# Differential measurements of jet substructure and partonic energy loss in
Au$+$Au collisions at $\sqrt{s_{\rm{NN}}}$ $=200$ GeV

M. S. Abdallah5, B. E. Aboona55, J. Adam6, L. Adamczyk2, J. R. Adams39, J. K.
Adkins30, G. Agakishiev28, I. Aggarwal41, M. M. Aggarwal41, Z. Ahammed60, I.
Alekseev3,35, D. M. Anderson55, A. Aparin28, E. C. Aschenauer6, M. U.
Ashraf11, F. G. Atetalla29, A. Attri41, G. S. Averichev28, V. Bairathi53, W.
Baker10, J. G. Ball Cap20, K. Barish10, A. Behera52, R. Bellwied20, P.
Bhagat27, A. Bhasin27, J. Bielcik14, J. Bielcikova38, I. G. Bordyuzhin3, J. D.
Brandenburg6, A. V. Brandin35, I. Bunzarov28, X. Z. Cai50, H. Caines63, M.
Calderón de la Barca Sánchez8, D. Cebra8, I. Chakaberia31,6, P. Chaloupka14,
B. K. Chan9, F-H. Chang37, Z. Chang6, N. Chankova-Bunzarova28, A.
Chatterjee11, S. Chattopadhyay60, D. Chen10, J. Chen49, J. H. Chen18, X.
Chen48, Z. Chen49, J. Cheng57, M. Chevalier10, S. Choudhury18, W. Christie6,
X. Chu6, H. J. Crawford7, M. Csanád16, M. Daugherity1, T. G. Dedovich28, I. M.
Deppner19, A. A. Derevschikov43, A. Dhamija41, L. Di Carlo62, L. Didenko6, P.
Dixit22, X. Dong31, J. L. Drachenberg1, E. Duckworth29, J. C. Dunlop6, N.
Elsey62, J. Engelage7, G. Eppley45, S. Esumi58, O. Evdokimov12, A.
Ewigleben32, O. Eyser6, R. Fatemi30, F. M. Fawzi5, S. Fazio6, P. Federic38, J.
Fedorisin28, C. J. Feng37, Y. Feng44, P. Filip28, E. Finch51, Y. Fisyak6, A.
Francisco63, C. Fu11, L. Fulek2, C. A. Gagliardi55, T. Galatyuk15, F.
Geurts45, N. Ghimire54, A. Gibson59, K. Gopal23, X. Gou49, D. Grosnick59, A.
Gupta27, W. Guryn6, A. I. Hamad29, A. Hamed5, Y. Han45, S. Harabasz15, M. D.
Harasty8, J. W. Harris63, H. Harrison30, S. He11, W. He18, X. H. He26, Y.
He49, S. Heppelmann8, S. Heppelmann42, N. Herrmann19, E. Hoffman20, L.
Holub14, Y. Hu18, H. Huang37, H. Z. Huang9, S. L. Huang52, T. Huang37, X.
Huang57, Y. Huang57, T. J. Humanic39, G. Igo9,∗, D. Isenhower1, W. W.
Jacobs25, C. Jena23, A. Jentsch6, Y. Ji31, J. Jia6,52, K. Jiang48, X. Ju48, E.
G. Judd7, S. Kabana53, M. L. Kabir10, S. Kagamaster32, D. Kalinkin25,6, K.
Kang57, D. Kapukchyan10, K. Kauder6, H. W. Ke6, D. Keane29, A. Kechechyan28,
M. Kelsey62, Y. V. Khyzhniak35, D. P. Kikoła 61, C. Kim10, B. Kimelman8, D.
Kincses16, I. Kisel17, A. Kiselev6, A. G. Knospe32, H. S. Ko31, L. Kochenda35,
L. K. Kosarzewski14, L. Kramarik14, P. Kravtsov35, L. Kumar41, S. Kumar26, R.
Kunnawalkam Elayavalli63, J. H. Kwasizur25, R. Lacey52, S. Lan11, J. M.
Landgraf6, J. Lauret6, A. Lebedev6, R. Lednicky28,38, J. H. Lee6, Y. H.
Leung31, C. Li49, C. Li48, W. Li45, X. Li48, Y. Li57, X. Liang10, Y. Liang29,
R. Licenik38, T. Lin49, Y. Lin11, M. A. Lisa39, F. Liu11, H. Liu25, H. Liu11,
P. Liu52, T. Liu63, X. Liu39, Y. Liu55, Z. Liu48, T. Ljubicic6, W. J. Llope62,
R. S. Longacre6, E. Loyd10, N. S. Lukow54, X. F. Luo11, L. Ma18, R. Ma6, Y. G.
Ma18, N. Magdy12, D. Mallick36, S. Margetis29, C. Markert56, H. S. Matis31, J.
A. Mazer46, N. G. Minaev43, S. Mioduszewski55, B. Mohanty36, M. M. Mondal52,
I. Mooney62, D. A. Morozov43, A. Mukherjee16, M. Nagy16, J. D. Nam54, Md.
Nasim22, K. Nayak11, D. Neff9, J. M. Nelson7, D. B. Nemes63, M. Nie49, G.
Nigmatkulov35, T. Niida58, R. Nishitani58, L. V. Nogach43, T. Nonaka58, A. S.
Nunes6, G. Odyniec31, A. Ogawa6, S. Oh31, V. A. Okorokov35, B. S. Page6, R.
Pak6, J. Pan55, A. Pandav36, A. K. Pandey58, Y. Panebratsev28, P. Parfenov35,
B. Pawlik40, D. Pawlowska61, C. Perkins7, L. Pinsky20, R. L. Pintér16, J.
Pluta61, B. R. Pokhrel54, G. Ponimatkin38, J. Porter31, M. Posik54, V.
Prozorova14, N. K. Pruthi41, M. Przybycien2, J. Putschke62, H. Qiu26, A.
Quintero54, C. Racz10, S. K. Radhakrishnan29, N. Raha62, R. L. Ray56, R.
Reed32, H. G. Ritter31, M. Robotkova38, O. V. Rogachevskiy28, J. L. Romero8,
D. Roy46, L. Ruan6, J. Rusnak38, N. R. Sahoo49, H. Sako58, S. Salur46, J.
Sandweiss63,∗, S. Sato58, W. B. Schmidke6, N. Schmitz33, B. R. Schweid52, F.
Seck15, J. Seger13, M. Sergeeva9, R. Seto10, P. Seyboth33, N. Shah24, E.
Shahaliev28, P. V. Shanmuganathan6, M. Shao48, T. Shao18, A. I. Sheikh29, D.
Shen50, S. S. Shi11, Y. Shi49, Q. Y. Shou18, E. P. Sichtermann31, R. Sikora2,
M. Simko38, J. Singh41, S. Singha26, M. J. Skoby44, N. Smirnov63, Y.
Söhngen19, W. Solyst25, P. Sorensen6, H. M. Spinka4,∗, B. Srivastava44, T. D.
S. Stanislaus59, M. Stefaniak61, D. J. Stewart63, M. Strikhanov35, B.
Stringfellow44, A. A. P. Suaide47, M. Sumbera38, B. Summa42, X. M. Sun11, X.
Sun12, Y. Sun48, Y. Sun21, B. Surrow54, D. N. Svirida3, Z. W. Sweger8, P.
Szymanski61, A. H. Tang6, Z. Tang48, A. Taranenko35, T. Tarnowsky34, J. H.
Thomas31, A. R. Timmins20, D. Tlusty13, T. Todoroki58, M. Tokarev28, C. A.
Tomkiel32, S. Trentalange9, R. E. Tribble55, P. Tribedy6, S. K. Tripathy16, T.
Truhlar14, B. A. Trzeciak14, O. D. Tsai9, Z. Tu6, T. Ullrich6, D. G.
Underwood4,59, I. Upsal45, G. Van Buren6, J. Vanek38, A. N. Vasiliev43, I.
Vassiliev17, V. Verkest62, F. Videbæk6, S. Vokal28, S. A. Voloshin62, F.
Wang44, G. Wang9, J. S. Wang21, P. Wang48, Y. Wang11, Y. Wang57, Z. Wang49, J.
C. Webb6, P. C. Weidenkaff19, L. Wen9, G. D. Westfall34, H. Wieman31, S. W.
Wissink25, J. Wu11, J. Wu26, Y. Wu10, B. Xi50, Z. G. Xiao57, G. Xie31, W.
Xie44, H. Xu21, N. Xu31, Q. H. Xu49, Y. Xu49, Z. Xu6, Z. Xu9, C. Yang49, Q.
Yang49, S. Yang45, Y. Yang37, Z. Ye45, Z. Ye12, L. Yi49, K. Yip6, Y. Yu49, H.
Zbroszczyk61, W. Zha48, C. Zhang52, D. Zhang11, J. Zhang49, S. Zhang12, S.
Zhang18, X. P. Zhang57, Y. Zhang26, Y. Zhang48, Y. Zhang11, Z. J. Zhang37, Z.
Zhang6, Z. Zhang12, J. Zhao44, C. Zhou18, X. Zhu57, M. Zurek4, M. Zyzak17
(STAR Collaboration)  1Abilene Christian University, Abilene, Texas 79699
2AGH University of Science and Technology, FPACS, Cracow 30-059, Poland
3Alikhanov Institute for Theoretical and Experimental Physics NRC ”Kurchatov
Institute”, Moscow 117218, Russia  4Argonne National Laboratory, Argonne,
Illinois 60439  5American University of Cairo, New Cairo 11835, New Cairo,
Egypt  6Brookhaven National Laboratory, Upton, New York 11973  7University of
California, Berkeley, California 94720  8University of California, Davis,
California 95616  9University of California, Los Angeles, California 90095
10University of California, Riverside, California 92521  11Central China
Normal University, Wuhan, Hubei 430079  12University of Illinois at Chicago,
Chicago, Illinois 60607  13Creighton University, Omaha, Nebraska 68178
14Czech Technical University in Prague, FNSPE, Prague 115 19, Czech Republic
15Technische Universität Darmstadt, Darmstadt 64289, Germany  16ELTE Eötvös
Loránd University, Budapest, Hungary H-1117  17Frankfurt Institute for
Advanced Studies FIAS, Frankfurt 60438, Germany  18Fudan University, Shanghai,
200433  19University of Heidelberg, Heidelberg 69120, Germany  20University of
Houston, Houston, Texas 77204  21Huzhou University, Huzhou, Zhejiang 313000
22Indian Institute of Science Education and Research (IISER), Berhampur 760010
, India  23Indian Institute of Science Education and Research (IISER)
Tirupati, Tirupati 517507, India  24Indian Institute Technology, Patna, Bihar
801106, India  25Indiana University, Bloomington, Indiana 47408  26Institute
of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000
27University of Jammu, Jammu 180001, India  28Joint Institute for Nuclear
Research, Dubna 141 980, Russia  29Kent State University, Kent, Ohio 44242
30University of Kentucky, Lexington, Kentucky 40506-0055  31Lawrence Berkeley
National Laboratory, Berkeley, California 94720  32Lehigh University,
Bethlehem, Pennsylvania 18015  33Max-Planck-Institut für Physik, Munich 80805,
Germany  34Michigan State University, East Lansing, Michigan 48824  35National
Research Nuclear University MEPhI, Moscow 115409, Russia  36National Institute
of Science Education and Research, HBNI, Jatni 752050, India  37National Cheng
Kung University, Tainan 70101  38Nuclear Physics Institute of the CAS, Rez 250
68, Czech Republic  39Ohio State University, Columbus, Ohio 43210  40Institute
of Nuclear Physics PAN, Cracow 31-342, Poland  41Panjab University, Chandigarh
160014, India  42Pennsylvania State University, University Park, Pennsylvania
16802  43NRC ”Kurchatov Institute”, Institute of High Energy Physics, Protvino
142281, Russia  44Purdue University, West Lafayette, Indiana 47907  45Rice
University, Houston, Texas 77251  46Rutgers University, Piscataway, New Jersey
08854  47Universidade de São Paulo, São Paulo, Brazil 05314-970  48University
of Science and Technology of China, Hefei, Anhui 230026  49Shandong
University, Qingdao, Shandong 266237  50Shanghai Institute of Applied Physics,
Chinese Academy of Sciences, Shanghai 201800  51Southern Connecticut State
University, New Haven, Connecticut 06515  52State University of New York,
Stony Brook, New York 11794  53Instituto de Alta Investigación, Universidad de
Tarapacá, Arica 1000000, Chile  54Temple University, Philadelphia,
Pennsylvania 19122  55Texas A&M University, College Station, Texas 77843
56University of Texas, Austin, Texas 78712  57Tsinghua University, Beijing
100084  58University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
59Valparaiso University, Valparaiso, Indiana 46383  60Variable Energy
Cyclotron Centre, Kolkata 700064, India  61Warsaw University of Technology,
Warsaw 00-661, Poland  62Wayne State University, Detroit, Michigan 48201
63Yale University, New Haven, Connecticut 06520  ∗Deceased

###### Abstract

The STAR collaboration presents jet substructure measurements related to both
the momentum fraction and the opening angle within jets in $p+p$ and Au$+$Au
collisions at $\sqrt{s_{\rm{NN}}}$ $=200$ GeV. The substructure observables
include SoftDrop groomed momentum fraction ($z_{\rm{g}}$), groomed jet radius
($R_{\rm{g}}$), and subjet momentum fraction ($z_{\rm{SJ}}$) and opening angle
($\theta_{\rm{SJ}}$). The latter observable is introduced for the first time.
Fully corrected subjet measurements are presented for $p+p$ collisions and are
compared to leading order Monte Carlo models. The subjet $\theta_{\rm{SJ}}$
distributions reflect the jets leading opening angle and are utilized as a
proxy for the resolution scale of the medium in Au$+$Au collisions. We compare
data from Au$+$Au collisions to those from $p+p$ which are embedded in
minimum-bias Au$+$Au events in order to include the effects of detector
smearing and the heavy-ion collision underlying event. The subjet observables
are shown to be more robust to the background than $z_{\rm{g}}$ and
$R_{\rm{g}}$.

We observe no significant modifications of the subjet observables within the
two highest-energy, back-to-back jets, resulting in a distribution of opening
angles and the splittings that are vacuum-like. We also report measurements of
the differential di-jet momentum imbalance ($A_{\rm{J}}$) for jets of varying
$\theta_{\rm{SJ}}$. We find no qualitative differences in energy loss
signatures for varying angular scales in the range $0.1<$
$\theta_{\rm{SJ}}$$<0.3$, leading to the possible interpretation that energy
loss in this population of high momentum di-jet pairs, is due to soft medium-
induced gluon radiation from a single color-charge as it traverses the medium.

††preprint:  v13

##  I Introduction

Since the start of heavy-ion collisions at RHIC, all the experiments have
aimed at elucidating the properties of the hot and dense emergent state of
matter called the quark-gluon plasma (QGP) Adams et al. (2005); Adcox et al.
(2005); Back et al. (2005); Arsene et al. (2005). Measurements in heavy-ion
collisions aim at studying various aspects of the QGP connected to its initial
state, bulk evolution, and interactions with hard-scattered partons (quarks
and gluons). Jets Sterman and Weinberg (1977), which are clusters of final-
state particles resulting from the Quantum Chromodynamics (QCD) evolution,
i.e., fragmentation of hard-scattered partons, are a well established probe of
the QGP. The progenitor partons are produced almost immediately with large
enough $Q^{2}$, the 4-momentum transfer squared of the hard process, such that
its formation time is less than that of the QGP. For each hard-scattered
parton, the resulting parton shower traverses the QGP, probing its entire
lifetime, and are measured as collections of collimated final state particles
(jets) in the detectors. Therefore any modifications to the jet energy and
structure in Au$+$Au relative to those in $p+p$ or $p+$Au collisions Adams et
al. (2003a); Adler et al. (2003) are interpreted as effects arising due to the
transport properties of the QGP111While cold nuclear matter effects on jet
production have been recently quantified in theoretical frameworks Kang et al.
(2015), their effects on jet fragmentation are still considered to be
negligible Aaboud et al. (2018a). and are often referred to as jet quenching
Gyulassy and Wang (1994); Baier et al. (1995, 1997a); Zakharov (1996). First
generation measurements at RHIC, which studied the phenomenon of jet quenching
utilized high momentum hadrons as proxies for jets and found a marked
suppression of high transverse momentum ($p_{\mathrm{T}}$) hadron yield Adams
et al. (2003b); Adcox et al. (2002). In addition, in high multiplicity or
central Au$+$Au collisions the measured yields of associated hadrons in the
back-to-back azimuthal region, with respect to a high-$p_{\mathrm{T}}$ trigger
particle, were suppressed when compared to those in $p+p$ or $d+$Au collisions
Adams et al. (2003a); Adler et al. (2003). Comparison of the high $p_{\rm{T}}$
hadron yield in Au$+$Au collisions to the yield in binary-scaled $p+p$
collisions, provided evidence of suppression and energy loss of color-charged
partons in the QGP due to increased medium-induced radiation and scattering
within the medium along the parton shower.

The next generation measurements utilized reconstructed jets (i.e., groups of
particles clustered via algorithms) that provided a better proxy for the
initial hard-scattered parton’s kinematics Sterman and Weinberg (1977);
Moretti et al. (1998); Blazey et al. (2000); Ellis et al. (2008); Cacciari et
al. (2012); Salam (2010); Ali and Kramer (2011), and which facilitated direct
comparisons to calculations and models that implemented partonic energy loss
in the medium Gyulassy et al. (2003); Wang (2005); Wiedemann (2010); Zapp et
al. (2013). Jet nuclear modification factors and coincidence measurements at
RHIC Adamczyk et al. (2014); Adare et al. (2016); Adamczyk et al. (2017a);
Timilsina (2016); Adamczyk et al. (2017b); Osborn (2019); Adam et al. (2020a)
and the LHC Aad et al. (2010); Chatrchyan et al. (2011); Chatrchyan et al.
(2012a); Aad et al. (2013a); Abelev et al. (2014); Aad et al. (2013b, 2014,
2015); Adam et al. (2015a, b, 2016); Khachatryan et al. (2017); Aaboud et al.
(2019a, b); Acharya et al. (2020a) also showed suppression of the jet yield,
implying jet energy loss. Since jets are collective objects, the third
generation of measurements studied modifications to the jet structure via the
jet fragmentation functions Chatrchyan et al. (2012b); Adamczyk et al. (2014);
Chatrchyan et al. (2014a); Aad et al. (2014); Aaboud et al. (2017, 2018a);
Sirunyan et al. (2018a); Aaboud et al. (2018b, 2019c), jet shapes Chatrchyan
et al. (2014b); Khachatryan et al. (2016a, b, c); Sirunyan et al. (2019), jet
mass Acharya et al. (2018); Sirunyan et al. (2018b); ATL (2018), and also to
their substructure via modified splittings Sirunyan et al. (2018c); Acharya et
al. (2020b); ATL (2019). From di-hadron, jet-hadron and jet structure
measurements, we observed that quenched jets have significantly enhanced
(suppressed) yields of low (high) momentum constituents. The enhanced soft-
constituents were found farther away from the jet axis, i.e., the periphery of
the jets. This has been recently understood as an important signature of the
medium response Blaizot and Mehtar-Tani (2015); Qin and Wang (2015); Mehtar-
Tani (2016); Connors et al. (2018); Cao and Wang (2021).

The modifications to the jet structure indicate the essential need for
studying jet quenching with a more differential approach. Since jet evolution
in vacuum is characterized by a momentum fraction and opening angle as given
by the DGLAP equations Gribov and Lipatov (1972); Dokshitzer (1977); Altarelli
and Parisi (1977), one might expect jet quenching mechanisms to depend on the
jet shower topology Mehtar-Tani and Tywoniuk (2017); Apolinário et al. (2021);
Mehtar-Tani et al. (2021). Inclusive jet quenching measurements essentially
integrate over all jet shower topologies. On the other hand, differential
measurements of energy loss for jets, when tagged based on their shower
topology via a substructure observable, can potentially isolate the varying
mechanisms of jet quenching, which in turn leads to further stringent
constraints on QGP transport parameters. In addition to energy loss being
related to path length through the medium Baier et al. (1997b, a); Zakharov
(1996); Zapp et al. (2006, 2011); Burke et al. (2014), jet-medium interactions
could also depend on the coherence length of the medium Casalderrey-Solana et
al. (2013); Mehtar-Tani and Tywoniuk (2015). Recent theoretical studies have
shown that, depending on medium coherence length Caucal et al. (2021a); Caucal
and Mehtar-Tani (2021); Caucal et al. (2021b), jets with similar kinematics
but with a two-prong vs. one-prong structure (where a prong is a jet-like
object within a jet) lose significantly different amounts of energy Mehtar-
Tani and Tywoniuk (2015, 2017); Chien and Vitev (2017); Apolinário et al.
(2018); Milhano et al. (2018); Mehtar-Tani and Tywoniuk (2020); Adhya et al.
(2020); Andres et al. (2020). This dependence is a direct consequence of the
transverse separation distance between the two prongs, at the time of
formation, being greater or less than the resolution/coherence length of the
medium Mehtar-Tani and Tywoniuk (2015, 2017). Since the latter cannot be
directly measured, the subjet angular separation is chosen as its
proxy.222Subjet separation distance at formation is approximately
$c~{}\tau_{f}~{}\theta$, where $\tau_{f}$ is the formation time and $\theta$
is the measured two-prong opening angle. This resolving power is a direct
application of the jet opening angle being greater or smaller than the
coherence length.

We calculate the di-jet asymmetry for trigger and recoil jets (see Fig. 1),
defined as

$A_{\rm{J}}\equiv\frac{p^{\rm{trigger}}_{\rm{T,jet}}-p^{\rm{recoil}}_{\rm{T,jet}}}{p^{\rm{trigger}}_{\rm{T,jet}}+p^{\rm{recoil}}_{\rm{T,jet}}},$
(1)

as a quantitative measure of jet quenching effects for jets of varying angular
scales. For di-jet selections in Au$+$Au collisions at RHIC, the highest
$p_{\rm{T}}$ jet is biased to originate preferentially from production
vertices in the periphery of the overlap region of the colliding ions Renk
(2013), often referred to as a surface bias. Since the quenched energy of
these recoil jets is found to be contained in soft particles (with
$0.2<p_{\rm{T}}<2$ GeV/$c$) that are distributed around the jet axis Adamczyk
et al. (2014), the dependence of quenching on the angular scales can be
studied by comparing the same measurement for narrow- vs. wide-angle jets. If
the jet opening angle, as defined by a substructure observable, is smaller
than the medium coherence length, the two prongs (hereafter referred to as
subjets) are unresolved by the medium and will be quenched as an effective
single color-charge Mehtar-Tani and Tywoniuk (2015). On the other hand, if the
jet opening angle is larger than the coherence length, the two prong remain
resolved within the medium and as a result, two color charges undergo
independent interactions with the medium, resulting in larger energy loss of
their parent parton. These differential types of measurements constitute a
first attempt at tagging jet populations impacted by varying energy loss
mechanisms such as medium induced radiation, as in the coherent/de-coherent
picture, or medium induced splittings that result in modifications to the jet
substructure.

The paper is organized as follows. Sect. II introduces the STAR detector and
the datasets used in this analysis along with the jet reconstruction
parameters. The measurements of SoftDrop observables are presented in Sect.
III including a study of the sensitivity of these observables to the
underlying event in heavy-ion collisions. In Sect. IV measurements of fully
corrected two-subjet observables in $p+p$ collisions are introduced and
compared to leading order Monte Carlo (MC) simulations. Their observability in
the heavy-ion collision environment is also discussed. The measurements of the
subjet observables in Au$+$Au collisions are presented in Sect. V along with
differential measurements of the di-jet asymmetry for recoil jets with varying
opening angle. A summary and discussion of the implications of these findings
and an outlook to the future regarding such differential measurements are
given in Sect. VI.

##  II Analysis details

###  II.1 STAR Detector

STAR is a large, multipurpose detector at RHIC Ackermann et al. (2003). It
consists of a solenoidal magnet and multiple detectors used for triggering,
tracking, particle identification and calorimetry. This analysis uses charged
tracks from the Time Projection Chamber (TPC) Anderson et al. (2003) and
neutral energy recorded by the Barrel Electromagnetic Calorimeter (BEMC) Beddo
et al. (2003). Charged tracks assigned to the primary vertex are required to
have a global distance of closest approach (DCA) to the primary vertex of less
than 1 cm, greater or equal to $20$ fit points in the TPC, and at least 52% of
the maximum number of fit points possible to eliminate split tracks. The BEMC
consists of 4800 individual towers, with a tower size of $0.05\times 0.05$ in
$\eta\times\phi$. Any event with a $p_{\rm{T}}>30$ GeV/$c$ charged-particle
track is discarded due to poor momentum resolution, and to be consistent,
events with BEMC tower $E_{\rm{T}}>30$ GeV are also rejected. To avoid the
double-counting of charged-particle track energy and the energy deposition in
the corresponding matched BEMC tower, the full track energy (assuming pion
mass) is subtracted from the tower energy. This procedure is referred to as a
100% hadronic correction. This approach has been used in past STAR
publications Adamczyk et al. (2017a); Adam et al. (2019, 2020b) with the
desirable effect of providing good jet energy resolution. Any towers with
$E_{\rm{T}}<0$ GeV after hadronic correction are ignored in the analysis.

###  II.2 Dataset and jet reconstruction

We analyze Au$+$Au collisions and the corresponding $p+p$ reference data at
$\sqrt{s_{\rm{NN}}}=$ 200 GeV recorded by STAR in 2007 and 2006, respectively,
with a high tower (HT) trigger requiring at least one online calorimeter tower
with $E_{\rm{T}}>5.4$ GeV. The triggered data corresponds to an integrated
luminosity of 11.3 pb-1 and 0.6 nb-1 for $p+p$ and Au$+$Au collisions,
respectively. We also utilize $p+p$ data at the same center of mass energy
taken in 2012 333This dataset and its corresponding simulations and detector
corrections are identical in procedure to a previous STAR publication Adam et
al. (2020b) for the fully corrected measurements. Events from all datasets are
required to have the primary vertex within 30 cm of the center of the TPC
detector along the beam direction. Centrality in Au$+$Au events estimates the
overlap of the two colliding nuclei and is determined by the raw charged-
particle multiplicity in $|\eta|<0.5$ within the TPC Adamczyk et al. (2017a).
We report results for the most central (0-20%) Au$+$Au collisions.

In HT triggered Au$+$Au collisions we utilize two separate jet collections,
both clustered on tracks and towers (denoted as Ch$+$Ne in the figures) with
the anti-$k_{\rm{T}}$ algorithm Cacciari et al. (2008, 2012) with the
resolution parameter $R=0.4$, called HardCore and Matched di-jets. HardCore
jets are clustered with constituents (tracks and towers) with
$2<p_{\rm{T}}~{}(E_{\rm{T}})<30$ GeV/$c$ (GeV), and Matched jets utilize
constituents with $0.2<p_{\rm{T}}(E_{\rm{T}})<30$ GeV/$c$ (GeV) and are
geometrically matched to the HardCore jets Adamczyk et al. (2017a) as shown in
Fig. 1. Due to the high $p_{\rm{T}}$ constituent threshold, the HardCore jets
are effectively free of combinatorial background. The background is subtracted
from the Matched jets via the constituent subtraction method Berta et al.
(2014), with parameters $\alpha=2$ and the maximum allowed distance between a
particle and a ghost is set to $1.0$ in order to suppress the underlying event
contribution to the jet. Di-jet pairs are selected with the trigger HardCore
jet ($\Delta
R_{\mathrm{jet,HT}}=\sqrt{(\phi_{\mathrm{jet}}-\phi_{\mathrm{HT}})^{2}+(\eta_{\mathrm{jet}}-\eta_{\mathrm{HT}})^{2}}<0.4$)
and recoil HardCore jet ($\Delta\phi_{\rm{jet,HT}}>2\pi/3$), both having
minimum jet $p_{\rm{T}}$ requirements ($p^{\rm{trigger}}_{\rm{T,jet}}>16$
GeV/$c$, $p^{\rm{recoil}}_{\rm{T,jet}}>8$ GeV/$c$). We also require that the
trigger HardCore jet has larger transverse momenta than the recoil HardCore
jet which results in the di-jet asymmetry as defined in Eq. 1 to be positive
for HardCore di-jets. We do not impose any momentum thresholds on the Matched
di-jets and as a result the Matched $A_{\rm{J}}$ can be positive or negative.

Figure 1: Description of the di-jet event selection noting the trigger and
recoil jets along with the HardCore and Matched jets which include the hard
and soft constituents in the black and red colored arrows, respectively. The
high tower trigger is shown in the thick black shaded region in the trigger
jet region. The thrust axes for HardCore and Matched jets can be slightly
different since they are associated via $\Delta R$ matching criterion.

To make meaningful comparisons to the Au$+$Au data, the $p+p$ reference events
are embedded into the 0-20% most-central Au$+$Au data from the minimum-bias
dataset 444The STAR minimum-bias trigger requires an event to have signals in
both forward scintillator Vertex Position Detectors (VPD), along with a
requirement of at least one neutron in each Zero Degree Calorimeter (ZDC).
This biases towards a requirement of hadronic interaction of both the Au-ions.
to capture the effect of the large fluctuations in background energy density
in high multiplicity Au$+$Au collisions. The embedded reference is denoted as
$p+p~{}\oplus$ Au$+$Au henceforth. The relative difference in detector
performance is taken into account since the TPC experiences a degradation in
efficiency as the event multiplicity increases. Thus, charged-particle tracks
in a $p+p$ event are artificially removed according to the tracking efficiency
ratio between Au$+$Au and $p+p$ collisions, which is approximately $90\%$ for
most track momenta and rapidity. This procedure consequently enables a direct
comparison of the $p+p$ data to Au$+$Au data at the detector-level, including
the effects of the fluctuating underlying event. A description of the detector
effects necessary to compare a model calculation with the measured data at the
detector-level is provided in the Appendix.

Systematic uncertainties in the embedded $p+p~{}\oplus$ Au$+$Au reference are
indicated by the shaded region and are estimated by the difference in detector
performance for both the TPC and the BEMC between the two datasets as was done
in the previous publication Adamczyk et al. (2017a). The ratio of the TPC
tracking efficiencies for Au$+$Au and $p+p$ collisions is approximately $90\pm
7\%$. The effect of this systematic uncertainty is assessed by repeating the
$p+p$ embedding procedure with the respective minimum ($83\pm$) and maximum
($97\pm$) relative efficiency. The uncertainty due to the tower gain is
assessed by repeating the measurement and varying the energy of all towers by
$\pm 2$%. The resulting uncertainty from the tower energy scale is negligible
compared to that of the tracking efficiency. The final reported uncertainties
are the quadrature sum of the relative tracking efficiency uncertainty and the
relative tower energy scale uncertainty. There are no systematic uncertainties
on the Au$+$Au data presented in this measurement since it is at the detector-
level and thus uncertainties are only presented for our embedded reference.

##  III SoftDrop jet substructure

The SoftDrop Dasgupta et al. (2013); Larkoski et al. (2014) grooming algorithm
removes soft, wide-angle radiation from a sequentially clustered jet. This is
achieved by recursively de-clustering the jet’s branching history and
discarding prongs until the transverse momenta $p_{\rm{T,1}},p_{\rm{T,2}}$ of
the current pair of prongs fulfill the SoftDrop conditions,

$\begin{split}z_{\rm{g}}&=\frac{\min(p_{\rm{T,1}},p_{\rm{T,2}})}{p_{\rm{T,1}}+p_{\rm{T,2}}}>z_{\text{cut}}\left(\frac{R_{\rm{g}}}{R_{\rm{jet}}}\right)^{\beta},\\\
R_{\rm{g}}&=\Delta
R_{\rm{1,2}}=\sqrt{\Delta\eta^{2}_{\rm{1,2}}+\Delta\phi^{2}_{\rm{1,2}}},\end{split}$
(2)

where $R_{\rm{g}}$ is the opening angle between the two prongs and
$R_{\rm{jet}}$ is the jet resolution parameter. The current analysis sets
$\beta=0$, and we adopt the default choice $z_{\text{cut}}=0.1$ Larkoski et
al. (2015). In $p+p$ collisions, the SoftDrop grooming procedure results in
reducing the non-perturbative contributions to the jet which aids in
translating the splitting in a jet tree to a partonic splitting via the DGLAP
splitting functions. The two SoftDrop observables, $z_{\rm{g}}$ and
$R_{\rm{g}}$, were shown to be sensitive to the momentum and angular scales in
$p+p$ collisions in a recent STAR publication Adam et al. (2020b), wherein the
data were compared to both MC event generators and theoretical calculations.
Measuring the $z_{\rm{g}}$ in heavy-ion collisions opens up the possibility of
studying modifications to the splitting kernel, a characteristic aspect in
some energy loss models Casalderrey-Solana et al. (2013); Mehtar-Tani and
Tywoniuk (2015), but it could also indicate changes due to quenching of the
subjets after a vacuum-like fragmentation. A diagrammatic representation of
the SoftDrop algorithm on a recoil jet is shown in Fig. 2, which highlights
the de-clustered tree and the leading and subleading prongs which are utilized
in the measurements of $z_{\rm{g}}$ and $R_{\rm{g}}$. It is important to note
that the first selected split could indeed be different for HardCore and
Matched jets due to the inclusion of the softer components of the jet.

Figure 2: Visualization of the SoftDrop de-clustering step applied on a recoil
jet resulting in the selection of the leading and subleading prongs.

Figure 3: Distributions of softDrop $z_{\rm{g}}$ (top) and $R_{\rm{g}}$
(bottom) for trigger (left) and recoil (right) jets for Au$+$Au data (filled
symbols) and the $p+p~{}\oplus$ Au$+$Au reference (open symbols). The shaded
regions represent systematic uncertainty in the embedded reference. The red
and black points represent HardCore and Matched jets, respectively.

Figure 3 shows the SoftDrop $z_{\rm{g}}$ (top) and $R_{\rm{g}}$ (bottom) for
trigger (left) and recoil (right) jets with $p_{\rm{T}}>16$ GeV/$c$ and
$p_{\rm{T}}>8$ GeV/$c$, respectively. The Au$+$Au data are represented by
solid symbols compared to the $p+p~{}\oplus$ Au$+$Au results in open markers.
HardCore (Matched) jets are shown in the red squares (black circles). For both
$z_{\rm{g}}$ and $R_{\rm{g}}$ we find no significant difference in the shape
of the distributions between Au$+$Au and $p+p~{}\oplus$ Au$+$Au as a
consequence of jet quenching. The apparent peak in the HardCore $z_{\rm{g}}$
distribution (as seen in the red markers in the top right panel) is due to a
kinematic constraint arising from a jet constituent threshold of $2$ GeV/$c$.
We observe significant differences in the $R_{\rm{g}}$ distribution between
HardCore and Matched jets (both trigger and recoil) where the latter peaks at
values closer to $0.33$. Given that HardCore jets are less affected by the
combinatorial background, the Matched jet $R_{\rm{g}}$ shows its sensitivity
to the underlying event. The $0.33$ peak of the Matched jet $R_{\rm{g}}$ is
indicative of a geometric selection of particles at the edge of an $R=0.4$ jet
that pass the grooming requirement and are contained within the jet.

We further quantify the effect of the underlying event on SoftDrop observables
by embedding $p+p$ events into minimum-bias Au$+$Au events. Jets are found in
both $p+p$ and $p+p~{}\oplus$ Au$+$Au embedding data and these jets are then
matched geometrically. The SoftDrop observables in the two datasets are
compared via a 2D correlation. The left panels in Fig. 4 show this correlation
where the $x$-axis represents the observable from the $p+p$ jet and the y-axis
the corresponding value for the embedded, constituent subtracted
$p+p~{}\oplus$ Au$+$Au jet. In the right panels, individual projections of the
$z_{\rm{g}}$ (top right) and $R_{\rm{g}}$ (bottom right) are shown with the
$p+p$ data in filled black circles and the $p+p~{}\oplus$ Au$+$Au data in
filled red boxes.

Figure 4: Left panels: Correlation studies due to the heavy-ion underlying
event for SoftDrop $z_{\rm{g}}$ (top) and $R_{\rm{g}}$ (bottom). Right panels:
The projections along x- and y-axis shown with only statistical errors.

While the 1-dimensional $z_{\rm{g}}$ distributions in the two datasets are
similar, we do not observe a significant diagonal correlation between
substructure observables. The effect of the underlying event is prominent in
the $R_{\rm{g}}$, where the correlation shows a particular failure mode of the
SoftDrop algorithm (with default parameters $z_{\rm{cut}}=0.1$ and $\beta=0$)
in which particles from the underlying event, that are not correlated with the
jet by definition, make it through the grooming procedure and end up being
selected as the first, hardest split. One can indeed modify the grooming
procedure to reduce the non-diagonal component in the correlation by varying
the grooming criterion Mulligan and Ploskon (2020). Since we aim to tag jets
based on their inherent angular scales via an opening angle, the subsequent
bias on the surviving jet population due to a momentum fraction threshold
essentially gets varied and convoluted for jets of varying jet kinematics.
Thus, we present a new class of observables that characterizes jet
substructure via reclustered subjets.

##  IV Momentum and angular scales via subjets

Figure 5: Visualization of the subjet definition and the selection of the
leading and subleading subjets which are utilized in the selection of
narrow/wide jets. The thrust axes for HardCore and Matched jets can be
slightly different since they are associated via $\Delta R$ matching
criterion. Figure 6: Distributions of fully unfolded two-subjet observables
$z_{\rm{SJ}}$ in the top panels and $\theta_{\rm{SJ}}$ in the bottom panels
for inclusive jets in $p+p$ collisions shown in the red star markers, compared
to leading order MC event generators PYTHIA 8 (black), PYTHIA 6 (blue) and
Herwig 7 (magenta) for low-$p_{\rm{T}}$ jets on the left to high-$p_{\rm{T}}$
jets on the right. The shaded red regions represent the systematic
uncertainties in the data points.

The idea of utilizing subjets to probe jet substructure has been explored
recently in theoretical studies where subjets are considered as advantageous
probes to quantify jet-medium interactions Apolinário et al. (2018). We
introduce and measure subjet observables for the first time where
anti-$k_{\rm{T}}~{}R=0.4$ jet constituents are reclustered with the
anti-$k_{\rm{T}}$ clustering algorithm with smaller $R_{\rm{SJ}}$ and the two
highest $p_{\rm{T}}$ subjets are considered as shown in Fig. 5. The momentum
fractions and opening angle are defined as follows,

$\begin{split}z_{\rm{SJ}}&=\frac{\min(p_{\rm{T,SJ1}},p_{\rm{T,SJ2}})}{p_{\rm{T,SJ1}}+p_{\rm{T,SJ2}}},\\\
\theta_{\rm{SJ}}&=\Delta R(\rm{SJ1,SJ2}),\end{split}$ (3)

where $\rm{SJ1}$ and $\rm{SJ2}$ are the leading and sub-leading subjets,
respectively. The fully corrected subjet distributions, $z_{\rm{SJ}}$ (top)
and $\theta_{\rm{SJ}}$ (bottom) in $p+p$ collisions are measured for inclusive
anti-$k_{\rm{T}},~{}R=0.4$ jets. Figure. 6 shows $z_{\rm{SJ}}$ and
$\theta_{\rm{SJ}}$ with a subjet radius of $R_{\rm{SJ}}=0.1$ for various jet
$p_{\rm{T}}$ selections increasing from left to right. The data in the red
star markers (along with the total systematic uncertainty in the shaded red
regions) were corrected via an iterative Bayesian unfolding technique as
implemented in the RooUnfold framework Adye (2011). The correction procedures
and systematic uncertainties are identical to the procedure outlined in a
recent STAR publication Adam et al. (2020b).

There are four major sources of uncertainties, described in order of
importance as the source and its corresponding variation in parentheses:
tracking efficiency in $p+p$ collisions ($\pm 4\%$), BEMC tower energy scale
($\pm 3.8\%$), hadronic correction ($50\%-100\%$), and the unfolding
correction. The systematic uncertainties due to the unfolding procedure
include changing the iteration parameter $(2-6)$ and varying the shape of the
prior distribution. The default prior in the unfolding procedure is PYTHIA 6
Sjostrand et al. (2006) with the STAR tune Adam et al. (2019, 2020b), where
PYTHIA 8 Sjöstrand et al. (2015) using the Monash tune and HERWIG 7 Bahr et
al. (2008); Bellm et al. (2016) using the EE4C tune serve as systematic
variations. The data are compared to leading order MC predictions such as
PYTHIA 6 (blue), PYTHIA 8 (black) and HERWIG 7 (pink). The $z_{\rm{SJ}}$
distributions show small but significant differences for $p_{\rm{T,jet}}>25$
GeV/$c$ with the MC predictions, whereas the $\theta_{\rm{SJ}}$ exhibit very
good agreement between data and predictions. We also find a characteristic
change in the shape of the $z_{\rm{SJ}}$ distribution as the jet $p_{\rm{T}}$
increases. The mean value of the $\theta_{\rm{SJ}}$ shifts to smaller values
and one of the subjets effectively captures the jet core. We also note that
the $\theta_{\rm{SJ}}$ distribution is quantitatively similar for the
different MC, which have different parton showers and hadronization models and
accurately reproduce the distribution in data, which points to the stability
of the $\theta_{\rm{SJ}}$ observable.

Before measuring these substructure observables in Au$+$Au collisions, we
studied the impact of the underlying event by embedding PYTHIA 8 $p+p$ events
into Au$+$Au minimum-bias events. For a given subjet radius
($R_{\rm{SJ}}=0.1$) we estimated an effective subjet $p_{\rm{T}}$ threshold in
order to reduce sensitivity to the fluctuating background. A subjet
$p_{\rm{T}}$ threshold of $p_{\rm{T}}>2.97$ GeV/$c$ was calculated by taking
the mean $(\mu)$ plus $3\sigma$ limit estimated from random cone
studies555This procedure involves dropping circles of radius $R=0.1$ inside
the PYTHIA 8 jets embedded in minimum-bias Au$+$Au events with a random center
$\eta-\phi$ within the jet cone.. It is important to note that the subjet
selection criteria is based on absolute $p_{\rm{T}}$ as opposed to SoftDrop,
which employs a momentum fraction ($z_{\rm{cut}}$) threshold. Given that these
jets undergo interactions with the medium at a characteristic energy scale, a
momentum fraction cut could impose a hitherto unknown, varying survivor bias
in the selected jet population based on the jet kinematics. By selecting jets
based on a subjet $p_{\rm{T,SJ}}>2.97$ GeV/$c$ cut, the selection scale is
constant with respect to jet momenta and the bias in the surviving jet
population can be theoretically quantified.

Figure 7: Left panels: Correlation studies of the two subjet observables
$z_{\rm{SJ}}$ (top row) and $\theta_{\rm{SJ}}$ (bottom row) similar to Figure
4. Right panels: The projections along x- and y-axis shown with only
statistical errors.

The effects of the underlying event on the two subjet observables are also
explored in a procedure identical to the one described in the previous
section. Figure 7 shows the correlation matrix on the left and the individual
distributions on the right for $z_{\rm{SJ}}$ (top row) and $\theta_{\rm{SJ}}$
(bottom row). In contrast to SoftDrop observables, we find that both subjet
observables, $z_{\rm{SJ}}$ and $\theta_{\rm{SJ}}$, have a relatively strong
diagonal correlation along with an overlap in the distributions themselves as
shown in the right panels of Fig. 7. The robustness of the two subjet
observables facilitates a direct comparison between Au$+$Au and $p+p~{}\oplus$
Au$+$Au results where the effect of the underlying event is effectively
negated.

Figure 8: Distributions of subjet observables $z_{\rm{SJ}}$(top) and
$\theta_{\rm{SJ}}$(bottom) for trigger (left panels) and recoil (right panels)
jets. The Au$+$Au plots are shown in the filled markers whereas the open
markers represent $p+p~{}\oplus$ Au$+$Au which includes the shaded regions
representing systematic uncertainty. The red and black points represent
HardCore and Matched jets respectively.

Figure 8 shows the subjet $z_{\rm{SJ}}$ (top) and $\theta_{\rm{SJ}}$ (bottom)
distributions for trigger jets (left panels) with $p_{\rm{T}}>16$ GeV/$c$ and
recoil (right panels) jets with $p_{\rm{T}}>8$ GeV/$c$. HardCore and Matched
jets are shown in the red squares and black circles, respectively, with
$R_{\rm{SJ}}=0.1$ subjets. For both the HardCore and Matched jet distributions
in each panel of Fig. 8, the differences between the Au$+$Au data and the
$p+p~{}\oplus$ Au$+$Au reference distribution are negligible indicating, once
again, no significant modification of the jet substructure due to jet
quenching. Given that the substructure results are similar, we may conclude
that the recoil jets in the kinematic range studied in this analysis, fragment
in a vacuum-like environment. The $\theta_{\rm{SJ}}$ for Matched jets, in
stark contrast to the SoftDrop $R_{\rm{g}}$, peaks at small values which
include a natural lower cutoff at the subjet radius. Di-jet pairs are selected
based on the recoil Matched jet $\theta_{\rm{SJ}}$, and we define narrow
(wide) recoil jets as $0.1~{}(0.2)<\theta_{\rm{SJ}}<0.2~{}(0.3)$. The narrow
(wide) jets have a $\theta_{\rm{SJ}}$ finding purity of 98% (75%) determined
from the correlation matrix shown in the bottom left panel of Fig. 7.

##  V Di-jet asymmetry dependence on angular scale

Figure 9: Distributions of HardCore di-jet Asymmetry ($A_{\rm{J}}$) for events
with leading and subleading cuts of 16 GeV/$c$ and 8 GeV/$c$, respectively.
The filled markers correspond to Au$+$Au data and the open markers along with
the shaded regions show $p+p~{}\oplus$ Au$+$Au reference. The black
distributions do not have any cuts on $\theta_{\rm{SJ}}$ whereas for the blue
and red distributions, selections on recoil Matched jets with
$0.1<\theta_{\rm{SJ}}<0.2$ and $0.2<\theta_{\rm{SJ}}<0.3$ are applied. The
vertical error bars represent statistical uncertainty on the data points.

The differential measurements of momentum asymmetry for HardCore and Matched
di-jets (in $|A_{\rm{J}}|$) are shown in Fig. 9 and Fig. 10, respectively. The
black, blue and red markers represent recoil jets with selections on their
corresponding Matched jet $\theta_{\rm{SJ}}$ with the ranges
$[0.1,0.4],[0.1,0.2]$ and $[0.2,0.3]$ for inclusive, narrow and wide jets,
respectively. The selection on the $\theta_{\rm{SJ}}$ reflects the available
resolution due to the statistics in the data sample. We observe a clear di-jet
imbalance indicating jet quenching effects in Au$+$Au collisions for all
HardCore jets including the wide angle jets. The Matched jets on the other
hand are momentum balanced at RHIC energies, as is evident by the overlap
between the Au$+$Au (filled) and $p+p~{}\oplus$ Au$+$Au (open) markers. This
is consistent with our earlier measurements Adamczyk et al. (2017a), and
agrees with the observation that both wide and narrow angle matched jets are,
respectively, balanced with the reference with little change in their overall
shapes. This indicates that the lost energy from the HardCore di-jets is
recovered in the softer particles ($0.2<p_{\rm{T}}<2.0$ GeV/$c$) distributed
around the jet cone of $R=0.4$. While one might expect that for wider jets,
the energy loss would spread to larger angles, we observe that within the
available experimental resolution of $\theta_{\rm{SJ}}$, there is no
significant difference in the energy loss signature of jets with
$0.1<\theta_{\rm{SJ}}<0.3$.

Figure 10: Distributions of Matched di-jet Asymmetry ($|A_{\rm{J}}|$) for
events with leading and subleading cuts of $16$ GeV/$c$ and $8$ GeV/$c$ (for
HardCore jets), respectively. The filled markers correspond to Au$+$Au data
and the open markers along with the shaded regions show $p+p~{}\oplus$ Au$+$Au
reference. The black distributions do not have any cuts on the subjet
$\theta_{\rm{SJ}}$ whereas for the blue and red distributions, selections on
recoil Matched jets with $0.1<\theta_{\rm{SJ}}<0.2$ and
$0.2<\theta_{\rm{SJ}}<0.3$ are applied. The vertical error bars represent
statistical uncertainty on the data points.

##  VI Conclusions and discussion

We present the first differential measurement of partonic energy loss in
Au$+$Au collisions at $\sqrt{s_{\rm{NN}}}$ $=200$ GeV for jets tagged via
their opening angle. The energy loss is quantified with measurements of the
momentum asymmetry $A_{\rm{J}}$ of specially selected di-jet pairs. The
differential nature of these measurements involves identifying and selecting
jets of a particular topology or substructure, i.e., those that have narrow
vs. wide opening angles. Since we compare Au$+$Au data to an embedded
$p+p~{}\oplus$ Au$+$Au reference, we require the substructure observable to be
sensitive to the jet kinematics, while simultaneously being insensitive to the
heavy-ion underlying event. For SoftDrop observables with $z_{\rm{cut}}=0.1$
and $\beta=0$, we find that the groomed jet radius ($R_{\rm{g}}$) is impacted
by the fluctuating underlying event and this results in a significant fraction
of jets tagged with a fake splitting as shown in Fig. 4. This effect arises
from background particles which satisfy the grooming criteria, thus
complicating the use of $R_{\rm{g}}$, particularly for larger opening angles.

While the fake split fraction might be reduced by limiting the analysis to
high-$p_{\rm{T}}$ jets or by varying the SoftDrop grooming parameters, we
instead introduced a new class of subjet observables, $z_{\rm{SJ}}$ and
$\theta_{\rm{SJ}}$. In the present analysis the subjets are reclustered via
the anti-$k_{\rm{T}}$ algorithm with the jet’s constituents as input and with
a smaller resolution parameter $R_{\rm{SJ}}=0.1$. We present the fully
corrected subjet observables ($\theta_{\rm{SJ}}$ and $z_{\rm{SJ}}$) for $p+p$
collisions, both of which display a gradual change in the jet shape from a
broad to a narrow distribution as the jet momentum increases. This evolution
with jet momentum, as shown in Fig. 6, indicates a transition from large
momentum sharing ($z_{\rm{SJ}}$ peaked at large values) between the two
leading subjets to a gradually more asymmetric momentum sharing for higher
$p_{\rm{T}}$ jets. More importantly for our study, these subjet observables
meet the requirement of being both sensitive to the jet kinematics and
insensitive to the heavy-ion background via an absolute $p_{\rm{T}}$ threshold
on the subjets as shown in the correlation studies in Fig. 7. This achievement
contrasts with the SoftDrop method which uses a fractional momentum cut, thus
has a jet $p_{\rm{T}}$ dependent bias due to the combination of quenching and
surface bias effects on jet selection criteria at RHIC energies.

In comparing the substructure distributions for Au$+$Au data and the
$p+p~{}\oplus$ Au$+$Au reference for both trigger/recoil HardCore/Matched
jets, we observe no significant differences in all cases, indicating that the
splittings identified in jets via the subjet method are vacuum-like.
Measurements of $A_{\rm{J}}$ for recoil jets of varying $\theta_{\rm{SJ}}$
demonstrate no significant differences in the momentum balance/imbalance of
Matched/HardCore di-jet pairs for recoil jets with $0.1<\theta_{\rm{SJ}}<0.2$
or $0.2<\theta_{\rm{SJ}}<0.3$. These results support the conclusion that these
particular selected di-jets do not undergo significantly different jet-medium
interactions under varying angular scales.

We can now develop a consistent picture of partonic energy loss for specially
selected di-jets at RHIC energies based on three significant features that we
observe in our data. The first is that these recoil jets are expected to have
smaller path-lengths in the medium on average, owing to the restrictive di-jet
requirements which favor tangential production vertices, in comparison to an
inclusive or semi-inclusive jet population. The second is the observation that
the jet substructure distributions are comparable for Au$+$Au and
$p+p~{}\oplus$ Au$+$Au indicating vacuum like splitting. Third, the recovery
of the quenched energy for recoil Matched jets is independent of the jet
opening angle measured via the $\theta_{\rm{SJ}}$. Thus, we infer that the
recoil jet’s first hard splitting during jet evolution possibly happens at
formation times comparable to the shorter in-medium path length for tangential
di-jets, resulting in vacuum like distributions. Given that the HardCore
recoil jets do undergo quenching, as shown by an imbalanced $A_{\rm{J}}$, the
medium interaction that these jets undergo happens at earlier times when the
hard-scattered parton is traversing the medium.

These three features, together with the surface bias of unmodified trigger
jets, lead us to a qualitative interpretation of the data that energy loss in
these recoil jets is due to medium induced radiation from a single color
charge. Because of the relatively small-scale resolution of the subjet opening
angle in this measurement $(\Delta\theta_{\rm{SJ}}=0.1)$, we were able to
observe di-jet balance/imbalance for both narrow and wide jets. From the
similarity of the results for narrow and wide jets we conclude that there is
no observational evidence of the characteristic signature of coherent or de-
coherent energy loss as the range of sampled jet opening angles encompasses
the medium coherence length scale. The differential measurements presented
here can now be utilized in stringent tests of various quenching models, and
also interpretations resulting from jet selection and fragmentation biases.
These studies lead the community towards a study of soft gluon radiation in
the QGP, as in the QCD analog of the Landau-Pomeranchuk-Migdal effect Landau
and Pomeranchuk (1953); Migdal (1956); Wang et al. (1995); Zapp et al. (2011),
which has long been expected to be a significant factor in parton energy loss
at RHIC.

## Acknowledgements

We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL,
and the Open Science Grid consortium for providing resources and support. This
work was supported in part by the Office of Nuclear Physics within the U.S.
DOE Office of Science, the U.S. National Science Foundation, the Ministry of
Education and Science of the Russian Federation, National Natural Science
Foundation of China, Chinese Academy of Science, the Ministry of Science and
Technology of China and the Chinese Ministry of Education, the Higher
Education Sprout Project by Ministry of Education at NCKU, the National
Research Foundation of Korea, Czech Science Foundation and Ministry of
Education, Youth and Sports of the Czech Republic, Hungarian National
Research, Development and Innovation Office, New National Excellency Programme
of the Hungarian Ministry of Human Capacities, Department of Atomic Energy and
Department of Science and Technology of the Government of India, the National
Science Centre of Poland, the Ministry of Science, Education and Sports of the
Republic of Croatia, RosAtom of Russia and German Bundesministerium für
Bildung, Wissenschaft, Forschung and Technologie (BMBF), Helmholtz
Association, Ministry of Education, Culture, Sports, Science, and Technology
(MEXT) and Japan Society for the Promotion of Science (JSPS).

*

##  Appendix A Detector effects and comparisons

The Au$+$Au data in this publication are compared to an embedded reference at
the detector-level which presents the measurement without any correction for
detector effects. We therefore provide the relevant performance parameters for
the STAR detector, mainly the TPC and the BEMC. This enables predictions of MC
models or theoretical calculations to be directly applied to the detector-
level data. For charged-particle tracks in the TPC, the tracking efficiency is
shown in Fig. 11 as a function of the track $p_{\rm{T}}$ for particles at mid-
rapidity ($|\eta|<1.0$). The red and black markers show the efficiencies for
$p+p$ and Au$+$Au 0-20% events taken during 2006 and 2007, respectively. The
tracking efficiency is also assumed to be flat as a function of track momentum
for $2.0<p_{\rm{T}}<30$ GeV/$c$ for both datasets. The TPC also produces a
momentum smearing which is modeled by

$\sigma=-0.026+0.02\cdot
p^{\rm{true}}_{\rm{T}}+0.003\cdot(p^{\rm{true}}_{\rm{T}})^{2},$ (4)

taken to be the same for both $p+p$ and Au$+$Au collisions.

Figure 11: TPC tracking efficiencies for the 2006 $p+p$ and 2007 Au$+$Au
datasets utilized in the embedding studies for tracks within $|\eta|<1.0$.

The BEMC has a spatial segmentation of $0.05\times 0.05$ in ($\eta,\phi$) with
an energy resolution of $\sigma(E_{\rm{T}})=14\%/\sqrt{E_{\rm{T}}}$ Beddo et
al. (2003). The hadronic correction procedure described at the beginning of
Sect. II ensures that the energy deposited by charged-particles in the BEMC is
not double-counted, such that $\sigma(E_{\rm{T}})$ estimates the error in the
neutral energy of a jet.

In addition to the preceding detector effects, the impact of the heavy-ion
underlying event on the jet momentum and substructure observables should be
taken into account for direct comparison with the data presented here. These
effects for the HardCore and Matched jet momenta are presented in the
supplemental material of an earlier publication Adamczyk et al. (2017a). The
left panels of Fig. 4 and Fig. 7 of this reference show the effect of the
heavy-ion underlying event on the substructure observables.

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acmlicensed

http://dx.doi.org/10.1145/3077286.3077293

978-1-4503-5024-2/17/04

$15.00

# Acquisition and use of knowledge over a restricted domain by intelligent
agents

Juliao Braga

Nizam Omar

Mackenzie University  Rua Consolacao, 930  Sao Paulo, SP, Brazil
<EMAIL_ADDRESS>Mackenzie University  Rua Consolacao, 930  Sao Paulo, SP,
Brazil<EMAIL_ADDRESS>Luciana F. Thome

Fluminense Federal University  Av. Gal. Milton T. Souza, s/n  Niterói, RJ,
Brazil<EMAIL_ADDRESS>
(23 March 2017)

###### Abstract

This short paper provides a description of an architecture to acquisition and
use of knowledge by intelligent agents over a restricted domain of the
Internet Infrastructure. The proposed architecture is added to an intelligent
agent deployment model over a very useful server for Internet Autonomous
System administrators. Such servers, which are heavily dependent on arbitrary
and eventual updates of human beings, become unreliable. This is a position
paper that proposes three research questions that are still in progress.

###### keywords:

ACM proceedings; Multi Agents; text distillation; knowledge base; semantics;

††conference: ACM SE ’17 April 13–15, 2017, Kennesaw, GA, USA††titlenote:
(Produces the permission block, and copyright information). For use with SIG-
ALTERNATE.CLS. Supported by ACM.

<ccs2012> <concept> <concept_id>10010520.10010553.10010562</concept_id>
<concept_desc>Computer systems organization Embedded systems</concept_desc>
<concept_significance>500</concept_significance> </concept> <concept>
<concept_id>10010520.10010575.10010755</concept_id> <concept_desc>Computer
systems organization Redundancy</concept_desc>
<concept_significance>300</concept_significance> </concept> <concept>
<concept_id>10010520.10010553.10010554</concept_id> <concept_desc>Computer
systems organization Robotics</concept_desc>
<concept_significance>100</concept_significance> </concept> <concept>
<concept_id>10003033.10003083.10003095</concept_id> <concept_desc>Networks
Network reliability</concept_desc>
<concept_significance>100</concept_significance> </concept> </ccs2012>

[500]Computer systems organization Embedded systems [300]Computer systems
organization Redundancy Computer systems organization Robotics [100]Networks
Network reliability

##  1 Introduction

Paul Horn, in 2001, inspired by the living system physiology presented an IBM
proposal for the future of computer systems [14]. His work argued that the
efforts of specialists in the maintenance, control and operation of computer
systems could be minimized and consequently have their costs reduced
dramatically. The community, composed mainly of researchers continued to
advance in the researches of this knowledge domain becoming a paradigm named
by Horn as Autonomic Computation.

Contributions have been expanded by multidisciplinary research groups and the
results have been surprising [17]. A number of applications, particularly in
software, have enabled, for example, the technology of space probes [21],
rather Unmanned Space Vehicles (USVs) [15].

The interest aroused has led to the application of Intelligent Agents or
Intelligent Elements (IEs) in the Infrastructure of the Internet,
concentrating basically on the protocols and techniques like Software Defined
Networking (SDN) [20, 18, 22] will encourage the development of new
initiatives in this direction. It is important to develop case studies and
experiments on the entire spectrum of applications for the Internet
Infrastructure. In this sense, the renewed experience and expansion of
research groups will make an effective contribution to improving and
consolidating the studies that are being carried out to date, especially the
principle of interdisciplinary cooperation.

Section 2 presents the abstract IEs model and the respective application
domain. From the abstract model this section continues to the implementation
model with its physical characteristics. Section 3 describes the architecture
for knowledge acquisition and its functional components. Section 4 presents
the steps involved in the process of knowledge acquisition and the research
questions involved. Section 5 presents the conclusions with the identification
of future problems. Section 6 concludes the authors’ acknowledgments.

##  2 The Application Domain and its characteristics

The Autonomous Architecture for Restricted Domains (A2RD) model is presented
in Figure 1 and divided into four layers, described below. The model serves
the interest of establishing an architecture of intelligent elements under the
administrative domain of ASs, which is known as the designation given to the
networks that form the Internet.

Figure 1: Four Layer Abstract Model of Autonomous Architecture for Restricted
Domains (A2RD). Source: [3]

The model can exist in any of the $2^{32}$ possible ASs [13]. However, on
02/03/2017 there were 56,710 active ASs on the Internet (originating traffic),
according to CIDR-report111http://www.cidr-report.org/as2.0/. The number of an
AS is unique, controlled by the Regional Internet Registers (RIRs) and / or
National Internet Registers (NIRs) and is called the Autonomous System Number
(ASN). Thus, the largest possible value of x is 56710, corresponding to
AS56710, at the date above. There is no conflict between the model being
deployed in any AS environment and being domain-restricted. In fact, the
implementations are independent, but with a high degree of interoperability
and, of course, intense cooperation, because ASes administrators depend on the
behavior of all the others. The IANA has reserved two contiguous ranges of ASs
numbers for private use [16]: 64512-65534 and 4200000000-4294967294.
Conveniently, these ASes numbers can be used to designate Intelligent Elements
in applications that need to represent subdomains.

The first of the four layers hosts the Intelligent Element (IE) named
Controller. Its identification is unique and definitive: x:0, that is, the
number 0 placed to the right side of the symbol :, following by the ASN that
hosting the model. Sometimes, to make clear which IE is being referenced, IE
is used before the identification, as for example, when affirming that the IE
Controller is IEx:0. Thus, if AS5 is the host domain of the model, then the
controlling element is IE5:0. No IE of the lower layers can exist, without the
prior consent of the IE Controller. It has the property of keeping oneself
organized (self-organization) and ensuring the self-organization of any IE of
the lower layers.

The second layer is represented by the so-called Specialized IEs. These
elements are identified by suffixes that can range from 1 to 9999. The
specialized elements support the IE Controller, in specific activities and
necessary to the respective functionalities. These activities range from
ensuring the interoperability of the entire system of implemented IEs, to the
establishment of specific functionalities, such as servers with end-to-end
characteristics [19], database access functionalities and semantic
repositories, proprietary software (similar to Southern SDN APIs) [22],
features required for lower-layer IEs. However, support for the IE Controller
is the primary objective of the Specialized IEs. This objective is who
determines the functionalities of the second layer. It is assumed that some
Specialized IEs may be Autonomic Elements or intelligent elements that execute
automatic processes, such as proprietary software and procedures associated
with legacy systems, among others. A Specialized IE can be created as
functions that only concern the IE Controller, especially when it depends on
the functionalities of IEs of the third layer.

In the third layer lies the largest IEs agglomeration, which is why it is
called the IE Colonies. Elements of this layer can be Autonomous, Autonomic or
Automatic, except Legacy and are directly responsible for the most important
activities of the application, including software reuse. They act under the
influence of a high degree of interoperability and cooperation between them
and between IEs of other layers and other domains / subdomains. They do not
directly participate in interconnections or exchange messages with other IEs
outside the domain, but they do so through the IEs of the upper layers. There
is intense semantic interoperability activity by these IEs, which have a high
capacity for self-learning due to continuous interactions with the domain
environment, and produce improvement effects on the knowledge of other IEs of
the colony itself and the IEs of the upper layers, IE Controller. In other
words, these IEs favor the learning of the entire cluster of IEs of the layer
model, which hour is being described. The IEs of the colonies receive an
identification with numeric suffixes, ranging from 10000 to 4294967295.

In the fourth layer are the Auxiliary IEs. This layer exists, in order to
allow the transfer of computing demands to a new set of IEs (successiveness of
the model). It reproduces, successively, the first, second, third and a new
fourth layers. This new IEs sequence has an additional suffix :j:0 for a new
IE Controller responsible for the following four new layers. In the new
second, third and fourth layers, the IDs of the IEs are postfixed with :j:id,
where j is a colony IE number that originated the new fourth layer and the id
is a number with the above specifications. A typical application for the
fourth layer are subdomains, such as home networks (homenet).

The figure 2 is the A2RD implementation model, where the small and colored
rectangles are IEs. It is seen that the IEs are arranged and distributed among
the layers, similar to what was said earlier about the abstract model. As an
example, IEs are implemented in the domain of an AS whose number is x. By this
same figure, it is observed that the IEs functionally important for the inter-
domain operations reside into the upper layers.

Figure 2: A2RD Implementation Model. Source: [1] [3]

It is observed in the implementation model that a classification of relevance
is the intensity of aggregation that an IE has in relation to the self-*
properties. If an IE, however, has some self-organizing capability, it must
participate directly linked to the IE Controller. Even if it participate in
the layer of Auxiliary IEs there may be a new IE Controller that logically
builds a new layer architecture.

On the other hand, the representation of the model is logical (abstraction of
the physical implementation). Physically, locating an IE in the domain
environment is essential. The best alternative is IP addressing, preferably
IPv6, for reasons of availability. The IE Controller must maintain a table
associating the logic reference with the IP designated by the IE Controller
itself, from the premise that an IPv6 block must be available at the beginning
of the implementation. However, this is not a fundamental issue, because as
will be seen in next section, in the name of security an IP relation as the IE
ID will be available in a primitive Domain Name System (DNS), the hosts file
allocated internally and with direct link to the IE Controller.

##  3 A2RD Use Case

The A2Rd implementation model has been tested on an Internet Routing
Registry222http://www.irrd.net/ (IRR) server. IRR is an important data base
for AS Administrators. But, as the IRR depends on the systematic update of the
human being it becomes an unreliable database. By eliminating human
intervention and letting the IEs update, the IRR becomes, surprisingly, a
reliable database. Figure 3 shows that there is no logical difference between
human intervention or not.

Figure 3: IRR model. Objects created by human beings (L) and objects created
by IEs (R)

Numerous IEs have been created, some specialized in the creation of objects,
others in the systematic updating of objects and others specialized in
capturing information in the various components that makes the AS operational.

##  4 Model for knowledge acquisition by IEs

This experience with de A2RD use case has led to the need to make IEs more
autonomous. So, the knowledge required for IEs is available on unstructured
bases, in particular, on those produced by the IETF Working Groups (WGs). But
they are present in other documents, unofficial and related to equipment and
techniques associated with the resources and facilities available in the field
of ASes. From this set of available bases, one of the most important is that
maintained by the RFC Editor333https://www.rfc-editor.org/ represented by more
than 8,000 documents called Request for Comments (RFCs).

Figure 4 shows the whole process of acquiring knowledge from the unstructured
bases (3) through an adaptation in (4) so that they can be submitted to
appropriate tools and techniques in (5), as IBM Watson techniques [11, 10],
whose preliminary result is stored in an intermediate knowledge base (6),
which when suffering interference from other more elaborate tools (7) and from
the IEs themselves (1), will give rise to an appropriate knowledge base (2).

Figure 4: Global knowledge capture model for IEs in a restricted domain.
Source: [1]

##  5 Research questions involved in the process of knowledge acquisition

The RFCs repository is constantly updated. Any effective use of this
repository implies a continuous and permanent process of manipulation,
involving four steps, three of which represent research questions that must be
studied.

  1. 1.

Capture of the RFC Editor repository in a systematic and continuous way.

  2. 2.

Lexical refinement of RFCs (Research question 1)

  3. 3.

Semantic distillation and construction of the knowledge base. (Research
question 2)

  4. 4.

Knowledge base used by IEs. (Research question 3)

These steps are represented and identified in Figure 5.

Figure 5: Characterization of the problem and its research questions. Source:
[1]

###  5.1 WordIETF

In step 2, which identifies research question 1, one has an immediate result.
This is a lexical and syntactical base, called WordIETF with a lot of
similarity to WordNet [9]. WordIETF is built on eXtensible Markup
Language444https://www.w3.org/TR/REC-xml/ (XML) and takes full advantage of
the building, by the RFC Editor, the RFC’s repository in XML
555https://www.rfc-editor.org/rfc-index.xml.

The construction of the WordIETF has been tested a series of techniques and
recommendations produced by various authors. "Computing is a Natural Science",
as said Peter Denning [4]. Semantics is essential for living organisms and
defines the relationship between the mind and the world [5].

More recently, authors have admitted several techniques using computational
morphology and there is a belief that the contribution of a database such as
WordIETF will be fundamental for the evolution of research questions 2 and 3
[7, 8, 6].

##  6 Conclusions

There are many challenges to the progress of the project, among them is the
construction of the WordIETF that can meet the demand for construction of
ontologies in the area of Internet Infrastructure. The WordIETF development
should be cooperative and although there are initiatives of researchers in the
area of Internet of Things (IoT) [12], and by those interested in the
Internetware paradigm of the Context Aware Supporting Environment for
Internetware666https://code.google.com/p/casei/ (CASEi), the authors find to
have a central coordination, such as the Internet Research Task Force (IRTF),
through a multi-stakeholder group.

Without exhausting other proposals it is necessary to develop methodologies
for the construction of IEs, in this case, identified as Intelligent Objects
(IOs). IO is an intelligent element built with quality, reusable and
preserving the knowledge of its life cycle, in the context of A2RD model
applications, strengthening the security environment proposed by the DTS model
and other related models. Construction of IOs, in an adequate and standardized
manner induces interdisciplinary cooperation and rapid development of IEs. The
challenge would be to use the methodology INTERA [2], adapted to the
construction of IOs. INTERA is a successful methodology used in Learning
Objects.

##  7 Authors’ Acknowledgments

This work was conducted during a scholarship supported by the International
Cooperation Program CAPES at the University of Saskatchewan, CA. Financed by
CAPES – Brazilian Federal Agency for Support and Evaluation of Graduate
Education within the Brazil’s Ministry of Education.

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