CERN - ALICE EXPERIMENTSUMMER STUDENTS PROGRAMME 2017

Development of the analysis methods for charm triangularflow measurment in Pb-Pb collisions in ALICE

Supervisors:Cristina TerrevoliAndrea Festanti

Student:Francesca Alemanno

Summer 2017

Abstract

The aim of my project is to implement the technique and the tools to study the D0 mesons withinthe ALICE analysis framework.During my work I analyzed ALICE data using the Computing Grid facilities and in this report Iwill present the measurement of the azimuthal anisotropy of the D0 meson production in Pb-Pbcollisions at

√sNN = 5.02 TeV, with the ALICE detector.

Introduction

The main goal of the ALICE experiment isthe characterization of the Quark Gluon Plasma(QGP) formed in Pb-Pb collisions at the LHC.Heavy flavours, charm and beauty, are used toinvestigate the properties of the QGP, becausethey are produced on short time scales compa-red to the QGP formation time and experiencethe entire evolution of the medium, interactingwith its constituents. One of the experimentalobservables sensitive to the properties of thismatter is the azimuthal distribution of particlesin the plane perpendicular to the beam direc-tion.The azimuthal anisotropy is characterized bythe Fourier coefficients vn = cos[n(ϕ −Ψn)]where ϕ is the azimuthal angle of the particle,Ψn is the angle of the initial state spatial planeof symmetry, and n is the order of the harmo-nic.The second Fourier coefficient v2, the ellipticflow, has been studied in detail in recent years:a v2 > 0 has been measured for D0 mesons(containing a charm quark), confirming that al-so heavy quarks participate to the collective ex-pansion of the system. The measurement of hi-gher order coefficients, for example the trian-gular flow v3 , helps to further investigate thetransport mechanisms of heavy quarks in themedium, since it is sensitive to their diffusioncoefficient.During my project I had the opportunity to par-ticipate in analyzing data on the WorldwideComputing Grid and I improved my program-ming capabilities and my knowledge aboutheavy ion physics.

1. ALICE Experiment

A Large Ion Collider Experiment (ALICE) isone of the four large experiments at the LargeHadron Collider (LHC), the accelerator builtat CERN where protons and Pb ions are ac-celerated to the highest energies ever reached.This experiment is dedicated to the study of theQuark-Gluon Plasma.

Figura 1: Alice Experiment.

2. QGP and Heavy-Ion Colli-sions

Figura 2: Phase diagram of QCD matter as afunction of temperature and net baryon density.

Quantum Chromodynamics calculations pre-dict that strongly-interacting matter under ex-treme conditions of high temperature and ener-gy density undergoes a transition from the ha-

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F. Alemanno - Summer Student Programme 2017 2

dronic phase to a colour-deconfined medium,called Quark-Gluon Plasma (QGP). Heavy-ioncollisions at ultra-relativistic energies providesuitable conditions for the QGP formation andfor characterizing its properties. The creationof this state of matter in the laboratory, andthe study of its properties are the main goals ofthe ultra-relativistic nuclear collision program.Heavy-Ion physics is a way to study matter atenergy densities like 10 µs after the Big Bangat temperatures 105 times larger than in the suncore.

How can we study this state of matter?

QGP can be characterized studying the produc-tion of heavy-flavour hadrons, in high energyheavy-ion collisions.

The geometry of the collision plays an impor-tant role in the study of nuclear matter effec-ts and QGP formation. The quantities used tocharacterize the collision geometry are:

• The impact parameter, which is the distan-ce between the centres of the two collidingnuclei.This quantity characterizes the centrali-ty of the collision: a central collision isone in which the two nuclei collide almo-st head-on and it has a small impact pa-rameter, a peripheral collision has a largeimpact parameter.

• The number of partecipant nucleons,Npart , which is the total number of pro-tons and neutrons that undergo at least oneinelastic collision.

• The number of binary collisions, Ncoll ,which is the total number of nucleon-nucleon collisions.

Semi-peripheral collisions

The nuclear overlap region in collisions withnon-zero impact parameter is not azimuthal-ly symmetric but has an almond shape whosedeformation changes with centrality (Fig 3.a).Consequently, the pressure gradients betweenthe centre of the overlap zone and its periphe-ry in an average collision vary with the azimu-th, being strongest in the direction of the reac-tion plane ΨRP, which coincides with the di-rection of the minor axis of the almond. Initialstate spatial anisotropy (Fig 3.b) converts intomomentum-space anisotropy in final state (Fig3.c).

Figura 3: Semi-peripheral collision.

F. Alemanno - Summer Student Programme 2017 3

3. Azimuthal Anisotropy

Flow pattern is quantified via a Fourierexpansion:

d2Ndϕd pT

=dN

2πd pT[1+2∑vncosn(ϕ−Ψn)]

(1)where n is the order of the harmonic, ϕ is theazimuthal angle of the particle and Ψn is the an-gle of the spatial plane of symmetry of harmo-nic n. This plane coincides with the reaction-plane direction in absence of fluctuations of thedistribution.

Fourier coefficient vn

The second Fourier coefficient v2, the ellipticflow, has been studied in detail in recent years:a v2 > 0 has been measured for D mesons (con-taining a charm quark), confirming that alsoheavy quarks partecipate to the collective ex-pansion of the system.

Figura 4: v2 of D0,D+ and D∗ as a function of pTat√

sNN = 5.02 TeV, compared with the same mea-surment at

√sNN = 2.76 TeV and with the π+ and

π− v2. (arXiv:1707.01005v1 [nucl- ex]4Jul2017).

The measurement of triangular flow v3, allowsto further investigate the transport mechanismof heavy quarks in the medium.

4. v3 measurement

Event-Plane Method

The D0 triangular flow has been measured withthe event-plane method.The event plane angle Ψ3 has been determinedevent-by-event and D0 yields were measured inthe regions:1. In plane:11π

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F. Alemanno - Summer Student Programme 2017 4

Event-Plane estimate

The reaction-plane angle can not be directlymeasured, but can be estimated from the parti-cle azimuthal distribution event-by-event. Theorientation of the reaction plane is estimatedwith the nth harmonic event-plane angle, ψn:

ψ3 =13

arctan3(Q3,y,Q3,x) (3)

For a given harmonic n, can be constructed thetwo-dimensional event-plane vector Qn star-ting from the measured azimuthal distributionof the particles produced in the event as:

Qn = (Qn,x,Qn,y) = (∑wicosnϕi,∑wisinnϕi)(4)

where ϕi is the azimuthal emission angle ofthe particles and wi are pT and ϕ weights tomake the event plane distribution flat: wi =wi,pT wi,ϕi , where:

wpT =

{2, pT > 2

pT, pT < 2

wϕ =1

dN/dϕThis pT function mimics the pT dependenceof the charged particle v3 and it improves theestimate of Ψ3 by enhancing the contributionof particles with a stronger flow signal (Phy-sRevC.90.034904).Q vector are obtained selecting: TPC trackswith |η | < 0.8, pT > 0.15, nT PCpoints > 50,χ2/nd f < 2, dca(rϕ)< 2.4 e dca(z)< 3.2.

Resolution factor

The measured flow coefficients need to be cor-rected for the finite event-plane angle resolu-tion.

The correction factor can be calculated usingtwo sub-events:

• sub-event A composed by TPC trackswith 0 < η < 0.8

• sub-event B composed by TPC trackswith −0.8 < η < 0

The event-plane resolution for the thirdharmonic is given by:

R3 =< cos[3(ψA3 −ψB3 )]> (5)

where ψA3 and ψB3 are the event-plane angles of

the two subevents.

5. Workflow

During my work I implemented a new task thatincludes:

• Event plane measurement

• Resolution estimate

• D0 reconstruction in-plane and out-of-plane

Furthermore I developed an analysis macro tofit invariant mass distributions and compute v3.I analyzed the data sample Pb-Pb @ 5.02 TeV.The number of analyzed events is 22 milions,with kINT7 trigger selection in the Centrali-ty class 30-50% with the centrality estimatorV0M.

D0 reconstruction and signal extraction

The results presented in this report are basedon the reconstruction and selection of the D0

F. Alemanno - Summer Student Programme 2017 5

hadronic decay channel D0 → Kπ with bran-ching ratio 3.89%.D0 meson has mass m = 1.864 Gev/c2 andcτ = 123 µm, so the separation between pri-mary and secondary vertex requires a good ca-pability to disentangle distance of the order offew hundred microns.The standard method for studying this particlesis to study the invariant mass of opposite char-ge pairs Kπ . The combinatorial background isrejected with topological selection and ParticleIdentification strategy to select K and π .The main topological selections applied toextract the signal were:

• Require that K and π share a secondaryvertex.

• Require a minimum distance of primaryand secondary vertex.

• Require a minimum impact parameter(i.e. distance between the prolongationof the secondary tracks and the primaryvertex) of a few hundred µm.

• Require a minimum value on the cosineof the pointing angle (i.e. the angle bet-ween the D0 flight line and the sum of thedaughter track momenta).

And for particle identification (PID):

• Specific energy loss: particles passing th-rough matter loose energy mainly by ioni-zation and average energy loss can be cal-culated with Bethe-Bloch formula so onecan identify particle by measuring energydeposition and momentum

• Time Of Flight: particles with same mo-mentum have different speed due to theirdifferent mass.

The D0 raw yields were extracted in 6 pT bins(2-16 GeV/c) from fit to the invariant mass di-stribution.The signal is parametrized through Gaus-sian function and the background through anexponential function.

Event-Plane Ψ3

The 3rd harmonic event-plane angle, Ψ3, hasbeen estimated in different cases: withoutweight, with only pT weight and with pT andϕ weight.

Figura 6: Without weight.

Figura 7: Only pT weight.

Figura 8: With pT and ϕ weight.

The distribution used for this analysis is the one

F. Alemanno - Summer Student Programme 2017 6

with both pT and ϕ weight, reported in figure8.

Resolution factor R3

The resolution factor R3 is estimated as themean of:

R3 =< cos[3(ψA3 −ψB3 )]> (6)

and resulted to be 0.834.

Figura 9: cos[3(ψA3 − ψB3 )] in the 30 − 50%centrality class.

Distribution of the invariant mass

In figure 10 and 11 the invariant mass distri-butions in plane and out of plane, respectively,are shown. The fit of the invariant mass distri-bution in the different pT bins was stable andthe fit was extracted with a good significance.

Figura 10: Invariant mass. In plane regions.

Figura 11: Invariant mass. Out of plane regions.

Final Result

The v3 was calculated using the formula:

v3 =1

R3

π4

Nin−plane−Nout−o f−planeNin−plane +Nout−o f−plane

(7)

Figura 12: Triangular flow v3 as a function of pT.

The v3 distribution as a function of pT is sho-wn in figure 12: we can observe an hint of v3larger than 0. The vertical error bars rapresen-ts the statistical uncertainty which is calculatedby propagating the statistical uncertainties ofthe in plane and out of plane raw yields treatingthem as uncorrelated. The raw yields statisticaluncertainties were calculated as the root squareof the raw yields.In figure 13, the v2,v3 and v4 of charged parti-cle at different energy is shown.The D0v3 has similar magnitude as the charged

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Figura 13: vn distribution for charged particles (left,DOI: 10.1103/PhysRevLett.116.132302) comparedwith my result (right).

particle one in 30− 40%. But note that diffe-rent method was used for charged particles v3measurement.

6. Summary

In this work the D0 v3 in 30−50% Pb-Pb colli-sions at 5.02 TeV was shown. The v3 was eva-luated using the event plane method. I analyzedALICE data with a private task developed byme. Results show hint of D0 v3 larger than 0.Further studies on the uncertainties and moredifferential measurements can be developed.