 2$ scattering
rate is sampled. If a scattering occurs, the thermal parton involved can
become part of the jet, leaving a negative contribution in the fluid, or
become a source of energy-momentum to be deposited in the QGP. In Fig. 3, the
elastic and inelastic processes are studied in turn assuming a running
$\alpha_{s}(\mu^{2})$.

Focusing on the result without $2\to 2$ scatterings, labeled as no recoil in
Fig. 3, one sees that including elastic scatterings leads to additional energy
loss compared to that incurred via radiative processes alone. Unlike the LBT
simulation where partons are long-lived and thus recoils are ever present, for
a virtuality ordered shower in MATTER the importance of these elastic
scatterings needs to be highlighted due to the highly variable lifetime of
partons in the shower. Furthermore, the comparison between light and heavy
flavor allows to appreciate how much these recoils affect partons of different
masses. Our calculations show that heavy and light quarks are similarly
affected, which can be an artifact of not using $\hat{q}(t,M)$, thus
motivating its calculation by combining SCET of Ref. [55] with Ref. [60].
Outside of Fig. 3, $2\to 2$ scattering is always included in calculations
containing MATTER.

|
---|---
Figure 4: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
0-10% centrality. The difference between $\hat{q}^{HTL}$ and $\hat{q}(t)$ is
significant especially at high $p_{T}$.

As the virtuality dependent $\hat{q}(t)$ is smaller compared to the Hard
Thermal Lool (HTL) result, the $R_{AA}$ tends to be much closer to $1$ for
$\hat{q}(t)$ (dotted lines) compared to the one for $\hat{q}^{HTL}$ (dashed
lines) as depicted in Fig. 4. This effect is seen in both light and heavy
flavor results at high $p_{T}$, as expected.

The MATTER alone result is not to be compared with data, instead it gives a
sense how different physics ingredients in MATTER affect its results, which
are present in the overall comparison of MATTER+LBT $R_{AA}$ againts data.

###  IV.3 $R_{AA}$ from the combined MATTER and LBT simulation

|
---|---
Figure 5: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
0-10% centrality. Here we are varying the parametrization of $\hat{q}(t)$
which is monotonically decreasing when $c_{1}$ and $c_{2}$ increase. The ratio
in the bottom plots are taken with respect to the $c_{1}=10,c_{2}=100$ case
with $\hat{q}(t)$ parametrization [see Eq. (9)]. A running
$\alpha_{s}(\mu^{2})$ is used in all calculations involving LBT.

The combination of MATTER and LBT simulations is done by separating, in
virtuality, the parton evolution in MATTER from that in LBT. The virtuality at
which the switch is performed is a parameter, which for light flavor was tuned
to $t_{s}=4$ GeV2.

A multi-stage $R_{AA}$ calculation using a virtuality-independent
$\hat{q}^{HTL}$ alone shows an over suppression of $R_{AA}$ compared to data
for both light and heavy flavors. Additionally, the slope seen in the
experimental data in the region $p_{T}\gtrsim 10$ GeV is steeper than what is
obtained in our multi-stage $R_{AA}$ calculation using $\hat{q}^{HTL}$. A
simple re-scaling of the overall normalization of $\hat{q}^{HTL}$ would not be
enough to explain the slope seen in the data. In fact, a virtuality-dependent
$\hat{q}$ whose value is suppressed as virtuality increases, such as that
found Ref. [59], helps in this regard. Employing a virtuality-dependent
$\hat{q}$ shows a significant effect on parton evolution not only in MATTER,
but more importantly in the multi-stage MATTER+LBT evolution, affecting
simultaneously light flavor and D-meson $R_{AA}$ seen in Fig. 5. It is the
combination of a multi-stage simulation together with a virtuality-dependent
$\hat{q}$ that is responsible for the agreement between the theoretical
calculation and the data, in line with findings from the previous two
sections. Fig. 5 explores how different parameter values of $\hat{q}(t)$ in
Eq. (9) affect the $R_{AA}$, especially at high $p_{T}$.

####  IV.3.1 Effects of $\hat{q}$ and $t_{s}$ on $R_{AA}$

|
---|---
Figure 6: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
0-10% centrality. A bigger value of $t_{s}$ increases the effective length of
LBT based energy-loss. The ratio in the bottom plots are taken with respect to
the $c_{1}=10,c_{2}=100$ case of the $\hat{q}(t)$ parametrization. A running
$\alpha_{s}(\mu^{2})$ is used in all calculations involving LBT.

Fig. 6 studies the effect of varying the switching scale $t_{s}$, with a
larger $t_{s}$ implying a longer parton evolution in the LBT regime. The LBT
mechanism generates significantly larger energy loss compared to the MATTER
evolution, especially at low $p_{T}$, and thus the $t_{s}=9$ GeV2 curve is
close to a purely LBT simulation. Combining results from Figs. 5 and 6, we see
that a parameter choice of $c_{1}=10,c_{2}=100,t_{s}=4$GeV2 provides the best
simultaneous description of the charged hadron and $D^{0}$ meson $R_{AA}$
data. To improve the description of $R_{AA}$ across all $p_{T}$, a Bayesian
analysis of the $\hat{q}(t)$ parameter space is planned.

####  IV.3.2 Effects of gluon splitting to heavy quark pair on $R_{AA}$

|
---|---
Figure 7: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
0-10% centrality. $c_{1}=10,\ c_{2}=100$ parameters values are employed in Eq.
(9). Ignoring the $g\rightarrow Q+\bar{Q}$ process in MATTER impacts the D
meson $R_{AA}$, while it has a smaller effect on the charged hadron $R_{AA}$.
A running $\alpha_{s}(\mu^{2})$ is used in all calculations involving LBT. The
dashed line in the ratio subplots divides MATTER+LBT no $g\to Q+\bar{Q}$ to
MATTER+LBT, while the dotted-dashed line divides MATTER+LBT HTL no $g\to
Q+\bar{Q}$ to MATTER+LBT HTL.

The novel physics ingredient that the present study allows to explore is the
creation of heavy flavor through $g\rightarrow Q+\bar{Q}$ in MATTER, as
presented in Sec. III.1.2. This process is best studied in a multi-scale
simulation where the in-medium heavy quark creation and their subsequent
evolution probes different virtuality regimes. Charmed quarks are the ideal
candidate for this study, as their lighter mass (compared to bottom/top
quarks) opens up the phase space for their in-medium dynamics, best
highlighting the benefits of a multi-stage approach. To explore charm
production from $g\rightarrow Q+\bar{Q}$, both the $D$ meson $R_{AA}$ and the
charged hadron $R_{AA}$ are investigated using the combined MATTER and LBT
simulation. As depicted in Fig. 7, ignoring this process has a roughly $20\%$
impact on $D$ meson $R_{AA}$, while less than $10\%$ is seen for the charged
hadron $R_{AA}$. Since we are only turning off the $g\rightarrow Q+\bar{Q}$
channel in MATTER, this has a smaller effect on the total charged hadron
spectra, as $D$ meson contribution is subdominant. However, the contribution
from gluon splitting to the total charm cross-section contribution is non-
negligible, as a previous study using PYTHIA [71] also reports. The novel
contribution the present simulation investigates is how different forms of
$\hat{q}$ affect the $g\to Q+\bar{Q}$ heavy-flavor production. A larger
$\hat{q}^{HTL}$ compared to $\hat{q}(t)$ reduces the parton virtuality, thus
shrinking the phase space for $g\to Q+\bar{Q}$, which ultimately generates
fewer charmed quarks and reduces the $R_{AA}$, for all curves but the solid
one, as seen in Fig. 7 (a). Overall, Fig. 7 (a) provides the phenomenological
importance to extend the SCET calculation of Ref. [55] on the process $g\to
Q+\bar{Q}$ in the future.

####  IV.3.3 $R_{AA}$ for $10-30\%$ and $30-50\%$ centrality

|
---|---
Figure 8: (Color online) Nuclear modification factor for D-mesons (a) and charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at 10-30% centrality. The parameters $c_{1}=10,\ c_{2}=100$ for the $\hat{q}(t)$ in Eq. (9) are chosen. A running $\alpha_{s}(\mu^{2})$ is used in all calculations involving LBT. |
---|---
Figure 9: (Color online) Nuclear modification factor for D-mesons (a) and
charged hadrons (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at
30-50% centrality. Here we choose $c_{1}=10,\ c_{2}=100$ for the $\hat{q}$
parametrization. A running $\alpha_{s}(\mu^{2})$ is used in all calculations
involving LBT.

The $R_{AA}$ results for the $10-30\%$ and $30-50\%$ centrality are studied in
Figs. 8 and Fig. 9. Here the “best” fit parameters used in the $\hat{q}(t)$
parametrization (i.e. $c_{1}=10,\ c_{2}=100$) are employed. One interesting
phenomenon to notice is the reversal in order between MATTER+LBT and LBT
calculation at high $p_{T}$ for the $D$ meson $R_{AA}$ from the most central
collisions to more peripheral collisions. Two important effects contribute to
this observation. First, heavy quarks are more suppressed in the MATTER phase
compared to light flavor partons at high $p_{T}$. This can be seen from both
the MATTER only simulations in Fig. 10 (a) as well as in MATTER+LBT
simulations, see Fig. 10 (b). Second, going from central to more peripheral
collisions, LBT simulations seem to be more affected by the amount of time
partons spend interacting with the QGP, compared to MATTER+LBT simulations.
Figure 11 shows that at higher $p_{T}$, the ratio of $R_{AA}$ between LBT and
MATTER+LBT simulations increases as the centrality increases for both D meson
and charged hadrons. The virtuality dependent $\hat{q}$ reduces the in-medium
contribution to MATTER evolution, making it closer to a vacuum-like (DGLAP)
evolution at high $p_{T}$, and thus the partons spend less time in the LBT
phase for MATTER+LBT simulations compared to LBT-only simulations. It is
important to recall that the same $\hat{q}(t)$ is used for both light and
heavy quarks throughout this work, and thus the observation that parton
evolution is more vacuum-like given our parametrization for $\hat{q}$ may not
necessarily hold for heavy flavors. In fact, a mass- and virtuality-dependent
$\hat{q}(t,M)$ is needed to enhance future multi-scale heavy flavor evolution
studies, as was mentioned when discussing Eq. (10). In the present work,
however, as centrality increases, simulations based solely on LBT evolution
are more sensitive to the reduction in QGP space-time volume compared to
MATTER+LBT simulations.

|
---|---
Figure 10: (Color online) Nuclear modification factor for MATTER only simulations (a) and for MATTER+LBT simulations (b) in $\sqrt{s_{NN}}=5.02$ TeV Pb-Pb collisions at the LHC at 0-10% centrality. $c_{1}=10,\ c_{2}=100$ parameters values are employed in Eq. (9). A running $\alpha_{s}(\mu^{2})$ is used in all calculations involving LBT. |
---|---
Figure 11: (Color online) Ratio of nuclear modification factor between LBT and
MATTER+LBT for D-mesons (a) and charged hadrons (b) in $\sqrt{s_{NN}}=5.02$
TeV Pb-Pb collisions at the LHC at 0-10%, 10-30%, 30-50% centrality.
$c_{1}=10,\ c_{2}=100$ parameters values are employed in Eq. (9). A running
$\alpha_{s}(\mu^{2})$ is used in all calculations involving LBT.

Finally, note that in all our $R_{AA}$ calculations involving MATTER, the p-p
baseline is using the MATTER vacuum results. The differences between PYTHIA
and MATTER vacuum in p-p for charged hadrons and D mesons are found in [11,
72]. This is essentially a comparison between PYTHIA, which generates an
angular ordered shower, and MATTER which generates a virtuality ordered
shower. If PYTHIA was used as the p-p baseline calculation, then the $R_{AA}$
may be further improved in some $p_{T}$ ranges, at the expense of calculation
consistency. We choose to err on the side of a consistent calculation.

##  V Conclusion

This study explored how different physics entering a multi-stage description
of jet partons interaction with the QGP affect both the D meson and the
charged hadron $R_{AA}$. For the LBT regime, the effects of a running
$\alpha_{s}(\mu^{2})$ was studied. For the MATTER regime, we highlighted the
effects of including scattering as well as considering a virtuality dependent
$\hat{q}$ and found that both make a large contribution to the value of
$R_{AA}$. The virtuality dependent $\hat{q}$ offers a possible explanation for
the diminishing value of the interaction strength $\hat{q}/T^{3}$ at the LHC
from previous extractions [21]. However, neither of these two models alone is
sufficient for describing the $R_{AA}$ at the $p_{T}$ range we are interested
in.

We find that the best simultaneous description of the D meson and charged
hadron $R_{AA}$ requires the explicit inclusion of both the high-energy and
high-virtuality regime as well as the high energy and low virtuality regime of
parton energy-loss. In this work, these have been modeled using the MATTER and
the LBT schemes within the JETSCAPE framework. The specific form of the
$\hat{q}(t)$ parametrization is still under investigation, yet we can already
state that the suppression of $\hat{q}$ at higher virtuality mostly increases
$R_{AA}$ at high $p_{T}$. We have also explored where, in virtuality, the
transition point lies between these two regimes and how changing it affects
the resulting $R_{AA}$. A higher switching scale $t_{s}$ implies that partons
will evolve longer in the LBT regime and lose more energy. While we have found
that our simple exploration of the parameter space already provides a decent
simultaneous description of both light and heavy flavor $R_{AA}$, a Bayesian
analysis could improve the description even further. This work also shows
where improved theoretical calculations are needed to better phenomenological
simulations. Though a virtuality dependent $\hat{q}(t)$ does help to obtain a
closer comparison between simulations to data, using solely a virtuality-
dependent $\hat{q}(t)$ is not enough, both in terms of underlying physics
understanding and phenomenology. Indeed, $\hat{q}(t,M)$ may explain the
results found in Figs. 8 and Fig. 9. A similar argument holds for longitudinal
drag $\hat{e}$ and diffusion $\hat{e}_{2}$, which are know to play a part in
heavy flavors physics (e.g., [61]). Furthermore, the $g\to Q+\bar{Q}$ process
needs to be studied using SCET that was developed in Ref. [55], given how
phenomenologically important our study shows it to be (on the order of 20%).
Thus, our first phenomenological study highlights which physics of the multi-
scale evolution should be improved next to better explain heavy flavor
interaction in the QGP.

In the future, we plan to extend our simulation to bottom flavor and further
investigate heavy flavor jet and jet substructure observables. A detailed
comparison with inclusive jet observables is also of interest. The extension
of our framework to such observables should provide a better constraint on
$\hat{q}$.

## Acknowledgments

This work was supported in part by the National Science Foundation (NSF)
within the framework of the JETSCAPE collaboration, under grant number
OAC-2004571 (CSSI:X-SCAPE). It was also supported under ACI-1550172 (Y.C. and
G.R.), ACI-1550221 (R.J.F., F.G., and M.K.), ACI-1550223 (U.H., L.D., and
D.L.), ACI-1550225 (S.A.B., T.D., W.F., R.W.), ACI-1550228 (J.M., B.J., P.J.,
X.-N.W.), and ACI-1550300 (S.C., A.K., J.L., A.M., H.M., C.N., A.S., J.P.,
L.S., C.Si., I.S., R.A.S. and G.V.); by PHY-1516590 and PHY-1812431 (R.J.F.,
M.K. and A.S.), by PHY-2012922 (C.S.); it was supported in part by NSF CSSI
grant number OAC-2004601 (BAND; D.L. and U.H.); it was supported in part by
the US Department of Energy, Office of Science, Office of Nuclear Physics
under grant numbers DE-AC02-05CH11231 (X.-N.W.), DE-FG02-00ER41132 (D.O), DE-
AC52-07NA27344 (A.A., R.A.S.), DE-SC0013460 (S.C., A.K., A.M., C.S., I.S. and
C.Si.), DE-SC0021969 (C.S. and W.Z.), DE-SC0004286 (L.D., U.H. and D.L.), DE-
SC0012704 (B.S.), DE-FG02-92ER40713 (J.P.) and DE-FG02-05ER41367 (T.D., W.F.,
J.-F.P., D.S. and S.A.B.). The work was also supported in part by the National
Science Foundation of China (NSFC) under grant numbers 11935007, 11861131009
and 11890714 (Y.H. and X.-N.W.), under grant numbers 12175122 and 2021-867
(S.C.), by the Natural Sciences and Engineering Research Council of Canada
(C.G., M.H., S.J., and G.V.), by the Office of the Vice President for Research
(OVPR) at Wayne State University (Y.T.), by the São Paulo Research Foundation
(FAPESP) under projects 2016/24029-6, 2017/05685-2 and 2018/24720-6 (A. L. and
M.L.), and by the University of California, Berkeley - Central China Normal
University Collaboration Grant (W.K.). U.H. would like to acknowledge support
by the Alexander von Humboldt Foundation through a Humboldt Research Award.
C.S. acknowledges a DOE Office of Science Early Career Award. Computations
were carried out on the Wayne State Grid funded by the Wayne State OVPR. The
bulk medium simulations were done using resources provided by the Open Science
Grid (OSG) [73, 74], which is supported by the National Science Foundation
award #2030508. Data storage was provided in part by the OSIRIS project
supported by the National Science Foundation under grant number OAC-1541335.

## References

  * Wang [2016] X.-N. Wang, ed.,  _Quark-Gluon Plasma 5_ (World Scientific, New Jersey, 2016).
  * Bernhard  _et al._ [2019] J. E. Bernhard, J. S. Moreland, and S. A. Bass, Bayesian estimation of the specific shear and bulk viscosity of quark–gluon plasma, Nature Phys. 15, 1113 (2019).
  * Vujanovic  _et al._ [2020] G. Vujanovic, J.-F. Paquet, C. Shen, G. S. Denicol, S. Jeon, C. Gale, and U. Heinz, Exploring the influence of bulk viscosity of QCD on dilepton tomography, Phys. Rev. C 101, 044904 (2020), arXiv:1903.05078 [nucl-th] .
  * Tripolt [2021] R.-A. Tripolt, Electromagnetic and weak probes: theory, Nucl. Phys. A 1005, 121755 (2021), arXiv:2001.11232 [hep-ph] .
  * Geurts [2021] F. Geurts, Electromagnetic $\&$ Weak Probes: Experimental Overview, Nucl. Phys. A 1005, 121830 (2021), arXiv:2004.01801 [nucl-ex] .
  * Cao and Wang [2021] S. Cao and X.-N. Wang, Jet quenching and medium response in high-energy heavy-ion collisions: a review, Rept. Prog. Phys. 84, 024301 (2021), arXiv:2002.04028 [hep-ph] .
  * Connors  _et al._ [2018] M. Connors, C. Nattrass, R. Reed, and S. Salur, Jet measurements in heavy ion physics, Rev. Mod. Phys. 90, 025005 (2018), arXiv:1705.01974 [nucl-ex] .
  * Djordjevic and Heinz [2008] M. Djordjevic and U. W. Heinz, Radiative energy loss in a finite dynamical QCD medium, Phys. Rev. Lett. 101, 022302 (2008), arXiv:0802.1230 [nucl-th] .
  * Frawley  _et al._ [2008] A. D. Frawley, T. Ullrich, and R. Vogt, Heavy flavor in heavy-ion collisions at RHIC and RHIC II, Phys. Rept. 462, 125 (2008), arXiv:0806.1013 [nucl-ex] .
  * Sjöstrand [2020] T. Sjöstrand, The PYTHIA Event Generator: Past, Present and Future, Comput. Phys. Commun. 246, 106910 (2020), arXiv:1907.09874 [hep-ph] .
  * Kumar  _et al._ [2020a] A. Kumar _et al._ (JETSCAPE), JETSCAPE framework: $p+p$ results, Phys. Rev. C 102, 054906 (2020a), arXiv:1910.05481 [nucl-th] .
  * Nahrgang  _et al._ [2016] M. Nahrgang, J. Aichelin, P. B. Gossiaux, and K. Werner, Toward a consistent evolution of the quark-gluon plasma and heavy quarks, Phys. Rev. C 93, 044909 (2016), arXiv:1602.03544 [nucl-th] .
  * Brambilla  _et al._ [2020] N. Brambilla, V. Leino, P. Petreczky, and A. Vairo, Lattice QCD constraints on the heavy quark diffusion coefficient, Phys. Rev. D 102, 074503 (2020), arXiv:2007.10078 [hep-lat] .
  * Kumar  _et al._ [2022] A. Kumar, A. Majumder, and J. H. Weber, Jet transport coefficient q^ in lattice QCD, Phys. Rev. D 106, 034505 (2022), arXiv:2010.14463 [hep-lat] .
  * Putschke  _et al._ [2019] J. Putschke _et al._ , The JETSCAPE framework, (2019), arXiv:1903.07706 [nucl-th] .
  * Everett  _et al._ [2021a] D. Everett _et al._ (JETSCAPE), Phenomenological constraints on the transport properties of QCD matter with data-driven model averaging, Phys. Rev. Lett. 126, 242301 (2021a), arXiv:2010.03928 [hep-ph] .
  * Everett  _et al._ [2021b] D. Everett _et al._ (JETSCAPE), Multisystem Bayesian constraints on the transport coefficients of QCD matter, Phys. Rev. C 103, 054904 (2021b), arXiv:2011.01430 [hep-ph] .
  * Cao  _et al._ [2017] S. Cao _et al._ (JETSCAPE), Multistage Monte-Carlo simulation of jet modification in a static medium, Phys. Rev. C 96, 024909 (2017), arXiv:1705.00050 [nucl-th] .
  * Cao  _et al._ [2021] S. Cao _et al._ (JETSCAPE), Determining the jet transport coefficient $\hat{q}$ from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys. Rev. C 104, 024905 (2021), arXiv:2102.11337 [nucl-th] .
  * [20] Https://github.com/JETSCAPE/JETSCAPE.
  * Burke  _et al._ [2014] K. M. Burke _et al._ (JET), Extracting the jet transport coefficient from jet quenching in high-energy heavy-ion collisions, Phys. Rev. C 90, 014909 (2014), arXiv:1312.5003 [nucl-th] .
  * Majumder [2009] A. Majumder, The In-medium scale evolution in jet modification, (2009), arXiv:0901.4516 [nucl-th] .
  * Deng and Wang [2010] W.-t. Deng and X.-N. Wang, Multiple Parton Scattering in Nuclei: Modified DGLAP Evolution for Fragmentation Functions, Phys. Rev. C81, 024902 (2010), arXiv:0910.3403 [hep-ph] .
  * Wang and Guo [2001] X.-N. Wang and X.-f. Guo, Multiple parton scattering in nuclei: Parton energy loss, Nucl. Phys. A696, 788 (2001), arXiv:hep-ph/0102230 [hep-ph] .
  * Majumder [2012] A. Majumder, Hard collinear gluon radiation and multiple scattering in a medium, Phys. Rev. D85, 014023 (2012), arXiv:0912.2987 [nucl-th] .
  * Qin and Majumder [2010] G.-Y. Qin and A. Majumder, A pQCD-based description of heavy and light flavor jet quenching, Phys. Rev. Lett. 105, 262301 (2010), arXiv:0910.3016 [hep-ph] .
  * Jeon and Moore [2005] S. Jeon and G. D. Moore, Energy loss of leading partons in a thermal QCD medium, Phys. Rev. C 71, 034901 (2005), arXiv:hep-ph/0309332 .
  * Turbide  _et al._ [2005] S. Turbide, C. Gale, S. Jeon, and G. D. Moore, Energy loss of leading hadrons and direct photon production in evolving quark-gluon plasma, Phys. Rev. C 72, 014906 (2005), arXiv:hep-ph/0502248 .
  * Qin  _et al._ [2009] G.-Y. Qin, J. Ruppert, C. Gale, S. Jeon, and G. D. Moore, Jet energy loss, photon production, and photon-hadron correlations at RHIC, Phys. Rev. C 80, 054909 (2009), arXiv:0906.3280 [hep-ph] .
  * Baier  _et al._ [1997a] R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark - gluon plasma, Nucl. Phys. B 483, 291 (1997a), arXiv:hep-ph/9607355 .
  * Baier  _et al._ [1997b] R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigne, and D. Schiff, Radiative energy loss and p(T) broadening of high-energy partons in nuclei, Nucl. Phys. B 484, 265 (1997b), arXiv:hep-ph/9608322 .
  * Zakharov [1996] B. G. Zakharov, Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD, JETP Lett. 63, 952 (1996), arXiv:hep-ph/9607440 .
  * Arnold  _et al._ [2001] P. B. Arnold, G. D. Moore, and L. G. Yaffe, Photon emission from quark gluon plasma: Complete leading order results, JHEP 12, 009, arXiv:hep-ph/0111107 .
  * Arnold  _et al._ [2002] P. B. Arnold, G. D. Moore, and L. G. Yaffe, Photon and gluon emission in relativistic plasmas, JHEP 06, 030, arXiv:hep-ph/0204343 .
  * Arnold  _et al._ [2003] P. B. Arnold, G. D. Moore, and L. G. Yaffe, Effective kinetic theory for high temperature gauge theories, JHEP 01, 030, arXiv:hep-ph/0209353 .
  * Djordjevic and Gyulassy [2004] M. Djordjevic and M. Gyulassy, Heavy quark radiative energy loss in QCD matter, Nucl. Phys. A 733, 265 (2004), arXiv:nucl-th/0310076 .
  * Gyulassy  _et al._ [2000] M. Gyulassy, P. Levai, and I. Vitev, Jet quenching in thin quark gluon plasmas. 1. Formalism, Nucl. Phys. B 571, 197 (2000), arXiv:hep-ph/9907461 .
  * Wang and Zhu [2013] X.-N. Wang and Y. Zhu, Medium Modification of $\gamma$-jets in High-energy Heavy-ion Collisions, Phys. Rev. Lett. 111, 062301 (2013), arXiv:1302.5874 [hep-ph] .
  * Cao  _et al._ [2016] S. Cao, T. Luo, G.-Y. Qin, and X.-N. Wang, Linearized Boltzmann transport model for jet propagation in the quark-gluon plasma: Heavy quark evolution, Phys. Rev. C 94, 014909 (2016), arXiv:1605.06447 [nucl-th] .
  * Cao  _et al._ [2018] S. Cao, T. Luo, G.-Y. Qin, and X.-N. Wang, Heavy and light flavor jet quenching at RHIC and LHC energies, Phys. Lett. B 777, 255 (2018), arXiv:1703.00822 [nucl-th] .
  * Chen  _et al._ [2018] W. Chen, S. Cao, T. Luo, L.-G. Pang, and X.-N. Wang, Effects of jet-induced medium excitation in $\gamma$-hadron correlation in A+A collisions, Phys. Lett. B 777, 86 (2018), arXiv:1704.03648 [nucl-th] .
  * Shen  _et al._ [2016] C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass, and U. Heinz, The iEBE-VISHNU code package for relativistic heavy-ion collisions, Comput. Phys. Commun. 199, 61 (2016), arXiv:1409.8164 [nucl-th] .
  * Bass  _et al._ [1998] S. A. Bass _et al._ , Microscopic models for ultrarelativistic heavy ion collisions, Prog. Part. Nucl. Phys. 41, 255 (1998), arXiv:nucl-th/9803035 .
  * Bleicher  _et al._ [1999] M. Bleicher _et al._ , Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model, J. Phys. G 25, 1859 (1999), arXiv:hep-ph/9909407 .
  * Moreland  _et al._ [2015] J. S. Moreland, J. E. Bernhard, and S. A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92, 011901 (2015), arXiv:1412.4708 [nucl-th] .
  * Bernhard [2018] J. E. Bernhard,  _Bayesian parameter estimation for relativistic heavy-ion collisions_ , Ph.D. thesis, Duke U. (2018), arXiv:1804.06469 [nucl-th] .
  * Song and Heinz [2008] H. Song and U. W. Heinz, Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions, Phys. Rev. C 77, 064901 (2008), arXiv:0712.3715 [nucl-th] .
  * Bazavov  _et al._ [2014] A. Bazavov _et al._ (HotQCD), Equation of state in ( 2+1 )-flavor QCD, Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat] .
  * Huovinen and Petersen [2012] P. Huovinen and H. Petersen, Particlization in hybrid models, Eur. Phys. J. A 48, 171 (2012), arXiv:1206.3371 [nucl-th] .
  * Israel [1976] W. Israel, Nonstationary irreversible thermodynamics: A causal relativistic theory, Annals of Physics 100, 310 (1976).
  * Israel and Stewart [1979] W. Israel and J. Stewart, Transient relativistic thermodynamics and kinetic theory, Annals Phys. 118, 341 (1979).
  * Denicol  _et al._ [2012] G. S. Denicol, H. Niemi, E. Molnar, and D. H. Rischke, Derivation of transient relativistic fluid dynamics from the Boltzmann equation, Phys. Rev. D85, 114047 (2012), [Erratum: Phys. Rev.D91,no.3,039902(2015)], [arXiv:nucl-th/1202.4551] .
  * Denicol  _et al._ [2014] G. S. Denicol, S. Jeon, and C. Gale, Transport Coefficients of Bulk Viscous Pressure in the 14-moment approximation, Phys. Rev. C90, 024912 (2014), arXiv:1403.0962 [nucl-th] .
  * Majumder [2013] A. Majumder, Incorporating space-time within medium-modified jet event generators, Phys. Rev. C88, 014909 (2013), arXiv:1301.5323 [nucl-th] .
  * Abir and Majumder [2016] R. Abir and A. Majumder, Drag-induced radiative energy loss from semihard heavy quarks, Phys. Rev. C94, 054902 (2016), arXiv:1506.08648 [nucl-th] .
  * Luo  _et al._ [2018] T. Luo, S. Cao, Y. He, and X.-N. Wang, Multiple jets and $\gamma$-jet correlation in high-energy heavy-ion collisions, Phys. Lett. B782, 707 (2018), arXiv:1803.06785 [hep-ph] .
  * He  _et al._ [2015] Y. He, T. Luo, X.-N. Wang, and Y. Zhu, Linear Boltzmann Transport for Jet Propagation in the Quark-Gluon Plasma: Elastic Processes and Medium Recoil, Phys. Rev. C 91, 054908 (2015), [Erratum: Phys.Rev.C 97, 019902 (2018)], arXiv:1503.03313 [nucl-th] .
  * Caron-Huot [2009] S. Caron-Huot, Transverse diffusion (’q-hat’) at weak coupling, Nucl. Phys. A 820, 115C (2009).
  * Kumar  _et al._ [2023] A. Kumar _et al._ (JETSCAPE), Inclusive jet and hadron suppression in a multistage approach, Phys. Rev. C 107, 034911 (2023), arXiv:2204.01163 [hep-ph] .
  * Kumar  _et al._ [2020b] A. Kumar, A. Majumder, and C. Shen, Energy and scale dependence of $\hat{q}$ and the “JET puzzle”, Phys. Rev. C 101, 034908 (2020b), arXiv:1909.03178 [nucl-th] .
  * Cao and Majumder [2020] S. Cao and A. Majumder, Nuclear modification of leading hadrons and jets within a virtuality ordered parton shower, Phys. Rev. C 101, 024903 (2020), arXiv:1712.10055 [nucl-th] .
  * Bellac [2011] M. L. Bellac,  _Thermal Field Theory_, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2011).
  * Peskin and Schroeder [1995] M. E. Peskin and D. V. Schroeder,  _An Introduction to quantum field theory_ (Addison-Wesley, Reading, USA, 1995).
  * Combridge [1979] B. L. Combridge, Associated Production of Heavy Flavor States in p p and anti-p p Interactions: Some QCD Estimates, Nucl. Phys. B 151, 429 (1979).
  * Zhang  _et al._ [2004] B.-W. Zhang, E. Wang, and X.-N. Wang, Heavy quark energy loss in nuclear medium, Phys. Rev. Lett. 93, 072301 (2004), arXiv:nucl-th/0309040 .
  * Sirunyan  _et al._ [2018] A. M. Sirunyan _et al._ (CMS), Nuclear modification factor of D0 mesons in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, Phys. Lett. B 782, 474 (2018), arXiv:1708.04962 [nucl-ex] .
  * Khachatryan  _et al._ [2017] V. Khachatryan _et al._ (CMS), Charged-particle nuclear modification factors in PbPb and pPb collisions at $\sqrt{s_{\mathrm{N}\;\mathrm{N}}}=5.02$ TeV, JHEP 04, 039, arXiv:1611.01664 [nucl-ex] .
  * Acharya  _et al._ [2018] S. Acharya _et al._ (ALICE), Measurement of D0, D+, D∗+ and D${}_{s}^{+}$ production in Pb-Pb collisions at $\sqrt{{\mathrm{s}}_{\mathrm{NN}}}=5.02$ TeV, JHEP 10, 174, arXiv:1804.09083 [nucl-ex] .
  * Xu  _et al._ [2019] Y. Xu _et al._ , Resolving discrepancies in the estimation of heavy quark transport coefficients in relativistic heavy-ion collisions, Phys. Rev. C 99, 014902 (2019), arXiv:1809.10734 [nucl-th] .
  * Xing  _et al._ [2020] W.-J. Xing, S. Cao, G.-Y. Qin, and H. Xing, Flavor hierarchy of jet quenching in relativistic heavy-ion collisions, Phys. Lett. B 805, 135424 (2020), arXiv:1906.00413 [hep-ph] .
  * Norrbin and Sjostrand [2000] E. Norrbin and T. Sjostrand, Production and hadronization of heavy quarks, Eur. Phys. J. C 17, 137 (2000), arXiv:hep-ph/0005110 .
  * Vujanovic  _et al._ [2021] G. Vujanovic _et al._ (JETSCAPE), Multi-stage evolution of heavy quarks in the quark-gluon plasma, Nucl. Phys. A 1005, 121965 (2021), arXiv:2002.06643 [nucl-th] .
  * Pordes  _et al._ [2007] R. Pordes _et al._ , The Open Science Grid, J. Phys. Conf. Ser. 78, 012057 (2007).
  * Sfiligoi  _et al._ [2009] I. Sfiligoi, D. C. Bradley, B. Holzman, P. Mhashilkar, S. Padhi, and F. Wurthwrin, The pilot way to Grid resources using glideinWMS, WRI World Congress 2, 428 (2009).


# Open4Business (O4B): An Open Access Dataset for Summarizing Business
Documents

Amanpreet Singh
Department of Computer Science
Stony Brook University
Stony Brook, NY 11790
<EMAIL_ADDRESS>
Niranjan Balasubramanian
Department of Computer Science
Stony Brook University
Stony Brook, NY 11790
<EMAIL_ADDRESS>
Work done as an intern for SS&C Intralinks.

###### Abstract

A major challenge in fine-tuning deep learning models for automatic
summarization is the need for large domain specific datasets. One of the
barriers to curating such data from resources like online publications is
navigating the license regulations applicable to their re-use, especially for
commercial purposes. As a result, despite the availability of several business
journals there are no large scale datasets for summarizing business documents.
In this work, we introduce Open4Business (O4B), a dataset of 17,458 open
access business articles and their reference summaries. The dataset introduces
a new challenge for summarization in the business domain, requiring highly
abstractive and more concise summaries as compared to other existing datasets.
Additionally, we evaluate existing models on it and consequently show that
models trained on O4B and a 7x larger non–open access dataset achieve
comparable performance on summarization. We release the dataset, along with
the code 111https://github.com/amanpreet692/Open4Business which can be
leveraged to similarly gather data for multiple domains.

##  1 Introduction

Generating effective summaries of documents is critical in business and
corporate finance. Successful transactions in these domains often require
timely processing of hundreds of long, complex and diverse documents. For
instance, the due-diligence process in mergers and acquisitions requires the
involved parties to go through tons of paperwork [1]. Concise summaries can
save time and effort spent on reading entire documents.

However, it is challenging to obtain in-domain training data for fine-tuning
automatic summarization systems. The documents are often proprietary and
confidential or the access to the data itself could be ephemeral. Even with
the necessary access, the effort needed for an expert to create reference
summaries would be enormous. One way to circumvent these issues is to gather
publicly accessible data such as articles from business journals. While most
journals are published under licenses that prohibit their commercial use, in
recent years there has been a steady increase in open access journals which
have more lenient license terms with regards to copyrights and their re-use,
even commercially.

This work makes the following contributions to further research and quick
prototyping of summarization systems for business documents:

  1. i)

O4B - a dataset consisting of 17,458 open access business articles with
reference summaries.

  2. ii)

Evaluation of current SOTA abstractive models on O4B. We also compare it
extensively with other summarization datasets and another huge dataset which
is not open access.

  3. iii)

An open source implementation which can be used for dataset curation in other
domains as well.

##  2 Related work

Many widely-used summarization datasets mainly cover news articles [2, 3, 4],
with the exception of some that cover specific domains such as legislation [5]
and intellectual property [6]. Cohan et al. [7] previously used ArXiv and
PubMed research papers to generate abstracts of long documents. In the
financial domain, El-Haj [8] released the Annual Reports of around 4000
companies listed on London Stock Exchange as part of a MultiLing 2019 shared
task. Since Annual Reports are generally over 60 pages in length, the task was
geared towards generating longer summaries of about 1000 words, which is
computationally expensive for the current attention-based models.

Existing literature that align most closely with O4B, in terms of content and
the curation process are Ammar et al. [9] and S2ORC [10]. Both consist of a
huge volume of article records in multiple domains including business and
finance which can be useful for several tasks. Even though the former allows
commercial use, it doesn’t have full text of the articles. Contrastingly,
S2ORC has full text but prohibits commercial re-use as it was released under
the CC BY-NC license (See Appendix 6 for more details). Moreover S2ORC has not
been used for benchmarking in summarization as of this writing. We attempt to
overcome these shortcomings by providing the article abstract and full text
without restrictions on re-use as part of O4B. We also benchmark O4B and
compare it to a subset of S2ORC consisting of only business articles, referred
to as S2ORCB in the evaluation section.

##  3 Open4Business dataset

We introduce a new summarization dataset, Open4Business (O4B), by parsing open
access journal articles from the business domain to obtain their full text and
abstract. Only open source tools are used for gathering the data to encourage
re-use, and to maintain consistency with the open access theme of this work.
Figure 2 shows a sample summary from O4B.

###  3.1 Dataset curation

O4B is created from a collection of business articles obtained from multiple
publishers. We filtered this collection to only those articles which are open
access, retrieved and converted their full-text PDF into a structured XML
format, and extracted the abstracts as reference summaries. We detail each of
these steps below and outline the number of data samples through these stages
in Appendix 4.

##### Selecting open access articles:

To identify open access articles, we used the ISSN of business and financial
journals obtained from ISSN-GOLD-OA records [11], as well as a short list of
related keywords (e.g. business, finance, and entrepreneur) and cross-
referenced those with Crossref [12], a large scale metadata repository for
published articles. Using an existing implementation of Crossref
API222https://github.com/fabiobatalha/crossrefapi, we queried the Crossref
REST service to retrieve Document Object Identifier (DOI), license details and
other article metadata. We process the resulting list to only include articles
with open access licenses, specifically those of type ’CC BY (3.0/4.0)’.

##### Retrieving article PDFs:

Given the collection of relevant DOIs, we used Unpaywall [13], another
repository that provides the best open access resource locations for a given
article. We queried it using Unpywall333https://github.com/unpywall/unpywall
and then retrieved the PDF versions of the articles. Out of the 21,397 DOIs,
we were able to retrieve PDFs for 18,670. In some cases, there was no DOI
record or there were connectivity issues, while for others the DOIs were
pointing to non-business journals.

##### XML conversion and post-processing:

We used GROBID [14] to convert PDFs to a structured XML format. We have
considered only English-language articles that have abstracts. For each
article we retained only the main text body of the article and removed section
headings, tables, figures, citations, and other bibliographic references. The
resulting collection contains the text of 17,458 articles along with a
combination of their titles and abstracts as the gold summaries.

###  3.2 Dataset characteristics

To get a measure of the conciseness and abstractiveness of the summaries in
O4B, we compare it to a set of benchmark datasets [2, 4, 5, 7] from various
domains. Following [6], we compare the reference summaries against their
sources in terms of average length in words (to measure conciseness) and
unique n-grams (to measure abstractiveness), respectively. As shown in Table
1, O4B has the highest compression ratio indicating highly compact summaries.
The unique summary n-gram distributions shown in Figure 2 is comparable to
ArXiv and CNN-DailyMail(CNN/DM) datasets, which are highly abstractive in
nature. Also it has fewer extractive fragments than BillSum and Newsroom. As
we show in the next section, our benchmarking experiments indicate that pre-
training or fine-tuning on other datasets is not enough for obtaining high
scores on O4B, highlighting the need for this dataset.

Table 1: Comparison of Open4Business (O4B) with other summarization datasets Dataset | Total Docs |  | Mean Words
---
Doc
| Mean Words
---
Summary
| Compression
---
Ratio
BillSum | 22,218 | 1,240.21 | 181.98 | 6.81
Newsroom | 1,145,804 | 684.51 | 29.17 | 23.46
CNN/DM | 311,971 | 707.65 | 49.66 | 14.25
ArXiv | 215,500 | 5219.54 | 239.27 | 21.81
O4B | 17,458 | 4764.89 | 173.58 | 27.45

Figure 1: Summary sample from O4B

Figure 2: Comparison of unique summary n-grams

##  4 Evaluation

Since the focus of this work is solely on abstractive summarization, SOTA
encoder-decoder transformer based models [15] are used for benchmarking O4B.
PyTorch 1.5 implementations of Text-to-Text Transfer Transformer (T5) [16] and
a distilled version of BART [17] (dBART) provided by [18] are used for
evaluation. Off-the-shelf (base) variants of both the models are fine-tuned on
a single 16 GB GPU setup for 2 epochs with a batch size of 2 for consistent
comparisons444Fine-tuning larger models for longer will likely yield better
scores but here we only present basic bench-marking results.. For all
benchmarking experiments, both the models are fine-tuned on 512 and 1024
tokens each from the source text.

###  4.1 ROUGE-N benchmarking

The O4B benchmark ROUGE-(1/2/L) scores are shown in Table 2.

Table 2: ROUGE-N Metrics, RG: ROUGE, O4B: Open4Business Architecture | Tokens | RG-1 | RG-2 | RG-L
---|---|---|---|---
T5-base | 512 | 24.30 | 7.21 | 16.33
T5-O4B | 512 | 42.50 | 14.88 | 24.62
| 1024 | 45.34 | 17.39 | 26.31
dBART-base | 512 | 28.46 | 8.10 | 17.89
dBART-O4B | 512 | 43.55 | 15.95 | 25.25
| 1024 | 45.98 | 17.90 | 26.59

Benchmark scores from both the models without any fine-tuning are considered
as baselines. During fine-tuning, the models with the best ROUGE-2 score on
the dev set are saved as checkpoints. Both the models perform better when they
witness a longer portion of the input. But, this comes at cost of longer
training times, which increases proportionally with the input length. Overall,
the low performance numbers for T5 and dBART - specially for ROUGE-2,
indicates that the task of long document summarization is challenging by
itself, which is consistent with the findings in [7], [19] on the ArXiv and
PubMed datasets. Sample summaries generated by both the models are presented
in Appendix 3.

####  4.1.1  Error analysis

We observe two main types of errors: word-level repetition, and hallucinating
content that is not present in or supported by the input. Consider the sample:
The results show that a mixture of global and local smoothing improves non-
parametric estimation, while the local parts allow for the desired flexibility
to detect local features. The source article is about financial data-modeling
with sparse mentions of non-parametric estimation but the model combines this
information by lifting some text from the source and ignoring other essential
parts. Here, the original text is - Those mixtures are interesting because the
global parts can borrow the strength from a larger sample and have a smoothing
effect, while the local parts allow for the desired flexibility to detect
local features.

###  4.2 Transfer-learning tests with S2ORCB

To validate the effectiveness of both O4B and open access articles, we conduct
transfer-learning experiments. First, we fine-tune T5 and dBART models on O4B
and test on the S2ORCB dataset, a large collection of over 119k
summary/article pairs. S2ORCB is described in detail in Appendix 5. Here, we
consider 1024 source text tokens since that resulted in better benchmark
scores. Given the datasets, a sizeable difference is observed in the training
times as well. Results in 3(a) show that the models fine-tuned on O4B (T5-O4B
and dBART-O4B) achieve comparable performance to corresponding models fine-
tuned on the S2ORCB dataset. Second, we reverse the setup and fine-tune models
on the training portions of S2ORCB and then test on O4B. 3(b) indicates a
similar gap in performance between the transfer models versus the ones trained
on the target dataset (O4B in this case). The gaps hint at the challenges in
the summarization task on the O4B dataset that cannot be solved by simply
training on a larger dataset. In spite of the huge disparity in dataset sizes,
similar model performances indicate that O4B can be effectively utilized for
summarization systems.

Table 3: Transfer learning experiment results, RG: ROUGE

(a) Performance on S2ORCB test set Model | RG-1 | RG-2 | RG-L
---|---|---|---
T5-O4B | 45.52 | 17.85 | 26.83
T5-S2ORCB | 45.59 | 18.17 | 27.32
dBART-O4B | 46.11 | 18.26 | 27.04
dBART-S2ORCB | 47.36 | 19.47 | 28.26
Mean Difference | 0.66 | 0.60 | 0.855

(b) Performance on O4B test set Model | RG-1 | RG-2 | RG-L
---|---|---|---
T5-O4B | 45.34 | 17.39 | 26.31
T5-S2ORCB | 44.04 | 16.58 | 25.67
dBART-O4B | 45.98 | 17.90 | 26.59
dBART-S2ORCB | 45.72 | 17.79 | 26.35
Mean Difference | 0.78 | 0.46 | 0.44

##  5 Conclusions

Automatic summarization in business domain is hampered by the lack of access
to large scale datasets. Thus, we introduce Open4Business(O4B), a new dataset
that consists of open access articles and their abstracts. This presents a new
challenge for summarization systems which we hope spurs further research and
development of new methods for this domain.

## Acknowledgments

We would like to thank Prakash Kanchinadam and also the legal team at SS&C
Intralinks for the fruitful discussions and their administrative support in
this endeavor. We thank all anonymous reviewers for their feedback.

## References

  * Howson [2003] Peter Howson.  _Due diligence: The critical stage in mergers and acquisitions_ , pages 151–160.  Gower Publishing, Ltd., 2003.
  * See et al. [2017] Abigail See, Peter J Liu, and Christopher D Manning.  Get to the point: Summarization with pointer-generator networks.  _arXiv preprint arXiv:1704.04368_ , 2017.
  * Narayan et al. [2018] Shashi Narayan, Shay B Cohen, and Mirella Lapata.  Don’t give me the details, just the summary!  _Topic-aware Convolutional Neural Networks for Extreme Summarization. In_ , 2018.
  * Grusky et al. [2018] Max Grusky, Mor Naaman, and Yoav Artzi.  Newsroom: A dataset of 1.3 million summaries with diverse extractive strategies.  _arXiv preprint arXiv:1804.11283_ , 2018.
  * Eidelman [2019] Vladimir Eidelman.  Billsum: A corpus for automatic summarization of us legislation.  In _Proceedings of the 2nd Workshop on New Frontiers in Summarization_ , pages 48–56, 2019.
  * Sharma et al. [2019] Eva Sharma, Chen Li, and Lu Wang.  Bigpatent: A large-scale dataset for abstractive and coherent summarization.  _arXiv preprint arXiv:1906.03741_ , 2019.
  * Cohan et al. [2018] Arman Cohan, Franck Dernoncourt, Doo Soon Kim, Trung Bui, Seokhwan Kim, Walter Chang, and Nazli Goharian.  A discourse-aware attention model for abstractive summarization of long documents.  _arXiv preprint arXiv:1804.05685_ , 2018.
  * El-Haj [2019] Mahmoud El-Haj.  Multiling 2019: Financial narrative summarisation.  In _Proceedings of the Workshop MultiLing 2019: Summarization Across Languages, Genres and Sources_ , pages 6–10, 2019.
  * Ammar et al. [2018] Waleed Ammar, Dirk Groeneveld, Chandra Bhagavatula, Iz Beltagy, Miles Crawford, Doug Downey, Jason Dunkelberger, Ahmed Elgohary, Sergey Feldman, Vu A. Ha, Rodney Michael Kinney, Sebastian Kohlmeier, Kyle Lo, Tyler C. Murray, Hsu-Han Ooi, Matthew E. Peters, Joanna L. Power, Sam Skjonsberg, Lucy Lu Wang, Christopher Wilhelm, Zheng Yuan, Madeleine van Zuylen, and O. Etzioni.  Construction of the literature graph in semantic scholar.  In _NAACL-HLT_ , 2018.
  * Lo et al. [2020] Kyle Lo, Lucy Lu Wang, Mark Neumann, Rodney Kinney, and Daniel S. Weld.  S2ORC: The Semantic Scholar Open Research Corpus.  In _Proceedings of ACL_ , 2020.  URL https://www.aclweb.org/anthology/2020.acl-main.447.
  * Bruns et al. [2019] A Bruns, C Lenke, C Schmidt, and NC Taubert.  Issn-matching of gold oa journals (issn-gold-oa) 3.0. bielefeld university, 2019.
  * cro [2020] Crossref.  https://www.crossref.org/, 2020.
  * Piwowar et al. [2018] Heather Piwowar, Jason Priem, Vincent Larivière, Juan Pablo Alperin, Lisa Matthias, Bree Norlander, Ashley Farley, Jevin West, and Stefanie Haustein.  The state of oa: a large-scale analysis of the prevalence and impact of open access articles.  _PeerJ_ , 6:e4375, 2018.
  * GRO [2008–2020] Grobid.  https://github.com/kermitt2/grobid, 2008–2020.
  * Fabbri et al. [2020] Alexander R Fabbri, Wojciech Kryściński, Bryan McCann, Caiming Xiong, Richard Socher, and Dragomir Radev.  Summeval: Re-evaluating summarization evaluation.  _arXiv preprint arXiv:2007.12626_ , 2020.
  * Raffel et al. [2020] Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J Liu.  Exploring the limits of transfer learning with a unified text-to-text transformer.  _Journal of Machine Learning Research_ , 21(140):1–67, 2020.
  * Lewis et al. [2019] Mike Lewis, Yinhan Liu, Naman Goyal, Marjan Ghazvininejad, Abdelrahman Mohamed, Omer Levy, Ves Stoyanov, and Luke Zettlemoyer.  Bart: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension.  _arXiv preprint arXiv:1910.13461_ , 2019.
  * Wolf et al. [2019] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush.  Huggingface’s transformers: State-of-the-art natural language processing.  _ArXiv_ , abs/1910.03771, 2019.
  * Zhang et al. [2019] Jingqing Zhang, Yao Zhao, Mohammad Saleh, and Peter J Liu.  Pegasus: Pre-training with extracted gap-sentences for abstractive summarization.  _arXiv preprint arXiv:1912.08777_ , 2019.

##  Appendix A Appendices

###  A.1 Background

Traditionally, most of the journals have published under licenses which
restrict their re-use in some manner eg. CC BY-NC555Creative Commons-
NonCommercial., or prohibit mining them. The Open Access movement, which has
gained popularity in recent years, allows peer-reviewed articles to be made
available immediately for public without any copyright restrictions. Several
levels of open access publishing exist with each having its own set of
regulations. The readers are encouraged to read about these as it is essential
to be aware of any potential restrictions on re-use of what seems to be public
data. Consequently, only the the Gold Open Access level articles licensed as
CC BY 666https://creativecommons.org/licenses/by/4.0/ have been used to create
this Open4Business(O4B).

###  A.2 O4B through curation stages

O4B is built from open access business journals published by publishers such
as Scientific Research Publishing (SCIRP) 777https://www.scirp.org/ and
Multidisciplinary Digital Publishing Institute (MDPI)
888https://www.mdpi.com/. Through every step in the dataset curation process
as explained in the main paper, several potential data samples are filtered
out due to processing issues as shown in Table 4. After final post-processing,
remaining articles were split 80/10/10 to have a training, dev and test set of
13,966, 1,746 and 1,746 articles respectively.

Table 4: Data samples throughout pipeline stages Step | Number of samples
---|---
License Metadata Filtering (Crossref) | 21,397
Open Access URL Retrieval (Unpaywall) | 20,432
PDF Mining | 18,670
XML Conversion (GROBID) | 18,544
Final Post-processing | 17,458

###  A.3 Deriving S2ORCB from S2ORC

S2ORCB is derived from S2ORC by including only those articles that belong to
the business domain. S2ORC has the metadata for about 1.8 million business
articles but full text is not available for all of them. Thus, the records
were then filtered to include only those which had both the article abstracts
and full body text. After parsing the text, it is subject to similar post-
processing as O4B and any bibliographical references are subsequently removed.
Finally, S2ORCB is obtained with article full text as source, and a
combination of title and abstract as the reference summary similar to O4B.
S2ORCB is split with 95926, 11991 and 11991 articles in the train, dev and
test set respectively. Table 5 shows the mean word count in source and summary
for each of the splits in S2ORCB.

Table 5: S2ORC-Business(S2ORCB) Statistics Split | Description | Mean word count
---|---|---
Train | Source | 4611
| Summary | 186
Dev | Source | 4557
| Summary | 187
Test | Source | 4606
| Summary | 186

###  A.4 Sample generated summary

We present sample generated summaries from both T5 and dBART along with the
gold reference summary in Figure 3. As highlighted in the figure, following
instances of grammatical inconsistencies are observed in the generated
summaries starting from the top:

  1. i)

inconsistent spelling of the term polarization

  2. ii)

global bipolarization is explained by the polarization

  3. iii)

We conclude by the main conclusions seems incoherent

  4. iv)

evolution is not followed by patterns as per the source text

Figure 3: Generated summary sample from T5 and dBART with the corresponding
Gold (reference) summary. The portions in generated summary indicating
grammatical incoherence are highlighted.