Performance of the MPD experiment for the anisotropic flow measurement
P. Parfenov I. Selyuzhenkov A. Taranenko A. Truttse
hep-ex nucl-ex





^1 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe highway 31, Moscow, 115409, Russia
 ^2 Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
 ^3 GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany

petr.parfenov@cern.ch


The main goal of the future MPD experiment at NICA is to explore the QCD phase diagram in the region of highly compressed and hot baryonic matter in the energy range corresponding to the highest chemical potential. Properties of such dense matter can be studied using azimuthal anisotropy which is categorized by the Fourier coefficients of the azimuthal distribution decomposition. Performance of the detector response based on simulations with realistic reconstruction procedure is presented for centrality determination, reaction plane estimation, directed and elliptic flow coefficients.




§ INTRODUCTION

Studies of the quark-gluon matter thermodynamical properties is one of the main priorities in the number of experiments specializing in the physics <cit.>. Transverse azimuthally anisotropic flow measurements are one of the key methods to study the time evolution of the strongly interacted medium formed in the nucleous collisions. In the non-central collisions, initial spatial anisotropy results in the azimuthally anisotropic particle emission. The magnitude of the anisotropic flow is defined using the the Fourier coefficients v_k{Ψ_n} of azimuthal distribution of the emitted particles with respect to the reaction plane <cit.>:

    dN/d(φ - Ψ_n) = 1+2∑_k=1^∞v_kcos[ k(φ - Ψ_n) ],

where φ – is the azimuthal angle of particle, k – is the harmonic order and Ψ_n is the n-th order symmetry plane angle. v_1 is hence called directed flow, v_2 – elliptic flow.

In this  work centrality determination based on the multiplicity from TPC and anisotropic flow analysis for Au+Au collisions will be presented for the two energies corresponding the highest and lowest eneries of the  collider.



§ SIMULATION AND ANALYSIS

The future  detector will be capable of a 4π-spectrometer, detecting charged hadrons,
electrons and photons in heavy ion collisions at high luminosities in  energy range <cit.>. In
order to achieve this goal the detector comprises precise tracking system and highly-effective
particle identification system based on time-of-flight measurement and calorimetry.

Primary track selection based on the DCA distributions and implementation of the realistic tracking algorithm Cluster Finder () will be shown compared to the previous results <cit.>.

For the event generation the  (Ultra-relativistic Quantum Molecular Dynamics) <cit.> and  (The Los Alamos version of the Quark-Gluon String Model) <cit.> were used. The  is used for performance study of the reaction plane determination and anisotropic flow measurements for the beam energy 5 and 11 GeV while the is used for the reaction plane determination for the 11 GeV only. Used statistics is 1M events for each of the energy point and model choice. Further simulations were carried out using framework using  detector geometry and Cluster Finder () and Hit Producer () tracking algorithms for 5 and 11 GeV correspondingly.
Following cuts were used in the analysis:

	
  * |η|<1.5
	
  * 0.2<p_T<3 GeV/c
	
  * N_hits^TPC>32
	
  * 2 σ DCA cut for primary particle selection
	
  * particle identification (PID) – is the cuts from PDG codes (Monte Carlo information)	 

where DCA – is the distance of the closest approach between the reconstructed vertex and a charged particle track.

For the collective flow measurement event plane method was used <cit.>. Reaction plane was estimated from the energy deposition of the nuclear fragments in backward and forward rapidities in the forward hadron calorimeters (). Q-vector was calculated as follows:


    q_x^m=∑ E_i cos mφ_i/∑ E_i, q_y^m=∑ E_i sin mφ_i/∑ E_i.

The event plane angle was calculated as follows:

    Ψ_m^EP=TMath::ATan2(q_y^m,q_x^m),

where E_i is the energy deposition in the i-th module of , φ_i – its azimuthal angle. For m = 1 weights had opposite signs for backward and forward rapidities due to the antisymmetry of the v_1 as a function of rapidity.
The values of v_n itself could be calculated as follows:

    v_n=⟨cos[n(φ - Ψ_m^EP)]⟩/Res_n{Ψ_m^EP}, Res_n{Ψ_m^EP}=⟨cos[n(Ψ_m^EP-Ψ_m)]⟩,

where Res_n{Ψ_m^EP} is the event plane resolution, Ψ_m is the n-th order collision symmetry plane, which cannot be measured experimentally.
So, in order to estimate event plane resolution, the two-subevent method with extrapolation
algorithm was used <cit.>:

    Res^2_n{Ψ^EP,A_m,Ψ^EP,B_m} = ⟨cos[n(Ψ_m^EP,A-Ψ_m^EP,B)]⟩, Res_n{Ψ^EP_m } = Res_n(√(2)χ_A,B),

where χ_A,B – is the parameter proportional to the v_n and ∑ E_i, A and B represent two subevents - left(backward rapidity) and right(forward rapidity)
 detectors.
In this work v_1 and v_2 was measured with respect to 1-st order event plane (m=1).



§ RESULTS AND CONCLUSIONS



 §.§ Centrality determination

On the Figure <ref> (left) multiplicity of the primary charged particles produced in the Au+Au collisions calculated using TPC detector is shown. This distribution was used to introduce the centrality classes with equal number of particles in each class. Centrality resolution of used classification is shown on the Figure <ref> (right). In the 10-80% centrality range resolution σ_b/⟨ b ⟩∼ 5-10% for both  and  tracking algorithms.



 §.§ Azimuthal anisotropic flow

On the Figure <ref> resolution correction factor for v_1 and v_2 is shown. Since the  simulates nuclear fragments, one can see the deterioration of the resolution factor because more particles goes through the beam hole in the center of  unregistered. Other than that, results shows good performance in the wide centrality range 0-80% for all energies and tracking algorithms.


On the Figure <ref> one can see the directed v_1 and elliptic v_2 flow as a function of p_T. Signal after  simulation (true) is compared with one after reconstruction procedure (reco) which is how future experimental data will be analyzed. One can see that the difference between true and reco values is negligible.





§ SUMMARY


Track multiplicity of the emitted charged particles in TPC can be used for centrality determination with resolution 5-10% in a wide centrality range 10-80%.
Event plane orientation can be estimated using energy deposition in  with high resolution factor (Res_1{Ψ^EP_1}∼ 0.9, Res_2{Ψ^EP_1}∼ 0.7 for centrality 20-40%).
Directed (v_1) and elliptic (v_2) flow were extracted in simulations using event plane method. Results for the reconstructed (reco) and generated (true) values are in good agreement.




§ ACKNOWLEDGMENTS

This work was partially supported by the Ministry of Science and Education of the Russian Federation, grant N 3.3380.2017/4.6, and by the National Research Nuclear University MEPhI in the framework of the Russian Academic Excellence Project (contract No. 02.a03.21.0005, 27.08.2013).



§ REFERENCES


9


Czopowicz:2012ey 
T. Czopowicz [NA61/SHINE Collaboration],

Prog. Theor. Phys. Suppl.  193, 29 (2012)

[arXiv:1201.5829 [hep-ex]].



Poskanzer:1998yz 
A. M. Poskanzer and S. A. Voloshin,

Phys. Rev. C 58, 1671 (1998)

[nucl-ex/9805001].



MPD:2017
The MultiPurpose Detector (MPD) Concepual Design Report, http://mpd.jinr.ru/wp-content/uploads/2016/04/MPD_CDR_en.pdf


Svintsov:2017rac 
I. A. Svintsov, P. E. Parfenov, I. V. Selyuzhenkov and A. V. Taranenko,

J. Phys. Conf. Ser.  798, no. 1, 012067 (2017).



UrQMD
UrQMD User's Guide, https://urqmd.org/documentation/urqmd-3.4.pdf

LAQGSM
User Manual for the Code LAQGSM, http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-01-6804


