# The Music Meta Ontology: a flexible semantic model
for the interoperability of music metadata

###### Abstract

The semantic description of music metadata is a key requirement for the
creation of music datasets that can be aligned, integrated, and accessed for
information retrieval and knowledge discovery. It is nonetheless an open
challenge due to the complexity of musical concepts arising from different
genres, styles, and periods – standing to benefit from a lingua franca to
accommodate various stakeholders (musicologists, librarians, data engineers,
etc.). To initiate this transition, we introduce the Music Meta ontology, a
rich and flexible semantic model to describe music metadata related to
artists, compositions, performances, recordings, and links. We follow eXtreme
Design methodologies and best practices for data engineering, to reflect the
perspectives and the requirements of various stakeholders into the design of
the model, while leveraging ontology design patterns and accounting for
provenance at different levels (claims, links). After presenting the main
features of Music Meta, we provide a first evaluation of the model, alignments
to other schema (Music Ontology, DOREMUS, Wikidata), and support for data
transformation.

##  1 Introduction

A music analyst, a computational musicologist, a music librarian, and a data
engineer are working on a joint project. They need to contribute data from
various musical sources, ranging from music libraries, annotated corpora and
tune books, to audiovisual archives, radio broadcasts, and music catalogues.
All data is eventually merged/aggregated as interconnected corpora, and linked
to online music databases (e.g. MusicBrainz, Discogs) and knowledge bases
(e.g. Wikidata). This creates opportunities to link cultural heritage
artefacts to music industry data (streaming services, music professionals,
etc.) and viceversa.

This plot subsumes a recurring challenge for musical heritage projects [1].
Besides the individual requirements of each stakeholder – possibly rooted in
different music genres, periods and datasets, a fundamental requirement is the
interoperability of music metadata.

Music metadata (alias bibliographic, or documentary music data) is used to
consistently identify and describe musical works, their artists, recordings,
and performances. For music industry, it allows for efficient management and
distribution of music, which facilitate search and recommendation [2]. When
metadata is accurate, it ensures that artists receive proper credit and
compensation [3]. For musical heritage, metadata allows for the preservation
and dissemination of musical works and traditions, but also aid in the
research and study of music history and culture [4]. When integrating both
views, metadata can help to promote diversity and inclusivity in the music
industry by highlighting lesser-known genres and artists, while integrating
information and artefacts of cultural interest [5].

Hence, a model that can consistently describe metadata is highly desirable –
as it enables linking entities and concepts from various datasets (e.g. a
composer is linked to a tune that has no authors in another collection).
Semantic Web technologies can help achieve interoperability, as they
facilitate data access and integration, resource discovery, semantic reasoning
and knowledge extraction [6]. In the Resource Description Framework [7], data
is described as <subject-predicate-object> triples using ontologies, and
released as Knowledge Graphs (KGs).

To achieve interoperability, one possibility akin to [8] is to let
stakeholders design their own domain-specific ontologies, then use alignment
algorithms to find connections between them (e.g. MusicalWork and Composition
referring to the same concept). However, this approach comes with three major
drawbacks: (i) ontology alignment is error-prone, hence links would still
require manual inspection; (ii) even when alignment is sound, the semantics of
classes and relationships may vastly differ across domains, which in turn, may
create inconsistent alignments; (iii) it does not address the problem in the
long-term.

###  1.1 Challenges and requirements for interoperability

Another possibility is to reuse current ontologies for music metadata, such as
the Music Ontology (MO) [9] and the DOREMUS ontology [10]. However, modelling
music metadata across different genres and historical periods, to accommodate
various use cases over heterogeneous data sources poses a number of
challenges. First of all, it requires a perspective that harmonises all
requirements from different stakeholders – to design a model that can be
tailored to different data sources rather than to a single type of dataset. We
categorise the main challenges and requirements for metadata interoperability
as follows.

####  1.1.1 Domain specificity hampers interoperability

When looking at current ontologies, MO leans towards modelling discographic
data with a focus on contemporary music, whereas DOREMUS is inherently rooted
in classical music. These ontologies have been demonstrated to model metadata
from MusicBrainz and BBC Music [11], and from classical music libraries and
radio broadcasts for concerts programming [12], respectively. Their
specificity makes them appealing when downstream applications show
considerable overlap in terms of requirements and data. Examples include the
reuse of MO in the WASABI project [13], to support the semantic annotation of
audio music (emotions, lyrics, structures), but also for music recommendation
[14] and listening [15]; and the adoption of DOREMUS by Philarmonie de Paris,
Biblioteque National de France, and Radio France.

Nevertheless, when drifting from discographic data and classical music, or
attempting to reuse both models, addressing e.g. cultural heritage
requirements while fostering interoperability becomes difficult. Indeed, a
model reflecting the view and the interpretations ascribable to a musical
genre, stakeholder, or dataset type may be difficult to reuse and extend to
other domains. For instance, a music artefact may originate from oral
transmission or be the result of a creative process that does not necessarily
entail a formal composition process. The latter is common in songwriting, but
also in folk music whenever a set of tunes (collected from different
manuscripts) allows for the identification of a tune family [16]. Similarly,
when expressing relationships between musical artefacts (alias derivations),
it is important not to impose any modelling bias that may constrain possible
interpretations (e.g. an arrangement having proper musical identity vs simply
providing a different instrumentation). This is commonly referred to as
“dominance of concept” [12], whose definition should be left to users
depending on their data and domain expertise.

Rather than attempting to achieve consensus on musical concepts and jargon,
accounting for the interoperability calls for an abstraction layer for music
metadata (“zoom-out”) that can then be specialised, extended, and adapted to
address domain-specific requirements (“zoom-in”).

####  1.1.2 Expressivity is needed at different levels

Another requirement for interoperability and reuse across various data sources
is providing expressivity at different degrees, i.e. the possibility to
conveniently describe music metadata at the right level of detail. For
example, one data source may have granular/detailed information that requires
high semantic expressivity (a composition process spread over different time,
places, and involving more artists); whereas others may have basic (only the
name of an artist is known) or even incomplete and uncertain information (a
composition tentatively attributed to an artist).

Here, the WikiProject
Music111https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Music has been
successful in providing expressivity to represent music metadata from
different sources. As an extreme case of ontological flexibility, the schema
underlying Wikidata – an open-ended, multi-domain KG built collaboratively
like Wikipedia – is not specified in a previously agreed ontology, and the
high expressivity overly adds complexity to the model. This is due to
Wikidata’s scope being the most general.

####  1.1.3 Provenance is fundamental for data integration

Accounting for provenance is a central requirement for both cultural heritage
and music industry. This becomes fundamental when integrating Knowledge Graphs
from different datasets and stakeholders – as every single bit of data (each
triple) should be attributable to a dataset/KG. Furthermore, integrating
provenance is also needed within the context of a single dataset, at least for
claims and links.

Claims-Interpretations. Cultural heritage applications often require
representing debatable statements or claims [17, 18]. These are usually the
result of an interpretation process based on factual or documentary evidence
(a dataset, a manuscript, etc.), and following a methodology and/or theory.
Examples include personal information (e.g. the year/place of birth of a
composer), and authorship claims (e.g. a composition being attributed to an
artist).

Links and identifiers. These includes links to artists’ official websites, fan
pages, discussion forums, music reviews, record shops; as well as identifiers
from music databases (e.g. MusicBrainz, Discogs, AllMusic), streaming
platforms (e.g. Deezer, Spotify), and authoritative sources (e.g. ISNI, ISWC,
ISRC). As most links and identifiers are crowdsourced or automatically
inferred by entity linking algorithms, modelling provenance here promotes
traceability and accountability of data sources.

Notably, Wikidata addresses both these requirements, as every triple is
considered a statement per se, for which so-called references can be appended
and ranked. References may include information on the source, whether a
computational method was used, and a date of retrieval.

###  1.2 Our contribution

We leverage the expertise and complementary views of various music
stakeholders (musicologists, data engineers, music analysts, and heritage
archivists) to contribute:

  * •

The _Music Meta_ ontology, a rich flexible model to describe Western music
metadata and its provenance at different levels of granularity.

  * •

An example-driven validation of the model, focused on the data elicited from
four different stakeholders.

  * •

Code support to create Music Meta KGs without expert knowledge of the model,
with automatic alignments to the MO, DOREMUS, and Wikidata.

##  2 Related work

Besides metadata, the use of Semantic Web technologies in the music domain has
contributed several ontologies, covering a variety of musical aspects and
spanning both symbolic and audio music.

Among them, the Music Theory Ontology [19] describe theoretical concepts of
compositions, whereas the Music Score [20] and Music Notation [21] propose
granular ontologies to represent elements of music scores. OMAC expresses
features of musical entities but also musicological claims [22], while the
OMRAS project [23] contributed ontologies to describe music chords as well as
concepts related to tonality and temperament.

In the audio domain, ontologies describe music production [24], audio features
[25], effects [26]; an also model listening habits/taste [27], music-induced
emotions [28], music structure [29, 30], and musical similarities [31].

These ontologies have specific focus, and many were developed as stand-alone
projects, with little or no alignment [32]. Instead, some ontologies focus on
achieving interoperability between notations, taxonomies, and formats. These
include the Internet of Musical Things [33], where heterogeneous musical
objects are envisioned to coexist; the Music Annotation Pattern [34] which
allows to model music annotations in the JAMS format [35]; and the Hamse
ontology [36] describing musical features for musicological research.
Similarly, [37] models abstract annotations of musical works, rather than
concrete encodings.

Interoperability at the level of musical content level resulted in successful
MIR applications, such as the MIDI Linked Data Cloud [38] – integrating MIDI
music to learn embeddings over the resulting KG [39]; and ChoCo [40] – a chord
corpus integrating 18 chord datasets and enabling novel workflows for
computational creativity [41].

##  3 The Music Meta Ontology

Figure 1: Describing music artists as musicians, music ensembles, and
algorithms using the Graffoo notation (yellow boxes are classes, blue/green
arrows are object/datatype properties, purple circles are individuals, green
polygons are datatypes).

To derive requirements from various music stakeholders, we leverage the domain
expertise and views in Polifonia – a European H2020 project aiming to connect
“music, people, places and events” from the 16th century. The
interdisciplinarity of Polifonia, involving data engineers, anthropologists,
ethnomusicologists, historians of music, linguists, musical heritage
archivists, cataloguers, and creative professionals – makes it an ideal
testbed for this work.

Music Meta is part of the Polifonia Ontology Network [42], from which we reuse
the CORE module. This is done to consistently reuse general-purpose elements
of design (e.g. Person, Time, Place) and ontology design patterns. The reuse
of this module also ensures alignment with other foundational models (FOAF,
Dublin Core, etc.).

The ontology (prefixed as mm) is available at the following URI:
https://w3id.org/polifonia/ontology/music-meta/, and is released as open
source project under the CC-BY 4.0 on GitHub222https://github.com/polifonia-
project/music-meta-ontology.

###  3.1 Methodology

The development of Music Meta is driven by eXtreme Design (XD) [43], an agile
ontology engineering methodology that makes extensive use of ontology design
patterns (ODPs) – small ontologies that work as reusable templates for
recurrent modelling problems. An ODP is intuitive and compact, clearly and
formally defined, tackles a specific (sub)set of requirements, and is designed
for a modular reuse, enabling a pragmatic cognitive analysis [44].

In XD, a story-based approach guides the collection of requirements. A story
is a framework for _customers_ to describe their needs, and is composed of 4
sections: (i) the persona, a description of a typical user; (ii) the
overarching goal they need to address; (iii) the scenario, describing how the
goal will be address; (iv) the competency questions (CQs) translating needs
into formal requirements. Ontology modelling starts iteratively from the CQs,
and is based on the reuse of ODPs and existent templates.

####  3.1.1 From FRBR to Information Objects/Realisations

At the core of Music Meta lies the use of the Information-Realisation (IR) ODP
[45]. An _information object_ is a non-physical social object carrying
information that can have one or multiple materialisations (_information
realisations_). Each realisation is a particular physical object, or event,
realising the the information object, or involving the latter as a
participant. Both information object and realisation are intended as
information entities (IE), i.e. (social) objects created and/or used to
communicate, reason, and specify new entities. This allows to distinguish
between a piece of information (e.g. the _content_ of a composition) from how
it is materialised (e.g. as a performance).

On the other hand, both the Music Ontology [9] and DOREMUS [12] are built on
top of different flavours of FRBR[46] (FRBRer and FRBRoo, respectively). FRBR
is a conceptual model describing bibliographic resources at four levels: Work,
Expression, Manifestation, andItem. In contrast, the two levels of the IR
pattern map to Expression and Item, since Work and Manifestation are said to
provide non-informative conceptualisations [45]. Moreover, [47] argues that
FRBR’s Works – intended as “entities that pre-exist expressions”, cannot
represent improvisations or traditional music, as they do not derive from a
formal composition process leading to a realisation. FRBR’s Work is often
ambiguously intended as an entity retrospectively created for grouping
multiple expressions for cataloguing needs. As for the Manifestation level,
while its representation is straightforward in the bibliographic domain (e.g.
the printed version of a book), its correspondence in the music domain is not
fully intuitive, as it may relate to either a recording, a score, a compact
disc, or all the above – thereby introducing complexity and ambiguity.

Nevertheless, being aligned to two levels of FRBR, the IR ODP makes our model
leaner and flexible, while still achieving interoperability with FRBR-based
(music) ontologies. In fact, IE patterns are meant to boost the semantic
integration of contents, tools, platforms, resources that are silo-ed or non-
interoperable [45].

###  3.2 Main elements of design

From Polifonia’s CQs333https://github.com/polifonia-project/stories, we
identified those related to metadata, and aimed for a model capable to address
the requirements in Section 1.1. Music Meta follows a hierarchical design
(where each level extends the former to add expressiveness) and is
complemented by data transformation rules to conveniently translate one level
into another.

To enable data integration from existing knowledge bases and datasets, we
align Music Meta to other ontologies: the Music Ontology, DOREMUS, and
Wikidata, after having identified common/similar classes and properties.

####  3.2.1 Music artists

To represent music creatives the class mm:MusicArtist generalises over
musicians (mm:Musician), ensembles (mm:MusicEnsemble), and computational
methods (mm:MusicAlgorithm), as illustrated in Figure 1. Musicians are seen as
a specialisation of persons who can optionally be associated to a medium of
performance (e.g. voice, guitar), and be part of a music ensemble (e.g.
MusicGroup, Orchestra, Choir). Depending on the data available, the latter can
be expressed either through a membership relationship (core:isMemberOf), a
specialisation of the former, such as mm:isSingerOf, or through a
mm:MusicEnsembleMembership when the period of participation of the musician is
available.

All music artists can be associated to (one or more) mm:MusicGenre(s), express
influences or collaborations, and share a period of activity. Here, the start
date refers to the foundation for music ensembles, whereas the end date is
used for discontinued projects for algorithms.

####  3.2.2 Music inception

Figure 2: Abstracting music inception as an product of a creative process,
involving music artists in activities (music writing, instrumentation, etc.),
defined in time and space and according to different roles. Figure 3:
Describing a music entity and the elements it contains: Text, AbstractScore
and Instrumentation.

The focal point of Music Meta is the mm:MusicEntity class (Figures 2 and 3).
This class represents an Information Object, which is defined as the sum of
all the elements that make up a piece of music. A Music Entity is composed of
several components, including lyrics (generalised through mm:Text to also
account for mm:Libretto), the entailed musical content (mm:AbstractScore) and
its instrumentation (mm:Instrumentation).

A mm:AbstractScore provides an abstraction to describe the musical properties
of an entity, such as the form of a piece (mm:FormType), its constituents
parts (e.g. mm:Movement or mm:Section), and its key (mm:Key). Datatype
properties also describe the tempo of the composition (mm:tempo) and its order
(mm:orderNumber). A mm:Instrumentation can instead be formalised in a
mm:Score, which can be either digital or paper. Through the score, the
instrumentation describes one or more mm:MediumOfPerformance, each of which
has a cardinality (e.g. 3 violins).

It is also possible to describe relationships between different Music
Entities, defined by parthood (mm:hasPart) and derivation (mm:isDerivedFrom).
Derivations are used at the user’s discretion, based on the dominance of
concept [12] (whose criteria attribute proper identity to a musical entity)
and can be of different types: revision, transposition, cover, reconstruction,
reduction, etc. This makes it possible to describe different types of
compositions, rearrangements and modifications of an original piece, as well
as influences and more complex types of derivations. For example, the
production of a cover song (e.g. in a different musical genre) may keep the
lyrics and introduce a new composition and instrumentation, hence resulting in
a new mm:MusicEntity. In addition, Music Entities can be organised in
mm:Collection, according to a mm:CollectionConcept that binds them together.

In sum, the model provides flexibility across periods and genres as the
proposed classes allow generalisations to be made about the text, the musical
composition and its arrangement. (c.f. Section 1.1.1). Through the
specialisation of classes, depending on the target domain/application,
specificity can easily be achieved (c.f. Section 1.1.2). For example, a tune
family can be seen as a mm:Collection encompassing several tunes (as music
entities) based on specific criteria (e.g. similarity, provenance).

####  3.2.3 From performance to recording and broadcast

The realisation of a mm:MusicEntity is exemplified by mm:MusicalPerformance,
which can be either live (mm:LivePerformance) or in a studio
(mm:StudioPerformance). As illustrated in Figure 4, the place and time
interval of a performance are described by core:Place and core:TimeInterval –
involving one or more music artists (optionally, with a specific role). A
performance may also create a new mm:MusicEntity if, e.g., the execution
differs significantly from the original version.

A Music Entity can also be recorded by means of a mm:RecordingProcess, which
is a subclass of a mm:CreativeProcess. This makes it possible to describe
information about both the production (e.g., producers) and the technical
aspects of it (e.g., sound engineer, equipment used). The recording process
produces a mm:Recording, which is contained in a mm:Release.

Information about the broadcasting of a recording is modelled through the
mm:BroadcastingSituation class (an instance of the Situation ODP [48]), which
describes when and where the song was broadcast, and by which broadcaster
(mm:Broadcaster).

Figure 4: Describing performance, recording, broadcasting, publication, and
licensing.

####  3.2.4 Publishing and licensing information

The mm:PublicationSituation class describes information about the publication
of a release, which is common to the publication of a mm:Score (c.f. Figure
4). For both a release and a score, it describes when and where they were
published, and by a mm:Publisher.

Licence information is described by the mm:License class, which applies to
records, releases and scores.

####  3.2.5 Modelling links and integrating provenance

We propose a pattern based on _RDF*_ [49] to describe the provenance at
different levels (Figure 5). The use of RDF* is particularly useful for this
purpose, as it allows to embed provenance information to every triple in the
dataset. This simplifies and streamlines the model, eliminating the need for
n-ary relations or reification for each triple.

The proposed pattern is straightforward and comprises the class
core:Reference, which describes the source of the reference (using the class
core:Source) and the method used to obtain the annotation (using the class
core:SourceMethod). Additionally, the datatype properties core:confidence and
core:retrievedOn describe the confidence of the annotation and the date it was
produced, respectively.

Figure 5: Our pattern to describe provenance with RDF*.

###  3.3 Conversion rules and code support

To facilitate the reuse of Music Meta and its data conversion into OWL/RDF
Knowledge Graphs, we developed PyMusicMeta – a library to map arbitrary music
metadata into RDF triples. This enables a practical and scalable workflows for
data lifting to create Music KGs without expert knowledge of our ontological
model. The library is developed in Python as an extension of RDF-Lib [50].

With each triple, PyMusicMeta adds alignments to the supported schema whenever
possible. For example, the pseudo triple <DavidBowieURI, rdf:type,
mm:Musician> in Music Meta will be complemented with <DavidBowieURI, rdf:type,
http://purl.org/ontology/mo/MusicArtist> for Music Ontology, <DavidBowieURI,
rdf:type, http://erlangen-crm.org/E21_Person> for DOREMUS (via the Erlangen
Conceptual Reference Model [51]) and <DavidBowieURI, rdf:type,
https://www.wikidata.org/wiki/Q639669> for Wikidata; to achieve
interoperability of the Music KG.

##  4 Validation and Adoption

Following the XD methodology (c.f. Section 3.1), we validate Music Meta
against the competency questions (CQs) driving its design. In this context,
testing consists in formulating logical statements for each competency
question – using the ontology as a formal model. Logical statements are
encoded as SPARQL queries to evaluate the model. Examples of tested CQs
include “In which time interval did the creation process take place?” and
“Which is the language of the name/alias of a music artist?”. The complete
list of CQs, together with their correspondent SPARQL queries can be found in
the project’s repository. This also contributes a test framework where the
ontology is automatically tested using the available SPARQL queries [52],
whenever changes occur or new requirements are supported in future versions of
Music Meta.

Music Meta has already been used in ChoCo [40], the largest Harmony KG to
date, obtained from the integration of 18 MIR
datasets444https://github.com/smashub/choco. The ontology has also been
_specialised_ for folk metadata (Tunes Ontology) and _extended_ to describe
music datasets (CoMeta Ontology). All ontologies are part of the Polifonia
Ontology Network (PON) and can be found at https://github.com/polifonia-
project/ontology-network. We also provide documentation, examples, and
tutorials555https://polifonia-project.github.io/ontology-network/.

##  5 Conclusions

The interoperability of metadata is an essential requirement for the
integration of music datasets, which is currently hampered by the specificity
of existent ontologies.

Our work addresses interoperability requirements for the design of the Music
Meta ontology – a rich and flexible semantic model for (Western) music
metadata across different genres and periods, for various stakeholders and
music datasets. The model is based on the Information-Realisation ontology
design pattern, allowing to reduce complexity while maintaining alignment to
other ontologies (Music Ontology, DOREMUS). We validate Music Meta following
the XD methodology, to demonstrate the support of requirements collected from
various stakeholders (music analysts, archivists, musicologists, and data
engineers). The model has modular design – allowing users to describe music
data depending on their specificity and type, while providing provenance
support through RDF*.

We are extending the evaluation of Music Meta across cultural heritage and
music industry datasets, while working with our stakeholders to specialise the
model for the integration and release of Music Knowledge Graphs.

Acknowledgements This project has received funding from the European Union’s
H2020 research and innovation programme under grant agreement No 101004746.
The authors also acknowledge Philippe Rigaux, Peter van Kranenburg, Marco
Gurrieri, and Mari Wigham for their support and feedback throughout the design
of Music Meta.

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Forward-backward correlations in proton-proton collisions at the LHC energy: A
model based study

Joyati Mondal1$\star$, Somnath Kar1$\star$, Hirak Koley1, Srijita Mukherjee1,
Argha Deb1,2 and Mitali Mondal1,2 $\star$

1 Nuclear and Particle Physics Research Centre, Jadavpur University, Kolkata
700032, India

2 School of Studies in Environmental Radiation and Archaeological Sciences,
Jadavpur University, Kolkata 700032, India

*<EMAIL_ADDRESS>*<EMAIL_ADDRESS>*<EMAIL_ADDRESS>
50th International Symposium on Multiparticle Dynamics (ISMD2021)
12-16 July 2021

## Abstract

Forward-backward (FB) multiplicity and momentum correlations of produced
particles between symmetrically located pseudorapidity ($\eta$) intervals have
been studied using the $p$QCD inspired EPOS3 model with and without
hydrodynamical evolution of particles in proton-proton ($pp$) collisions at
the center-of-mass energy, $\sqrt{s}=13$ TeV. The pseudorapidity-gap
($\eta_{gap}$) dependence of FB correlation strength is compared with our
previously published results at $\sqrt{s}=$ 0.9, 2.76 and 7 TeV. The study
reveals that the general trends of FB correlation strength at $\sqrt{s}=13$
TeV are similar to our previous observations at lower center-of-mass energies.
We also find that the $\delta\eta$-weightage average of FB correlation
strength as a function of different center-of-mass energies ($\sqrt{s}=$ 0.9,
2.76, 7 and 13 TeV) tends to saturate at very high energy.

##  1 Introduction

Forward-backward correlation, a robust tool, plays important role in
understanding the dynamics of multiparticle interactions and their
hadronization in different collision systems. Various experiments including
CERN Super Proton Synchrotron (SPS) & the Large Hadron Collider (LHC), the
Tevatron, the Relativistic Heavy Ion Collider (RHIC) observed sizeable FB
correlation strength in heavy-ion collisions as well as in small collision
systems.
In this contribution, we have studied the FB multiplicity and momentum
correlation in $pp$ collisions at $\sqrt{s}=13$ TeV using the Monte-Carlo
event generator, EPOS3 [1, 2] featuring with and without hydrodynamical
evolution (abbreviated as “with and without hydro" in the rest of the texts)
of particles. We have compared our results with our previously published
results using the same model at $\sqrt{s}=$ 0.9, 2.76 and 7 TeV [3] and with
the available Quark-Gluon String Model (QGSM) predictions at the top LHC
energy [4].

##  2 Forward Backward Charged Particle Correlation Coefficient

Generally, FB correlations can be categorized into three main types [5]:
correlation between charged-particle multiplicities $(n-n)$, between mean or
summed transverse momenta of charged particles $(p_{T}-p_{T})$ and between
mean or summed transverse momenta in one $\eta$ interval and the multiplicity
of charged particles in another $\eta$ interval $(p_{T}-n)$. In our present
analysis, we have explored first two types of FB correlation in detail. The FB
correlation strength is measured in a coordinate system with origin $\eta=0$
which is the collision vertex. Two $\eta$ intervals are selected: one in the
forward ($\eta>0$) and another in the backward hemispheres ($\eta<0$) in the
center-of-mass system. FB multiplicity correlation coefficient
$b_{corr}(mult)$ and FB momentum correlation coefficient $b_{corr}\left(\Sigma
p_{T}\right)$ have been estimated using the following formula of Pearson
Correlation Coefficients [6]

$b_{corr}(mult)=\frac{\langle N_{f}N_{b}\rangle-\langle N_{f}\rangle\langle
N_{b}\rangle}{\langle N_{f}^{2}\rangle-\langle N_{f}\rangle^{2}}\text{,}$ (1)
$b_{corr}(\Sigma p_{T})=\frac{\langle\Sigma p_{T_{f}}\Sigma
p_{T_{b}}\rangle-\langle\Sigma p_{T_{f}}\rangle\langle\Sigma
p_{T_{b}}\rangle}{\langle(\Sigma p_{T_{f}})^{2}\rangle-\langle\Sigma
p_{T_{f}}\rangle^{2}}$ (2)

Here, $N_{f}$ and $N_{b}$ are the charged particle multiplicity in F and B
window respectively. $\Sigma p_{T_{f}}$ and $\Sigma p_{T_{b}}$ are the event
summed transverse momentum in F and B window respectively.

##  3 The EPOS3 Model

The EPOS3 model is based on Gribov-Regge multiple scattering theory [1]. In
this approach an individual scattering is labeled as a Pomeron which creates a
parton ladder carrying the transverse momentum from the initial hard
scatterings [2]. In a collision, many elementary parton-parton hard
scatterings form a large number of flux tubes that expand and are fragmented
into string segments. Higher string density forms “core" which undergoes full
3D+1 viscous hydrodynamical collective expansion expecting no jet parton
escape. Another part of lower string density forms “corona" where we can
expect the escape of jet partons. Using EPOS3 model, we have generated 3
million minimum-bias $pp$ events at $\sqrt{s}=13$ TeV, for each of the
options, with and without hydro.

##  4 Results

The whole analysis have been carried out following ALICE [7] and ATLAS [8]
kinematics. We have selected events having a minimum of two charged particles
in the chosen kinematic intervals.

ALICE kinematics | ATLAS kinematics
---|---
0.3 < $p_{T}$ < 1.5 (GeV) and |$\eta$| < 0.8 |  $p_{T}$> 0.1 (GeV) and |$\eta$| < 2.5

###  4.1 Dependence on the gap between FB windows ($\eta_{gap}$)

The variations of FB multiplicity and momentum correlation coefficients
estimated using Eq. 1 & 2 with $\eta_{gap}$ of window widths 0.4 and 0.5 for
EPOS3 simulated $pp$ events with and without hydro at $\sqrt{s}=13$ TeV
following ALICE (left panel) and ATLAS (right panel) kinematics have been
shown in Fig. 1. FB multiplicity correlations are compared to the QGSM
calculation [4].

Figure 1: (a) $b_{corr}(mult)$ and (b) $b_{corr}\left(\Sigma p_{T}\right)$ as
a function of $\eta_{gap}$.

###  4.2 Dependence on Collision Energy ($\sqrt{s}$)

Center-of-mass energy dependence of $\delta\eta$-weightage average of FB
multiplicity and momentum correlation is exhibited in Fig. 2 for both ALICE
and ATLAS kinematics. Red points represent corresponding experimental data.

Figure 2: (a) $\left<b_{corr}(mult)\right>_{\delta\eta}$ and (b)
$\left<b_{corr}\left(\Sigma p_{T}\right)\right>_{\delta\eta}$ as a function of
centre-of-mass energy ($\sqrt{s}$).

##  5 Conclusion

We have investigated the dependence of FB correlation strength on $\eta_{gap}$
at $\sqrt{s}=13$ TeV for EPOS3 simulated with and without hydro $pp$ events.
From the study we find that the FB correlation strengths decrease slowly with
the increase of $\eta_{gap}$ at $\sqrt{s}=13$ TeV for both EPOS3 hydro and
without hydro events which resemble our previous observations at lower center-
of-mass energies [3]. It is evident that our results are in qualitative
agreement with the available QGSM predictions [4]. We also find that the
$\delta\eta$-weightage average of FB correlation strength tends to saturate at
very high energy.

## Acknowledgements

The authors are thankful to the members of the grid computing team of VECC,
Kolkata and cluster computing team of Department of Physics, Jadavpur
University for providing uninterrupted facility for event generation and
analyses. We also gratefully acknowledge the financial help from the DHESTBT,
WB. J. M acknowledges DST-INDIA INSPIRE fellowship Scheme and S. K
acknowledges the financial support from UGC-INDIA DSK-PDF under Grant No.
F.4-2/ 2006(BSR)/PH/19-20/0039.

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