Master Thesis

Quantitative evaluation of muon track
matching eﬃciency with Muon Forward
Tracker and Muon Spectrometer at
LHC-ALICE

Kaede Kamano
18810015
High Energy Physics Laboratory,
Department of Mathmatical and Physical Sciences,
Graduate School of Humanities and Science,
Nara Women’s University
March 27, 2020

Abstract
ALICE has been researching physics in extremely high temperature and highdense matter that is generated by heavy-ion collision using LHC. One of them isto understand the mass generation mechanism by the chiral symmetry breaking.
The measurement target is low mass vector mesons that decay dimuon. Extensive
eﬀorts in the ALICE upgrade projects are currently being made toward LHC-Run3(2021-2024). One of the new detectors is the Muon Forward Tracker (MFT) thatconsists of 5 disks made of silicon pixel detectors that have high position resolution.
MFT is newly installed in the Muon Spectrometer (MUON). MUON has the hadron
absorber in front of the detector so that there is no way to get the track information
before the absorber. Muon has been measured the way to extrapolate the muontrack measured by MUON to the vertex. In this method, there are problems with the
track angles measurements that aﬀect the invariant mass measurements especiallyin low pT regions that is greatly aﬀected by the multiple scattering eﬀects in theabsorber. Track performance and rejection power of muon from hadron decay are
improved by installing MFT between the vertex and the absorber.
Track matching between MFT and MUON is crucial to improve the invariant
mass resolution and reject muons from hadron decays in the hadron absorber. Track
matching is connecting the same muon track before and after the absorber with
MFT and MUON. In the experiment, the MUON track is extrapolated throughthe absorber towards the primary vertex, and the best MFT track is chosen toconnect with that MUON track at the last MFT plane. In this study, the track
matching algorithm between MFT and MUON is developed and evaluated. We
need to consider the multiple scattering eﬀects in the absorber in the track matching.
Multiple scattering eﬀects of muons in the absorber is simulated, and the correlation
distribution of track position and angle of the muons measured by MUON at thecollision point side of the absorber, that is, on the MFT side. The size of thesearch window depends on the momentum of the muon track and the center of the
distribution of the track position and angle depends on the position and angle ofthe muon track measured by MUON. To use the same track matching algorithm invarious momentum regions, the correlation distribution of the position and angle isnormalized and the matching parameter R that can be used regardless of momentum
is developed. As a result, the background is significantly reduced.

Contents
1 Introduction1

1.1

Standard model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3

Quark-Gluon Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.4

High energy heavy-ion collisions . . . . . . . . . . . . . . . . . . . . . . . .

3

1.5

Chiral symmetry breaking and its restoration . . . . . . . . . . . . . . . .

4

1.6

Low mass vector meson . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.7

Previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

1.8

Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72 Experimental setup
2.1

8

Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.1.1

LHC schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92.2 ALICE Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.2.1

Muon Spectrometer (MUON) . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Muon Forward Tracker (MFT) . . . . . . . . . . . . . . . . . . . . .
3 Development of MFT-MUON track matching
3.1

11
15

Tracking with MFT and MUON . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Number of MFT track candidates for MUON track . . . . . . . . . . . . . 16
3.2.1

Multiplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.2 Multiple scattering eﬀect [15] . . . . . . . . . . . . . . . . . . . . .

17

3.2.3 Number of MFT track candidates . . . . . . . . . . . . . . . . . . . 18
3.3 Development of matching method with the correlation between track position and angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.1

Correlation between track position and angle . . . . . . . . . . . . . 19

3.3.2 Geant4 simulation setup . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.3 Number of candidates determined by correlation . . . . . . . . . . . 24
3.3.4 Confirmation of Geant4 simulation . . . . . . . . . . . . . . . . . . 27
I

3.4 Preparation for evaluation of matching algorithm . . . . . . . . . . . . . . 29
4 Evaluation of developed matching algorithm
4.1

34

Simulation tool for Heavy Ion Collisions . . . . . . . . . . . . . . . . . . . 34

4.2 Evaluation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5 Summary and Outlook

41

Acknowledgement

42

References

43

IIList of Figures
1

Elementary particles of the standard model. . . . . . . . . . . . . . . . . .

1

2

Phase diagram of QCD matter. [4] . . . . . . . . . . . . . . . . . . . . . .

2

3

The time evolution of a high energy heavy ion collision. [5] . . . . . . . . .

4

4

Quark mass in the QCD vacuum and the Higgs vacuum. Horizontal axis
shows total quark mass and vertical axis shows mass that arise out of the
Higgs mechanism. [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Quark mass in the QCD vacuum and the Higgs vacuum. Horizontal axis
shows total quark mass and vertical axis shows mass that arise out of the
Higgs mechanism. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

Obtained e+ e− distribution with fit result by KEK-PS E325 collaboration.
The points with error bars represent the data. The solid lines represent the
fit results with an expected ϕ → e+ e− shape and quadratic background.
The dashed lines represents the background. [10] . . . . . . . . . . . . . . .

7

7

The CERN accelerator complex. [11] . . . . . . . . . . . . . . . . . . . . .

88Long term LHC schedule. [12] . . . . . . . . . . . . . . . . . . . . . . . . .

99

3D schematic of ALICE detector for LHC-Run3. . . . . . . . . . . . . . . . 10

10

Schematic illustration of the ALICE Muon Spectrometer.[2] . . . . . . . .

11

Schematic illustration of muon tracker in ALICE (top) until LHC-Run 2
and (bottom) from LHC-Run 3. [13] . . . . . . . . . . . . . . . . . . . . . 12

12

General layout of MFT Half-Cone. [1] . . . . . . . . . . . . . . . . . . . . . 13

13

Half-disk-0. [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

Schematic illustration of the MFT / MUON reconstruction stages (left)
and schematic illustration of the MFT / MUON matching search window(right). [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

15

Charged-particle pseudo-rapidity density for ten centrality classes over a√broad η range in Pb-Pb collisions at sN N = 5.02 TeV. Boxes aroundthe points reflect the total uncorrelated systematic uncertainties, while
the filled squares on the right reflect the correlated systematic uncertainty(evaluated at η=0). Statistical errors are generally insignificant and smaller
than the markers. [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

16

Charged-particle density at the last MFT plane estimated by Figure 15.
Pseudo rapidity range is −3.5 < η < −2.5. . . . . . . . . . . . . . . . . . .

5

6

17

11

14

17

Schematic drawing of multiple scattering. . . . . . . . . . . . . . . . . . . . 18

III

18

(left) Standard deviation of angular distribution as a function of muontransverse momentum. (right) Standard deviation of position distribution
as a function of muon transverse momentum. . . . . . . . . . . . . . . . . . 18

19

The number of MFT track candidates determined by multiple scattering√at η = 3 of the last MFT plane in 0-5% central Pb-Pb collision at sN N =5.02 as a function of pT obtained from equation 1 . . . . . . . . . . . . . . 19

20

Schematic of muon passing through the absorber. . . . . . . . . . . . . . . 20

21

(left) Illustration of the expected distribution of the position and angle atthe entrance of the absorber for the muon that is x = 0 at the exit of theabsorber. (right) Schematic illustration of the muon passing through theabsorber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

22

(left) Red line indicating a possible association of the position and angle fortracks that originate near the vertex. Expected distribution of the position
and angle at the entrance of the absorber for the muon that is x = 0 at theexit of the absorber. (right) Schematic of the muon passing through theabsorber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

23

Schematic drawing of the Geant4 simulation setup . . . . . . . . . . . . . . 22

24

Event display of Geant4 simulation. Muon is injected from steel side atη = 3 (θ ∼ 5.7◦ ) towards the vertex (z = 0 m). . . . . . . . . . . . . . . . . 23

25

Correlation distribution of the position and angle of transverse momentum
pT = 1 GeV/c (left) and pT = 2 GeV/c (right). . . . . . . . . . . . . . . . . 23

26

Correlation distribution of the position and angle of transverse momentum
pT = 1 GeV/c simulated by Geant4. The red straight line indicating thecorrelation between the position and angle at the left side of the absorber(z = −0.9 m) of tracks that originate near the vertex. Each elliptical line
above the correlation distribution indicates eﬃciency. Overlap region of
the red line and each eﬃciency line are defined as the search window. . . . 24

27

One dimensional search window determined by the correlation distributionof the position and angle as a function of pT . . . . . . . . . . . . . . . . . . 25

28

The number of MFT track candidates at η = 3 of the last MFT plane√in 0-5% central Pb-Pb collision at sN N = 5.02 TeV as a function of pT
obtained from equation 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

29

Comparison of the number of MFT track candidates before and after background subtraction. Red dot represents the number of candidates before
background subtraction and blue dot represents after subtraction. . . . . . 27

30

Schematic drawing of the confirmation simulation setup. . . . . . . . . . . 28

IV

31

(left) Correlation between the position and angle at the entrance of theabsorber for muon that is injected from the exit of absorber towards thevertex at η = −3 (same situation as 3.2.2). (right) Correlation between theposition and angle at the entrance of the absorber for muons that reached
the range around pseudo-rapidity η = −3 at the exit of the absorber. . . . 29

32

Process to convert the elliptical distribution to circular distribution that
center is zero. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

33

Projection of Figure 33-4 onto the x-axis (left) and y-axis (right), respectively. Each histogram is fit by Gaussian function. . . . . . . . . . . . . . . 31

34

Standard deviation σx and σθx in step 4 as a function of pT . Each standard
deviation is obtained from the fit values of Figure 33. . . . . . . . . . . . . 31

35

Original distributions (left) and distributions after conversion (right) with
eﬃciency lines. The upper (lower) panel is pT = 1 GeV (pT = 2 GeV).
Contour lines of eﬃciency can be written regardless of transverse momentum. 32

36

Percentage of entries in the right panel of Figure 35 as a function of radiusr. Diﬀerent color dots indicate diﬀerent pT . . . . . . . . . . . . . . . . . . 33

37

Distribution of the position and angle for x direction at the last MFT plane.
pT of embedded single muon is shown in each panel. . . . . . . . . . . . . . 36

38

Distribution of the normalized position x and angle θx for x direction. pTof embedded single muon is shown in each panel. . . . . . . . . . . . . . . 36

39

Distribution of rx and ry. pT for embedded single muon is shown in eachpanel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

40

Distribution of rx . Red line represents embedded muon and blue line represents background. pT of embedded single muon is shown in each panel. . 38

41

Distribution of ry . Red line represents embedded muon and blue line represents background. pT of embedded single muon is shown in each panel. . 38

42

Distribution of R. Red line represents embedded muon and blue line represents background. pT of embedded single muon is shown in each panel. . 39

43

Distribution of R only for background. pT of embedded single muon isshown in each panel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

44

Ranking of how small the two-dimensional matching quality parameter Rof the embedded muon was among all entries. pT is shown in each panel. . 40

′

V

′

List of Tables
1

Geometrical parameters of the hadron absorber. . . . . . . . . . . . . . . . 10

2

Geometrical parameters of MFT. [1] . . . . . . . . . . . . . . . . . . . . . .

143

Main specification for MFT sensors [1] . . . . . . . . . . . . . . . . . . . .

14

4

Assigned values for multiple scattering calculations . . . . . . . . . . . . . 18

5

Assigned values in the Geant4 simulation . . . . . . . . . . . . . . . . . . . 22

6Comparison of the standard deviation between the simulation and the multiple scattering calculation (Section 3.2.2) at pT = 1 GeV/c. . . . . . . . . 23

7

Geometrical parameters of the hadron absorber in the confirmation simulation 27

8

Assigned parameters in the confirmation simulation. . . . . . . . . . . . . . 28

VI

1

Introduction

1.1Standard model

There are four fundamental forces which are gravitational, electromagnetic, strong andweak interactions. The standard model is the theory that describes the three of the four
fundamental forces, electromagnetic, strong, and weak interactions. All matter in theworld is made of atoms. Atom is made of nucleus and electrons. Nucleus is made of protons
and neutrons. Proton and neutron are made of quarks which are one of the elementary
particles. Elementary particle is the smallest component of matter. Elementary particlesof the standard model consist of elementary fermions and elementary bosons. Fermions areclassified into (anti-)quarks and (anti-)leptons, which follow the Pauli exclusion principle.
Bosons are classified into gauge bosons and scalar bosons. Gauge bosons are force carriers
that mediate the strong, weak, and electromagnetic interactions. Scalar bosons, namely
higgs bosons, give other particles their mass. Figure 1 shows the elementary particles ofthe standard model.

Figure 1: Elementary particles of the standard model.

1

1.2

Quantum Chromodynamics

The quantum chromodynamics (QCD) is the theory that describes the strong interaction
between quarks and gluons. QCD has two main properties such as color confinement andasymptotic freedom. Quarks and gluons have a color charge. Color charge is described byanalogy to the primary colors of light (red, green and blue). When a particle does not havea color charge, it is called "white". The strong interaction is mediated by exchanging gluons
that carry color charges. The strong force increases when the distance between color
charges is larger. The distance between color charges is beyond some critical distance,a new quark and anti-quark pair pop up from the vacuum. Therefore, quark can notexist by itself, and observed hadrons are always "white". This property is called color
confinement. While the strong interaction decreases when the distance between color
charges is smaller, and quarks and gluons can move freely like free particles. Quarks andgluons are not confined in hadrons under extremely high temperature and/or density.
This property is called asymptotic freedom.

1.3

Quark-Gluon Plasma

Quark-gluon plasma (QGP) is a state of matter where quarks and gluons are no longer
confined in hadrons under extremely high temperature and/or density. QGP is believed
to exist in the primordial universe up to a few microseconds after Big Bang or in neutronstars, as shown in Figure 2. Lattice QCD predicts the critical temperature Tc between
hadronic state and QGP state is Tc ∼ 160 MeV. QGP can be created experimentally by
momentarily generating high temperature and high pressure by high energy heavy ion
collision.

Figure 2: Phase diagram of QCD matter. [4]

2

1.4

High energy heavy-ion collisions

To create QGP, particle accelerators deliver relativistic high energy head-on collisions
between massive ions such as gold or lead nuclei. The collisions are dynamical processes
with a very short time scale. Figure 3 shows the time evolution of a high energy heavy
ion collision. The temperature scale of high energy heavy ion collision is 100 MeV ∼ 1012
K, and the timescale is 10 fm/c ∼ 10−23 seconds.
Initial state
Nuclei are accelerated at close to the speed of light. Therefore the thickness of nuclei
shrinks to 1/γ in direction of travel due to Lorentz contraction.

Pre-QGP
Partons that are constituents of nuclei interact by collision. A reaction surface that is ahigh density is made where the partons collide. Quarks and gluons are excited by thisenergy and scattered.

QGP state
Due to the repeated scattering of quarks and gluons on the reaction surface, the systemreaches thermalization and the temperature of the system rises above the phase transition
temperature Tc . Above Tc , quarks and gluons are not confined in hadrons, which is called
QGP state.

Hadronization
Over time, the system begins to cool, and hadrons are generated from partons. In thisstate, the ratio of particles is not fixed yet because inelastic collisions between particles
still exist. The temperature at which particle ratio is fixed is called the chemical freezeout temperature Tch . The system continues to expand, at some point, particles stop
interacting with each other, which is called kinematic freeze-out. The temperature ofthis state is called the kinematic freeze-out temperature Tf o . Hadrons travel and will beobserved by detectors.

3

Figure 3: The time evolution of a high energy heavy ion collision. [5]1.5Chiral symmetry breaking and its restoration

To understand chiral symmetry breaking and its restoration in QGP is one of the important research tasks in physics. Proton and neutron are made of quarks. The mass ofthe proton is mp ∼ 988 MeV/c2 . The valence quarks of the proton are two up quarks(mu ∼ 2.4 MeV/c2 ) and one down quark (md ∼ 4.8 MeV/c2 ). The total mass of thevalence quarks is just 2% of the proton mass. The quark mass arises out of the Higgs
mechanism.[6] The rest of the proton mass arises out of chiral symmetry breaking. As
the universe cooled after Big Bang, pair of quark and anti-quark was condensed in thevacuum by Bose-Einstein condensation. Therefore vacuum is no longer empty but filledwith a medium that has quark condensate. When matter moves, the matter has to thrust
quark condensate. This is the mechanism to give matter its mass. This transition from anempty vacuum to a vacuum filled with the quark condensate is called the chiral symmetry
breaking.
To probe the mass generation mechanism by the chiral symmetry breaking, what should
we observe? The quark condensate itself is not observable, but its strength depends on
temperature and density. Figure 4 shows the strength of the quark condensate depending
on temperature and density. We have two methods to prove the mass generation mechanism by the chiral symmetry breaking. First is to create an extremely high-temperature
matter (such as QGP) by colliding nuclei accelerated at close to the speed of light, andexamine a mass distribution of matter inside the extremely high-temperature matter.
Second is to inject particles whose character is well known into a nucleus, which is supposed to be a high-density medium, and examine the mass diﬀerence between the particles
before and after. [7]4Figure 4: Quark mass in the QCD vacuum and the Higgs vacuum. Horizontal axis shows
total quark mass and vertical axis shows mass that arise out of the Higgs mechanism. [8]1.6

Low mass vector meson

Low mass vector mesons ω and ϕ are some of the good tools to observe the mass modifications due to the chiral symmetry restoration. ω and ϕ mesons have a short lifetime,
therefore they are likely to decay in QGP that is the extremely high-temperature matter
where the strength of the quark condensate is smaller. ω and ϕ mesons have dimuon
decay mode. Dimuon is not aﬀected by the strong interaction in QGP. Low mass vector
mesons ω and ϕ mesons consist of light quarks. Figure 5 shows masses that arise out of
the Higgs mechanism vs total quark mass. Total quark mass is the quark mass in the
QGP vacuum. Masses of heavy quarks (c, t, b) are almost exclusively generated throughtheir coupling to the Higgs field, while masses of light quarks (u, d, s) are dominated by
the spontaneous chiral symmetry breaking. Therefore ω and ϕ are suited to observe themass modifications due to the chiral symmetry restoration.

5

Figure 5: Quark mass in the QCD vacuum and the Higgs vacuum. Horizontal axis shows
total quark mass and vertical axis shows mass that arise out of the Higgs mechanism. [9]1.7Previous research

In-medium modification of the ϕ meson at normal nuclear density has been measured
by KEK-PS E235 collaboration (2007). KEK-PS E325 was conducted at the KEK 12
GeV Proton-Synchrotron. Proton beam was injected to the fixed copper and carbon
targets to search for in-medium mass modifications of vector meson in the reaction 12′
GeV p + A → ϕ + X → e+ e− + X . Figure 6 shows the e+ e− distribution from ϕmeson. A significant√ excess on the low-mass side of the ϕ meson peak in observed in
the low βγ(= β/ 1 − β 2 ) region of ϕ meson (βγ < 1.25) with copper targets (Figure 6
upper right). This observation is consistent with the picture of the ϕ modification in the
nucleus. Thus, this study is one of the results that experimentally verified vector meson
mass modification at normal nuclear density.

6Figure 6: Obtained e+ e− distribution with fit result by KEK-PS E325 collaboration. The
points with error bars represent the data. The solid lines represent the fit results withan expected ϕ → e+ e− shape and quadratic background. The dashed lines represents the
background. [10]1.8

Motivation

Partial restoration of chiral symmetry is expected to occur in an extremely high-temperature
matter such as QGP or a high-density medium such as a nucleus. Chiral symmetry
restoration in QGP has not been observed yet. Low mass vector mesons ω and ϕ thathave dimuon decay mode are one of the good tools to observe the mass modifications dueto the chiral symmetry restoration in QGP. High mass resolution is needed to observe themass modification. The Muon Forward Tracker, a new silicon tracking detector installedin the existing muon detector in ALICE, will deliver a better mass resolution. Mass resolution is determined by tracking accuracy between new and old detectors. In this study,
the development and evaluation of the track matching between new and old detectors
using the correlation between track position and angle are discussed.

7

2

Experimental setup

2.1

Large Hadron Collider

At the Large Hadron Collider (LHC), the beam will stop for months to years between
physics experiments. This period is for maintenance and upgrades for the acceleratorsand detectors. The LHC is the most powerful particle collider built at the European
Organization for Nuclear Research (CERN) in 2008. The LHC consists of a 27-kilometerring of superconducting magnets with several accelerating structures to boost the energyof the particles. Two high energy hadron beams are accelerated at close to the speed oflight before they are made to collide. There are four main detectors located undergroundat the LHC’s interaction points that are ATLAS, CMS, LHCb, and ALICE.

Figure 7: The CERN accelerator complex. [11]8

2.1.1

LHC schedule

The LHC is shut down for two years from 2019 to the end of 2020 (Long Shutdown 2, LS2)
as shown in Figure 8. The ALICE collaboration is currently working for a major upgrade
during LS2. The new ALICE will have enhanced read-out capabilities and improved
accuracy and eﬃciency in tracking particles and identifying the interaction vertex. The
Muon Forward Tracker is also installed during LS2. The LHC will restart in 2021 andrun until the end of 2024 (Run 3).

Figure 8: Long term LHC schedule. [12]2.2

ALICE Detector

ALICE (A Large Ion Collider Experiment) has been designed to study QGP in heavy
ion collisions at LHC. High energy heavy ion collision experiment is the only experimentto access extremely high temperature and density where QGP is created. About twenty
detectors are set to detect various particles created by the heavy ion collisions. Extensive
eﬀorts in the ALICE upgrade projects are currently being made toward LHC-Run3 (20212024). Figure 9 shows the 3D schematic of ALICE detector for LHC-Run3. The heightof the ALICE detector is approximately 16 m and length is 20 m. Beam axis is definedas z axis, and the other horizontal axes are defined as x and y axes. The center of the
ALICE detector is defined (x,y,z)=(0,0,0).

9

Figure 9: 3D schematic of ALICE detector for LHC-Run3.

2.2.1

Muon Spectrometer (MUON)

Identification and measurement of muons in ALICE are currently performed by the Muon
Spectrometer (MUON) shown as 8 and 10 in Figure 9. MUON consists of a hadron
absorber (shown as Front absorber in Figure 10), a dipole magnet, five tracking chambers,
an iron wall and two trigger chambers. The schematic illustration of MUON is shown in
Figure 10. MUON acceptance covers the pseudo-rapidity region −4.0 < η < −2.5. The
hadron absorber made of carbon, concrete and steel suppresses all particles except muonscoming from vertex. It is placed between z = -0.9 m and z = -5.03 m, and the material
budget corresponds to ∼ 60X0 (∼ 10λint ). The hadron absorber provides a reliable muon
filter for momenta above 4 GeV/c (pT ∼ 0.5 GeV/c). Table 1 summaries the geometricalparameter of the hadron absorber. A dipole magnet provides a magnetic field of 0.7 T
in horizontal direction. A 1.2 m (∼ 7.2λint ) thick iron wall is placed between tracking(TRK1-5) and trigger (TRG1-2) systems as shown in Figure 10. The iron wall absorbs
the residual secondary hadrons emerging from the hadron absorber.
Table 1: Geometrical parameters of the hadron absorber.
Material Length (cm) Radiation length (cm)
Carbon225
18.8
Concrete
126
10.7
Steel
62
1.76
Total
413
-

10

Figure 10: Schematic illustration of the ALICE Muon Spectrometer.[2]MUON has provided a wealth of results. However, MUON has an critical limitationthat track information around the vertex region is not available. This is due to the large
distance of the tracking stations from the primary vertex and the multiple scattering in the
hadron absorber. The detail tracking information around the vertex region are completely
smeared out, therefore we have very limited possibilities to reject muons coming from semimuonic decays of pions and kaons that is an major background both in single muon anddimuon analyses especially at low masses and/or low pT . Also, the lack of details in thevertex region prevents us to disentangle prompt and displaced J/ψ production. Besides,
the degradation of the track direction resolution due to multiple scattering in the hadron
absorber greatly aﬀects the mass resolution especially at low masses in the region of ωand ϕ mesons.

2.2.2

Muon Forward Tracker (MFT)The Muon Forward Tracker (MFT) is a silicon pixel director added between the primaryvertex and the hadron absorber of the Muon Spectrometer, shown as 9 in Figure 9.
MFT acceptance covers the pseudo-rapidity region −3.6 < η < −2.45. Figure 11 shows
the schematic illustration of a muon tracker in ALICE until LHC-Run 2 (top) and from
LHC-Run 3 (bottom). MFT gives access to new measurements that are not possible with
the LHC-Run 2 MUON setup. The basic idea of MFT is to match the extrapolated muontracks coming from the tracking chambers (MUON) after the hadron absorber with the
tracks measured in MFT planes before the hadron absorber. Track around the primaryvertex is available by track matching between MFT and MUON. That gives us a better
mass resolution and rejection of muons from decay hadrons.

11

Figure 11: Schematic illustration of muon tracker in ALICE (top) until LHC-Run 2 and(bottom) from LHC-Run 3. [13]MFT consists of two half-MFT cones. Figure 12 shows the general layout of MFT halfcone. Each half-MFT cone consists of 5 half-disks positioned along the beam axis. A
half-disk consists of a disk spacer, a disk support, two printed circuit boards and thesensor ladders. Table 2 summarizes the geometrical parameters of MFT. The sensor
ladders consists of silicon pixel sensors soldered to a Flex Printed Circuit with aluminum
strips. Figure 13 shows the half-disk-0. Table 3 summarizes the main specification of
MFT sensors.

Physics program with MFTSome physics that can be measured with MFT are described below.
• Evaluation of the medium temperature and study of charmonium dissociation and′regeneration mechanism via measurements of prompt J/ψ and ψ production and12elliptic flow.
• Study of the degree of thermalization of heavy quarks in the medium via measurements of heavy flavor and charmonium elliptic flow.
• Extract of the energy density of the medium, the color charge and mass dependenceof parton in medium energy loss via measurements of heavy quark production separately for charm and beauty in the single muon channel and J/ψ from b-hadron
decay.
• Investigation of the chiral nature of the phase transition via measurement of low
mass vector mesons.

Figure 12: General layout of MFT Half-Cone. [1]13Table 2: Geometrical parameters of MFT. [1]Half-Disk0
12
3
4
Full MFT
Inner radius (mm) 25.0 25.0 25.0 38.2 39.2
Outer radius (mm) 92.6 98.0 104.3 130.1 143.5
z-position (mm)-460 -493 -531 -687 -768
No. sensors
64
64
76
112
132
896

Figure 13: Half-disk-0. [1]Table 3: Main specification for MFT sensors [1]Parameter
Value
Spatial resolution∼ 5µm
Pixel pitch∼ 25µmDetection eﬃciency> 99.5%Integration time
< 20µmSensor thickness
50µm
Binary output
1-bit
Power dissipation< 150 mW/cm2

14

3

Development of MFT-MUON track matching

3.1

Tracking with MFT and MUON

Figure 14 (left) shows the tracking flow with the MFT and MUON. Tracks are reconstructed by MFT and MUON separately. Most MFT tracks are from hadrons. Hadrons
stop at the absorber and only muons can go through the absorber. MFT that placed
upstream of the absorber has hundreds of tracks, while MUON that placed downstreamof the absorber has only several tracks. To reconstruct Global MFT/MUON tracks, thebest MFT track should be selected from MFT track candidates for one MUON track. The
MUON track is extrapolated throughout the absorber towards the primary vertex. The
search window is then determined at the last MFT plane taking into account the eﬀect ofmultiple scattering and energy loss in the hadron absorber as shown in Figure 14 (right).
When the momentum of the MUON track is smaller, the search window becomes larger
due to the eﬀect of multiple scattering and the number of the MFT track candidates
becomes larger. The MFT tracks in the search window are the matching candidates oneof which is supposed to match a MUON track. A matching quality parameter of each
MFT track candidate is calculated for a MUON track. A matching quality parameter is
explained in Section 4. The MFT track candidate that has the best matching quality is
selected as the best MFT track.

Figure 14: Schematic illustration of the MFT / MUON reconstruction stages (left) andschematic illustration of the MFT / MUON matching search window (right). [1]

15

3.2

Number of MFT track candidates for MUON track

The number of the MFT track candidates at the last MFT plane with the MUON track
extrapolated throughout the hadron absorber is calculated as below. The number ofcandidates < N > at arbitrary pseudo-rapidity is calculated as:< N >= σ(r) ∗ hx ∗ hy

(1)where σ(r) is the number of injected per unit area at the arbitrary pseudo-rapidity particles calculated from multiplicity. hx and hy are the width of the search windows of x andy directions respectively that is calculated from multiple scattering.

3.2.1

Multiplicity

dNch /dηIn this calculation, charged-particle pseudo-rapidity density in 0-5% centrality classes in√
Pb-Pb collision at sN N = 5.02 TeV measured by ALICE shown in Figure 15 is used.
Pb–Pb

ALICE
103

102

-5

-4

-3

-2

-1

0

1

2

3

4

5

sNN = 5.02 TeV
0– 5 %
5–10 %
10–20 %
20–30 %
30–40 %
40–50 %
50–60 %
60–70 %
70–80 %
80–90 %
Data (symmetrised)
Reflected
Uncorr. syst. unc.
Corr. syst. unc.

√η

Figure 15: Charged-particle pseudo-rapidity density for ten centrality classes over a broad√η range in Pb-Pb collisions at sN N = 5.02 TeV. Boxes around the points reflect the
total uncorrelated systematic uncertainties, while the filled squares on the right reflect
the correlated systematic uncertainty (evaluated at η=0). Statistical errors are generally
insignificant and smaller than the markers. [14]

To obtain the number of injected particles per unit area at the last MFT plane, random
numbers for x and y positions are generated in each pseudo-rapidity range until the numberof the entries in each pseudo-rapidity range reaches the number of charged-particles shownin Figure 15, as shown in Figure 16. In this calculation, the pseudo-rapidity range is−3.5 < η < −2.5, while the actual range is −3.6 < η < −2.45.

16

Figure 16: Charged-particle density at the last MFT plane estimated by Figure 15. Pseudo
rapidity range is −3.5 < η < −2.5.

3.2.2

Multiple scattering eﬀect [15]A charged particle traversing a medium is deflected by many small-angle scatters. Thisphenomenon is called multiple scattering. Most of the deflection is due to Coulomb
scattering from nuclei. The standard deviation of the angular distribution θ0 and theposition distribution x0 after charged particles transversing a medium can be calculated
as:
√

[

(

13.6 MeVLL
θ0 =z
1 + 0.038 ln
βcp
X0
X0
1
x0 = √ Lθ0
3

)]

(2)

(3)

where p is momentum, βc is velocity, z is charge number of the injected particle, and L
is the length of the medium. β can be calculated as:
β=

p
p
=√ 2
E
p + m2(4)17

Figure 17: Schematic drawing of multiple scattering.

Table 4 summaries the assigned values for multiple scattering calculations to get values
after a muon traverses the absorber.
Table 4: Assigned values for multiple scattering calculations
Variable
Assigned value
muon mass m
106 (MeV/c2 )-1charge number z
length of medium L 4.13 (m) = 60X0
Figure 18 shows the standard deviation of angular distribution θ0 and position distribution
x0 as a function of transverse momentum pT respectively when a muon transverses the
hadron absorber.

Figure 18: (left) Standard deviation of angular distribution as a function of muon transverse momentum. (right) Standard deviation of position distribution as a function ofmuon transverse momentum.

3.2.3

Number of MFT track candidates

Figure 19 shows the number of MFT track candidates determined by multiple scattering√at η = 3 of the last MFT plane in 0-5% central Pb-Pb collision at sN N = 5.02 TeV as afunction of pT obtained from equation 1. The number of injected particles per unit areaat η = 3 of the last MFT plane is ση=3 = 0.049 (mm−2 ) is calculated in Section 3.2.1.
18

<N>

50
45
40
35
30
25
20
15
10
5
0
0

1

2

3

4

5

p (GeV/c)T

Figure 19: The number of MFT track candidates determined by multiple scattering at√
η = 3 of the last MFT plane in 0-5% central Pb-Pb collision at sN N = 5.02 as a functionof pT obtained from equation 1

For example, when the muon is pT = 1 GeV/c, the number of MFT track candidates
determined by multiple scattering are calculated as:< N > = ση=3 ∗ hx ∗ hy
= 0.049 (mm−2 ) ∗ 28.8 (mm) ∗ 28.8 (mm)
∼ 41

(5)

There are approximately 41 MFT track candidates for one MUON track at pT = 1 GeV/c.
The number of MFT track candidates determined by multiple scattering is too large toconnect to one MUON track. Therefore we develop the matching method using the correlation between track position and angle to reduce the number of MFT track candidates.

3.3

Development of matching method with the correlation between track position and angle

3.3.1

Correlation between track position and angle

Most MFT track candidates are the background that does not match with the MUON
track. The background is reduced by the correlation between track position and angle.
The muon passing through the absorber from left to right in Figure 20 has a probability
distribution of the position and angle at the entrance of the absorber.

19

Figure 20: Schematic of muon passing through the absorber.

For example, suppose there is a muon that passes x = 0 at the end of the absorber(z = −5.03 m) as shown by the black arrow in Figure 21 (right). When the muon enters
the absorber from a higher/(lower) position, it should have a smaller/(bigger) angle atthe entrance of the absorber (z = −0.9 m) to connect to the muon that is x = 0 at
the exit of the absorber. The illustration of the distribution of the position and angle
at the entrance of the absorber for the muon that passes through x = 0 at the exit of
the absorber is shown in Figure 21 (left). Each standard deviation of the probability
distribution should be equivalent to the calculated values by the equation (2) and (3).
The standard deviation of the position distribution shown by hx in Figure 21 (left) is thesearch window determined by multiple scattering.

Figure 21: (left) Illustration of the expected distribution of the position and angle at theentrance of the absorber for the muon that is x = 0 at the exit of the absorber. (right)
Schematic illustration of the muon passing through the absorber.

The muons that originate only near the vertex need to be considered as a signal trackfrom the collisions. Red arrows in Figure 22 (right) shows the muons that originate near
the vertex. When the particles fly from the vertex towards the entrance of the absorber20(z = −0.9 m), the position x, y and angle θx , θy of the particles at the entrance of theabsorber shown by the red line in Figure 22 (left) are calculated as:
θx = ax(6)

where a is the slope that is calculated from the distance between the collision point andabsorber. When the collision point is Z = 0.0 (m), the position x, y and angle θx , θy ofthe particles at the entrance of the absorber are calculated as:
θx = 0.063x(7)

Figure 22: (left) Red line indicating a possible association of the position and angle fortracks that originate near the vertex. Expected distribution of the position and angle atthe entrance of the absorber for the muon that is x = 0 at the exit of the absorber. (right)
Schematic of the muon passing through the absorber.

In this example, tracks need to satisfy the two conditions. First is tracks come from thevertex. Second is tracks pass the end of the absorber at x = 0 with 0 degree. Then, theoverlap range of the red line and the blue distribution becomes the new search window
shown by hx in Figure 22 (left).

3.3.2

Geant4 simulation setup

To get a correlation distribution of the track position and angle, Geant4 simulation iscarried out. Geant4 is a toolkit for the simulation of the passage of particles throughmatter using Monte Carlo methods. Its application area includes high energy, nuclear
and accelerator physics, space science, and medical studies. [16], [17]In this simulation, an absorber that has the same length and material budget as the
hadron absorber of MUON (Table 1) is used. Particles go through the absorber from21the carbon side (z = −0.9 m) to the steel side (z = −5.03 m) in a real experimental
situation. However, to make the simulation easier, muons are injected from the steelside (z = −5.03 m) towards the vertex (z = 0.0 m) in this simulation. Confirmation ofthis simulation method by another simulation to confirm that the output has the sametendency regardless of the incident direction, is summarized in Section 3.3.4.
Figure 23 shows the variables used in the simulation. Since the pseudo-rapidity rangeof the MFT is −3.6 < η < −2.45 and η = −3 is almost at the center of the MFT,
the muon is injected at η = −3 from the steel side of the absorber toward the vertex.
η = −3 corresponds to an approximate angle of 5.7◦ . Incident position is set to xM U ON =0.501 (m) to be able to reach the vertex. Table 5 summaries the assigned values in thesimulation.
When muons reach the boundary between carbon and vacuum (z = −0.9 m), track positions xM F T and angles θM F T are recorded. Track positions and angles are not recorded
when muons decayed in the absorber and then other kinds of particles reached the boundary between carbon and vacuum.

Figure 23: Schematic drawing of the Geant4 simulation setup

Table 5: Assigned values in the Geant4 simulation
Variable
Assigned value
Incident position of z-axis-5.02 (m)0.501 (m)Incident position of x-axis xM U ON
Incident angle θM U ON
5.7◦
Figure 24 shows the event display of Geant4 simulation for an event. The red line indicatesa negative charge, the blue line indicates a positive charge, and the green line indicates aneutral charge. The red line that penetrates the absorber is the incident muon.
22

Figure 24: Event display of Geant4 simulation. Muon is injected from steel side atη = 3 (θ ∼ 5.7◦ ) towards the vertex (z = 0 m).

Figure 25 shows the correlation distribution of the position xM F T and angle θM F T of
pT = 1 GeV/c and pT = 2 GeV/c. The mean value of the angle θM F T ∼ 5.7 and theposition xM F T ∼ 89.8 indicate most muons went through the absorber straightly. Table 6
shows the comparison of the standard deviation between the simulation and the multiple
scattering calculation by equation (2) and (3) in Section 3.2.2 when pT = 1 GeV/c. The
standard deviation of the angle is almost same in the simulation and calculation, while
the standard deviation of the position is diﬀerent since there is no material informationof the absorber in the calculation.
θMFT (degree)T

xMFT-θMFT
160
Entries
99990
Mean x89.7
140Mean y5.702
Std Dev x
39.4120
Std Dev y
0.69931210

p = 2 (GeV/c)T

θMFT (degree)

p = 1 (GeV/c)
14

xMFT-θMFT
Entries
99986600
Mean x
89.81
Mean y5.7
Std Dev x
19.13500
Std Dev y 0.3332

14
12
10

8

100

8

6

80

6

4

60

4

2

40

2

0

20

0

0

−2
−150

400

300

200

−2
−150

−100

−50

0

50

100

150

200

250
300
x MFT (mm)

100

−100

−50

0

50

100

150

200

250
300
x MFT (mm)0Figure 25: Correlation distribution of the position and angle of transverse momentum
pT = 1 GeV/c (left) and pT = 2 GeV/c (right).
Table 6: Comparison of the standard deviation between the simulation and the multiple
scattering calculation (Section 3.2.2) at pT = 1 GeV/c.
σxσθSimulation
39.4 0.6993
Caluculation 28.8 0.6927

23

3.3.3

Number of candidates determined by correlation

Figure 26 shows the correlation distribution of the position and angle of pT = 1 GeV
simulated by Geant4, and the red line indicating the correlation between the position
and angle at the left side of the absorber (z = −0.9 m) of tracks that originate near
the vertex. Each elliptical line above the correlation distribution indicates eﬃciency.
Eﬃciency is defined as the percentage of entries inside the ellipse. Overlap region of the
red line and each eﬃciency line are defined as the search window. There is a respective
percentage of entries in each eﬃciency line. Eﬃciency cut is applied to both x and y
directions. Eﬃciency cuts of x and y directions are defined as ϵx and ϵy .

Figure 26: Correlation distribution of the position and angle of transverse momentum
pT = 1 GeV/c simulated by Geant4. The red straight line indicating the correlation
between the position and angle at the left side of the absorber (z = −0.9 m) of tracks
that originate near the vertex. Each elliptical line above the correlation distribution
indicates eﬃciency. Overlap region of the red line and each eﬃciency line are defined as
the search window.

Two-dimensional eﬃciency cut ϵxy is defined as:
ϵxy = ϵx ∗ ϵy(8)Figure 27 shows a one-dimensional search window determined by the correlation distribution of the position and angle as a function of pT .

24

Figure 27: One dimensional search window determined by the correlation distribution of
the position and angle as a function of pT .

The number of candidates < N > at arbitrary pseudo-rapidity is calculated from equation(1). Figure 28 shows the number of MFT track candidates after background subtraction
by the correlation between track position and angle at η = 3 of the last MFT plane in√
0-5% central Pb-Pb collision at sN N = 5.02 TeV as a function of pT obtained fromequation (1).

25

Figure 28: The number of MFT track candidates at η = 3 of the last MFT plane in 0-5%√
central Pb-Pb collision at sN N = 5.02 TeV as a function of pT obtained from equation
1.

For example, when MUON track is pT = 1 GeV/c and two-dimensional eﬃciency cut isϵxy ∼ 68%, the number of MFT track candidates after background subtraction by thecorrelation between track position and angle are calculated as:< N > = ση=3 ∗ hx ∗ hy
= 0.049 (mm−2 ) ∗ 11.8 (mm) ∗ 11.8 (mm)
∼ 6.8.

(9)

There are approximately 6.8 MFT track candidates after background subtraction by thecorrelation between track position and angle, while there are approximately 41 MFT track
candidates before background subtraction (equation (5)). Background can be significantly
reduced about 6 times. Figure 29 shows a comparison of the number of MFT track candidates between before and after background subtraction. Furthermore, the backgroundcan be reduced by the sign of charged particle and rough momentum matching between
MFT and MUON.

26

Figure 29: Comparison of the number of MFT track candidates before and after background subtraction. Red dot represents the number of candidates before backgroundsubtraction and blue dot represents after subtraction.

3.3.4

Confirmation of Geant4 simulation

In the Geant4 simulation in Section 3.3.2, muons are injected from the steel side (z =−5.03 m) towards the vertex (z = 0.0 m) to make the simulation easier, while particles
go through the absorber from the carbon side (z = −0.9 m) to the steel side (z = −5.03m) in a real experimental situation. In this section, another simulation to confirm theincident position does not aﬀect the results is summarized.
In this simulation, an absorber that has approximately the same length (4 m) and material
budget (55X0 ) as the hadron absorber of MUON is used, as shown in Table 7.
Table 7: Geometrical parameters of the hadron absorber in the confirmation simulation
Material Length (m) Material budget
Carbon220
18.8
Concrete
123
10.7
Steel
57
1.76
Total
400
The incident position of the z-axis is fixed at the vertex (z = 0 m) in this study. The
incident position of the x-axis is changed from -20 mm to 160 mm by 1 mm. The incident
angle is changed from 3.0◦ to 8.0◦ by 0.1◦ . In each position and angle, 100 muons are
injected. When muon reaches the range around η = −3 at the exit of the absorber, theposition xM F T and angle θM F T on the entrance of the absorber are recorded. η = −327

corresponds to the approximate angle of 5.7◦ . When muon that angel is 5.7◦ reaches theend of the absorber, the position of the x-axis is 475.9 mm. Here, the range aroundη = −3 is defined as 470.9 < x < 480.9 mm and 5.2◦ < θ < 6.2◦ . Figure 30 and Table
8 summarize the assigned parameters in the simulation. It is confirmed that the incident
position does not aﬀect the results.

Figure 30: Schematic drawing of the confirmation simulation setup.

Table 8: Assigned parameters in the confirmation simulation.
Variable
Assigned parameters
Incident position of z-axis
0 (mm): fixed
Incident position of x-axis -20<x<160 (mm): 1mm step
3.0◦ <θ<8.0◦ : 1◦ step
Incident angle
The left panel of Figure 31 left shows the correlation between the position and angle atthe entrance of the absorber for muons that are injected from the exit of absorber towards
the vertex at η = −3 (same situation as Section 3.2.2). The right panel of Figure 31 rightshows the correlation between the position and angle at the entrance of the absorber formuons that reaches the range around η = −3 at the exit of the absorber. The functionsof the ellipses drawn in the same colors are the same in both figures. The percentage ofentries in the ellipse is defined as eﬃciency. Eﬃciency lines (90, 70, 50%) defined in left
figure give consistent results (88, 68, 47%) in right figure.

28

Figure 31: (left) Correlation between the position and angle at the entrance of the absorberfor muon that is injected from the exit of absorber towards the vertex at η = −3 (samesituation as 3.2.2). (right) Correlation between the position and angle at the entrance of
the absorber for muons that reached the range around pseudo-rapidity η = −3 at the exitof the absorber.

3.4

Preparation for evaluation of matching algorithm

To select the best MFT track from the MFT track candidates, the likelihood of the MFT
track candidates is evaluated by the following factors. That is the correlation between the
track position and angle, and momentum and charged sign matching between MFT and
MUON. The new matching method simulated in Section 3.2.2 needs to be implemented
in the matching algorithm.
Steps to implement the new matching method are summarized below. First, correlation
distribution can be obtained from the MUON track. The size of the distribution depends
on the MUON track momentum. Second, the MFT track that is the nearest to the centerof the distribution is the best MFT track. To calculate the distance from the center ofthe ellipse is harder than calculating the distance from the center of the circle. In order tomake analysis easier, elliptical distribution given in Section 3.2.2 is converted to circular
distribution.
Figure 32 shows the process to convert the elliptical distribution to circular distributionthat center is zero. Each process is shown below. The step numbers are corresponding to
the numbers of the panel in Figure 32.
1. The original correlation distribution of the track position and angle at pT = 1 GeV/csimulated by Geant4. This is the same figure as Figure 26.
2. The center of Figure 32-1 is converted to zero. Each axis is converted by equation(10) and (11).
(θM F T + θM U ON
x2 = (xM U ON − xM F T ) − tan
2

)

/L

(10)
29

y2 = θM U ON − θM F T .

(11)

3. The y-axis in Figure 32-2 is multiplied by L/3 to make the dimension the same as
the x-axis and to make the distribution slope 45 degrees. L/3 is empirically foundout.
4. Figure 32-3 is rotated 45 degrees to align the major axis of the ellipse with thex-axis.
5. Figure 32-4 is converted ellipse to a circle by dividing each x and y value by eachstandard deviation. Each standard deviation is obtained from the fit values of Figure
33.

Figure 32: Process to convert the elliptical distribution to circular distribution that centeris zero.

The left (right) panel of Figure 33 shows a projection of Figure 32-4 onto the x-axis(y-axis), respectively. Each histogram is fit by Gaussian function. The same processes
are done for other pT . Figure 34 shows standard deviations σx and σθx in Figure 32-4 asa function of pT . The standard deviations vs. pT is fit by function (12).
σ = A1 /pT + A2 /p2T

(12)

where A1 and A2 are fit parameters. Equation (13) is obtained as the result of fitting.
Standard deviation in step 4 at certain pT can be calculated by equation (13).

30σx = 20.84/pT + 1.349/p2Tσθx = 8.603/pT + 2.072/p2T(13)

Figure 33: Projection of Figure 33-4 onto the x-axis (left) and y-axis (right), respectively.
Each histogram is fit by Gaussian function.

Figure 34: Standard deviation σx and σθx in step 4 as a function of pT . Each standard
deviation is obtained from the fit values of Figure 33.

Figure 35 (left) shows the original distributions and Figure 35 (right) shows the distributions after conversion with the eﬃciency lines. The upper (lower) panel of Figure 35
31

is pT = 1 GeV (pT = 2 GeV). The eﬃciency lines are defined as the percentage of entries
inside ellipse or circle. The size of the original distribution depends on pT , while the sizeof the distribution after all conversions described above does not depend on pT . Figure 36
shows the percentage of entries in the right panel of Figure 35 as a function of radius r. r
is defined as the distance from the center of the circular distribution after all conversion.
Diﬀerent color dots represent diﬀerent pT . All dots almost overlap. That is contour
lines of eﬃciency can be written regardless of pT . Therefore the MFT track that has
smaller r is more likely to be the best MFT track regardless of pT .

Figure 35: Original distributions (left) and distributions after conversion (right) with
eﬃciency lines. The upper (lower) panel is pT = 1 GeV (pT = 2 GeV). Contour lines of
eﬃciency can be written regardless of transverse momentum.

32

Figure 36: Percentage of entries in the right panel of Figure 35 as a function of radius r.
Diﬀerent color dots indicate diﬀerent pT .

33

4

Evaluation of developed matching algorithm

The developed matching algorithm is evaluated using HIJING [18].

4.1

Simulation tool for Heavy Ion Collisions

HIJING (Heavy Ion Jet INteraction Generator) is a Monte Carlo event generator particle
production in high energy nuclear collisions. After HIJING generates particles emitted
by high energy nuclear collisions, GEANT4 is used to simulate detector responses. In
Monte Carlo simulation, we can know the true information of the particles in the events
such as the particle ID, interaction points, momentum vector, and their mother particles.
Therefore we can verify how well the developed matching algorithm performs to evaluate
track candidates.

4.2

Evaluation setup√
In this evaluation, central Pb-Pb collision in centrality 0-5% at sN N = 5.5 TeV isgenerated by HIJING and single muon that ϕ range is 0◦ < ϕ < 360◦ is embedded
at η = −3 for each event. Tracks generated by HIJING are the background in theevaluation. Detector responses are simulated by GEANT4. 30 events are simulated foreach pT (pT = 1, 2, 3 GeV). Each MFT hit at the last MFT disk is scored for the MUON hitof the embedded single muon by calculating matching quality parameters. The matchingquality parameters in the x and y directions rx and ry are defined as:√rx =x′ 2 + θx′ 2

√

ry =
′

′

′

(14)

y ′ 2 + θy′ 2

(15)

′

where x , θx , y , θy are the values after the conversion from elliptical to circular distribution
in Section 3.4. They are calculated as:[(

θM F T + θM U ON
x = (xM U ON − xM F T ) − tan
2

)

′

]

/L /σx′θx = [(θM U ON − θM F T ) ∗ L/3] /σθx[(θM F T + θM U ON
y = (yM U ON − yM F T ) − tan2′′θy = [(θM U ON − θM F T ) ∗ L/3] /σθy

(16)

(17)
)

]

/L /σy

(18)

(19)

34

The rx (ry ) is the distance from the center of the 2 dimensional histogram (θx (θy ) vs.
′′x (y )) that is the circular distribution as shown in the right pannel of Figure 35. The
track that have the smallest rx or ry is chosen as the best MFT track in each direction. rx
and ry are the one-dimensional matching quality parameters. Two-dimensional matchingquality parameter R considering both rx and ry is defined as:

R = rx + ry√=

x′ 2 + θx′ 2 + y ′ 2 + θy′ 2 .

(20)

The track that has the smallest R among the track candidates is chosen as the best
MFT track. Since this is a simulation, we can check which track is a single muon in the
MFT track candidates. Therefore, when we arrange R in ascending order, we can get
the ranking of how small R of the embedded muon is among all entries. In this simulation, true positions and momentum vectors from simulated information not reconstructed
information are used at the last MFT disk and the first MUON tracking chamber.

4.3

ResultFigure 37 shows the distribution of track position and angle in the x-direction for 10
events on the last MFT plane. The center of the distribution is (0, 0) and most of thehit points are on the linear line. Distributions have a similar tendency regardless of pT
of the signal (embedded single muon). The distribution of the position and angle fory-direction has the same tendency as x-direction. Figure 38 shows the distribution of the′′normalized position x and angle θx . The distribution spreads as pT of embedded single′′
muon increases because x and θx are normalized values by σx and σθx which depend on′
pT of the signal (equation 16 and 17). The distribution of the normalized position y and′angle θy has the same tendency. Figure 39 shows the distribution of rx and ry. The
distribution spreads as pT of the signal increases because rx and ry are normalized valuesby σx , σθx , σy and σθy which depend on pT of the signal (equation 14 to 19).

35

Figure 37: Distribution of the position and angle for x direction at the last MFT plane.
pT of embedded single muon is shown in each panel.

′′

Figure 38: Distribution of the normalized position x and angle θx for x direction. pT ofembedded single muon is shown in each panel.

36Figure 39: Distribution of rx and ry. pT for embedded single muon is shown in eachpanel.

Figure 40, 41, 42 shows rx , ry and R respectively. Red line represents embedded muonand blue line represents background. The red line (embedded single muon) has a peak ina small region around from 0 to 3 mm, while the blue line (background) spreads evenly
to large region for all rx , ry and R as expected. rx and ry have similar results. R, which
combines the two of rx and ry , has a lower background ratio than rx and ry alone. R
can reduce the amount of the background by almost an order of magnitude compared torx and ry at any pT , especially at low R. The ratio of background to signal decreases
with increasing pT especially for R as shown in Figure 42. Figure 43 shows R only forbackground. Peak position is smaller in lower pT than higer pT . R distribution is sharpin lower pT , while R distribution is smooth in higer pT This is because R is normalized
value by the standard deviation which depends on pT shown in Figure 34 and backgroundbefore normalization is similar in any pT . Therefore this aﬀects the ratio of backgroundto signal.

37

Figure 40: Distribution of rx . Red line represents embedded muon and blue line represents
background. pT of embedded single muon is shown in each panel.

Figure 41: Distribution of ry . Red line represents embedded muon and blue line represents
background. pT of embedded single muon is shown in each panel.

38

Figure 42: Distribution of R. Red line represents embedded muon and blue line represents
background. pT of embedded single muon is shown in each panel.

Figure 43: Distribution of R only for background. pT of embedded single muon is shownin each panel.

39

Figure 44 shows the ranking of how small R of the embedded muon is among all entries.
The possibility that the true MFT track is chosen as the best MFT track significantly
increases as pT increases because the size of the search window is smaller for larger pT .
matching between MFT and MUON. Background can be halved by the sign of charged
particle.

Figure 44: Ranking of how small the two-dimensional matching quality parameter R of
the embedded muon was among all entries. pT is shown in each panel.

40

5Summary and Outlook

In this study, the track matching algorithm between MFT and MUON using the correlation between track position and angle is developed. Track matching between MFT and
MUON is important for precise tracking around the vertex and to improve signal-to-noise
ratio S/N and mass resolution. The number of both MFT track candidates was calculated when using the correlation and when not using. The matching method using thecorrelation between track position and angle can improve S/N significantly about 6 times
with high eﬃciency.
The developed track matching method must be implemented in the matching algorithm.
The MFT track that is the nearest to the center of the distribution is the best. To calculate the distance from the center of the ellipse is harder than calculating the distancefrom the center of the circle. To make analysis easier, elliptical distribution is converted
to circular distribution. After conversion from elliptical to circular distribution, contour
lines of eﬃciency can be written regardless of transverse momentum. Therefore the distance between the center and the track point in the circular distribution is the likelihoodof the MFT track candidate regardless of pT .
The developed matching method is evaluated using HIJING. The matching quality parameter R is developed. The possibility that the true MFT track is chosen as the best
MFT track significantly increases with pT increasing. In evaluation, the ranking of how
small matching quality parameter R of the embedded muon is among all entries is calculated.
Here’s what we can do as a next step. When matching quality parameter R of the true
MFT track is second, that matching quality parameter R may be close to the value of thefirst matching quality parameter R. A comparison of the diﬀerence between R for the true
MFT track and background can give other matching quality parameters. In this simulation, true positions and momentum vectors from simulated information not reconstructed
information are used at the last MFT disk and the first MUON tracking chamber. Reconstructed standalone tracklets of MFT and MUON are considered the position resolutionof detectors. Therefore R should be worse than this evaluation when using reconstructed
information. We have to check how well R works when using reconstructed standalone
tracklets. Also, a magnetic field is applied parallel to the beam axis. Charged particles
are deflected by a magnetic field, especially for low momentum. MFT and MUON canmeasure the sign of charged particle, therefore the background can be halved. Roughmomentum matching between MFT and MUON can reduce background. Also, we needmore statistics to evaluate the developed matching method more precisely. The MFT is
installed in 2020 and LHC-Run 3 will start in 2021. Therefore the new matching method
must be implemented in the matching algorithm before LHC-Run 3.

41

Acknowledgement
I wish to express my sincere appreciation to Prof. Kenta Shigaki. He invited me to thisresearch and always supervised me despite being in a diﬀerent university. I would like tothank Asst. Prof. Maya Shimomura and Asst. Prof Takashi Hachiya for always supporting me nearby. Without their support, I could not finish this work. I would like to thankDr. Yorito Yamaguchi for his various advice from physics to presentation materials.
Prof. Hisaki Hayashii and Prof. Kenkichi Miyabayashi gave diﬀerent perspective comments. That helped me to understand my work better. I would like to thank Kosei
Yamakawa san and Takumi Osako kun who instructed me analysis framework of ALICE.
I also would like to thank my colleagues in Nara and Hiroshima. Thanks to them, I could
enjoy this two years more. Finally, I must express my gratitude to my family, Tsutomu,
Rumi, and Saki. They have always supported what I want to do.
この研究を支えてくださった全ての方々に感謝しています。ありがとうございました。

42

References[1] ALICE Collaboration, "Technical Design Report for the Muon Forward Tracker" ,CERN-LHCC-2015-001[2] ALICE Collaboration, "Addendum of the Letter of Intent for the upgrade of the
ALICE experiment : The Muon Forward Tracker" , CERN-LHCC-2013-014[3] M. Kuroda, "ALICE 実験前方ピクセル検出器導入時の物理性能評価", Master thesis,
Hiroshima University, (2018).
[4] "Phase
diagramof
QCD
https://cds.cern.ch/record/2025215.
[5] Tapan K. Nayak, "HeavyIons:
arXiv:1201.4264 (2012).

matter:Quark-Gluon

Plasma"Results from the Large Hadron Collider",[6] C. Quigg, "Spontaneous Symmetry Breaking as a Basis of Particle Mass",
arXiv:0704.2232 (2007).
[7] "物質に質量を与えるクォーク凝縮現象を支持する実験的証拠を得ることに成功",
https://www.s.u-tokyo.ac.jp/ja/press/2004/02.html.
[8] "Hadron Properties in Nuclear Matter and Dilepton Emission in Relativistic HeavyIon Collisions", http://niham.nipne.ro/rp9/[9] X. Zhu, "DD̄ correlations as a sensitive probe for thermalization in high energy
nuclear collisions", Phys.Lett.B. 647 (2007) 366-370.
[10] KEK-PS E325 Collaboration, Evidence for In-Medium Modification of the ϕ Meson
at Normal Nuclear Density , Phy. Rev. Lett. 98, 042501, 2007.
[11] "The CERN accelerator complex", https://cds.cern.ch/record/2197559.
[12] "Longer term LHC schedule",
https://lhc-commissioning.web.cern.ch/lhc-commissioning/schedule/LHC-long-term.htm.
[13] A. Uras, "The ALICE MFT Project:
Motivations and Expectations",
http://llr.in2p3.fr/sites/qgp2012/Talks/Etretat_2012_Uras2.pdf.
[14] ALICE Collaboration, "Centrality dependence of the pseudorapidity density distri√bution for charged particles in Pb-Pb collisions at sN N = 5.02 TeV", Phys.Lett.
B772 (2017) 567-577.
[15] H. Bichsel, D.E. Groom, and S.R. Klein, "27. Passage of particles through matter",
http://pdg.lbl.gov/2005/reviews/passagerpp.pdf.
[16] S. Agostinelli et al. (GEANT4 Collaboration), "GEANT4: A Simulation toolkit,”
Nucl. Instrum. Meth. A 506, 250 (2003).
[17] J. Allison et al., "Geant4 developments and applications,” IEEE Trans. Nucl. Sci.
53, 270 (2006).
[18] X. Wang and M. Gyulassy, "HIJING 1.0: A Monte Carlo Program for Parton andParticle Production in High Energy Hadronic and Nuclear Collisions", arXiv:nuclth/9502021 (1995).
REFERENCES

43