Azimuthally differential pion femtoscopy relative to the second and third harmonic in Pb-Pb 2.76 TeV collision from ALICE

TL;DR

This paper investigates azimuthally differential pion femtoscopy in Pb-Pb collisions at 2.76 TeV, revealing how source geometry and flow fields influence femtoscopic measurements and their relation to initial collision conditions.

Contribution

It introduces a detailed analysis of femtoscopic source shape deformation relative to second and third harmonic event planes using event shape engineering techniques.

Findings

Radii modulations reflect source geometry and flow velocity fields.

Event shape selection enhances understanding of initial geometry effects.

Results are compared with theoretical models.

Abstract

Azimuthally differential femtoscopic measurements, being sensitive to spatio-temporal characteristics of the source as well as to the collective velocity fields at freeze-out, provide very important information on the nature and dynamics of the system evolution. While the HBT radii modulations relative to the second harmonic event plane reflect mostly the spatial geometry of the source, the third harmonic results are mostly defined by the velocity fields. Radii variations with respect to the third harmonic event plane unambiguously signal a collective expansion and anisotropy in the flow fields. Event shape engineering (ESE) is a technique proposed to select events corresponding to a particular shape. Azimuthally differential HBT combined with ESE allows for a detailed analysis of the relation between initial geometry, anisotropic flow and the deformation of source shape. We present azimuthally differential pion femtoscopy with respect to second and third harmonic event planes as a function of the pion transverse momentum for different collision centralities in Pb-Pb collisions at sqrt(s_NN) = 2.76 TeV. All these results are compared to existing models. The effects of the selection of the events with high elliptic or triangular flow are also presented.

Equations

$$C(\mathbf{q},\Delta \phi )=N[(1-\lambda )+\lambda K(\mathbf{q})(1+G(\mathbf{q},\Delta \phi ))],$$

$$G(\mathbf{q},\Delta \phi )=\exp [-q_{\mathrm{out}}^2{R}_{\mathrm{out}}^2(\Delta \phi )-q_{\mathrm{side}}^2{R}_{\mathrm{side}}^2(\Delta \phi )-q_{\mathrm{long}}^2{R}_{\mathrm{long}}^2(\Delta \phi )-2q_{\mathrm{out}}{q}_{\mathrm{side}}{R}_{\mathrm{os}}^2(\Delta \phi )$$

$$-2q_{\mathrm{side}}{q}_{\mathrm{long}}{R}_{\mathrm{sl}}^2(\Delta \phi )-2q_{\mathrm{out}}{q}_{\mathrm{long}}{R}_{\mathrm{ol}}^2(\Delta \phi )],$$

$$R_{\mu }^2(\Delta \phi )=R_{\mu ,0}^2+2R_{\mu ,2}^2\cos (2\Delta \phi ),R_{\mathrm{os}}^2(\Delta \phi )=R_{\mathrm{os},0}^2+2R_{\mathrm{os},2}^2\sin (2\Delta \phi ),$$

Full text

††volume: 00

\journalname

Nuclear Physics A \runauth \jidnupha \jnltitlelogoNuclear Physics A

\dochead

XXVIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions

(Quark Matter 2017)

1 Introduction

The correlation of two identical particles at small relative momentum, commonly known as intensity, or Hanbury Brown-Twiss (HBT), interferometry, is an effective tool to study the space-time structure of the emitting source in relativistic heavy-ion collisions [2]. Due to the position-momentum correlations in particle emission, the so-called HBT radii become sensitive to the collective velocity fields, from which information about the dynamics of the system evolution can be extracted. Azimuthally differential femtoscopic measurements can be performed relative to the direction of different harmonic flow planes [3]. In particular, measurements of the HBT radii relative to the second harmonic flow provide information on the final shape of the system, which is expected to become more spherical compared to the initial state due to stronger in-plane expansion. In contrast, the azimuthal dependence of the HBT radii relative to the third harmonic flow plane can originate only from the the anisotropies in collective flow gradients, and the observation of any HBT radii azimuthal dependence will unambiguously signals a collective expansion and anisotropy in the flow fields [1]. Event shape engineering (ESE) is a relatively new technique which selects on the magnitude of the flow vector [4]. This selection can provide more control on the initial shape of the source.

2 Experimental analysis and results

The data Pb–Pb data used in this analysis were collected by ALICE in 2011. The Time Projection Chamber (TPC) was used to reconstruct the tracks in the pseudorapidity range $|\eta|<0.8$ as well as to identify pions via the specific ionization energy loss d$E$/d$x$ associated with each track. In addition to the TPC, the Time-Of-Flight (TOF) detector was used for identifying pions with transverse momentum $p_{\mathrm{T}}$ $>$ 0.5 GeV/c. The second and third harmonic event plane angles, $\Psi_{2}$ and $\Psi_{3}$, were determined using TPC tracks.

The correlation function $C({{\bf q}})$ was calculated as the ratio of $A({{\bf q}})$ and $B({{\bf q}})$, where ${\bf q}={\bf p}_{1}-{\bf p}_{2}$ is the relative 3-momentum of two pions, $A({\bf q})$ is the same-event distribution of particle pairs, and $B({\bf q})$ is the background distribution of uncorrelated particle pairs obtained using mixed events technique. The Bertsch-Pratt [5] out–side–long coordinate system was used [5]. The correlation function is fitted to

[TABLE]

where $N$ is the normalization factor, $\lambda$ is the chaoticity, and $\Delta\varphi=\mathrm{\varphi_{pair}}-\Psi_{2(3)}$. The function $G({{\bf q}},\Delta\varphi)$ describes the Bose-Einstein correlations and $K({{\bf q}})$ is the Coulomb correction. In this analysis the Gaussian form of $G({{\bf q}},\Delta\varphi)$ was used [6]:

[TABLE]

where the parameters $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$ are traditionally called HBT radii in the out, side, and long directions. The cross-terms $R_{\rm os}^{2}$, $R_{\rm sl}^{2}$, and $R_{\rm ol}^{2}$ describe the correlation in the out-side, side-long, and out-long directions, respectively.

[TABLE]

where $\mu={\rm out,side,long,sl,and~{}ol}$. Fitting the radii’s azimuthal dependence with the functional form of Eq.3 allows us to extract the average radii and the amplitude of oscillations [7] for the second harmonic results.

Figure 1 [7] shows the relative amplitudes of the radius oscillations $R^{2}_{{\rm out},2}/R^{2}_{{\rm side},0}$, $R^{2}_{{\rm side},2}/R^{2}_{{\rm side},0}$, $R^{2}_{{\rm long},2}/R^{2}_{{\rm long},0}$, and $R^{2}_{{\rm os},2}/R^{2}_{{\rm side},0}$. We observe similar results to that of STAR, however the STAR results [8, 9] show on average larger oscillations for $R_{\rm side}^{2}$. Our relative amplitudes for $R^{2}_{\rm out,2}/R^{2}_{\rm side,0}$, $R^{2}_{\rm side,2}/R^{2}_{\rm side,0}$, and $R^{2}_{{\rm os},2}/R^{2}_{{\rm side},0}$ show a clear centrality dependence, whereas the $R^{2}_{\rm long,2}/R^{2}_{\rm long,0}$ is very close to zero for all centralities, similarly to the results from RHIC [8].

The final source eccentricity at freeze-out $\varepsilon_{\rm final}$ can be estimated with an accuracy within 20–30% as $\varepsilon_{\rm final}\approx 2R_{{\rm side},2}^{2}/R_{{\rm side},0}^{2}$ [10]. Figure 2 [7] presents $2R_{{\rm side},2}^{2}/R_{{\rm side},0}^{2}$ for different $k_{\rm{T}}$ ranges as a function of the initial-state eccentricity for six different centralities. We find a smaller final-state anisotropy in the LHC regime compared to RHIC energies [11, 8]. In Fig. 2, we also compare our results to the 3+1D hydrodynamic calculations [12], this model slightly underestimates the final source eccentricity.

Figure 3 shows the relative amplitudes of the radius oscillations $R^{2}_{{\rm out},3}/R^{2}_{{\rm side},0}$, $R^{2}_{{\rm side},3}/R^{2}_{{\rm side},0}$, and $R^{2}_{{\rm os},3}/R^{2}_{{\rm side},0}$. The relative amplitudes for $R^{2}_{\rm out,3}/R^{2}_{\rm side,0}$ and $R^{2}_{\rm side,3}/R^{2}_{\rm side,0}$ have negative values for all centralities and $k_{\rm{T}}$ cuts. We compare our results with the 3+1D hydrodynamic calculations [12], where the relative amplitudes $R^{2}_{{\rm side},3}/R^{2}_{{\rm side},0}$ and $R^{2}_{{\rm os},2}/R^{2}_{{\rm side},0}$ agree quantitatively, and the relative amplitudes $R^{2}_{{\rm out},3}/R^{2}_{{\rm side},0}$ agree qualitatively with the 3+1D hydrodynamical calculations [12]. The relative amplitudes of the third harmonic results exhibit weak centrality and $k_{\rm{T}}$ dependence. According to the 3+1D hydrodynamical calculations, the negative signs of oscillations of $R_{\mathrm{o}ut}$ and $R_{\mathrm{s}ide}$ are an indication that the initial triangularity has been washed-out or even reversed due to the triangular flow. In the event shape engineering analysis, events were selected based on the magnitude of the second (third) order flow vector $q_{2}$ ($q_{3}$) [4], the Forward Multiplicity detector (FMD) was used to select on the magnitude of the flow vectors (-3.4 $<$ $\eta_{\mathrm{FMDC}}$ $<$ -1.7, 1.7 $<$ $\eta_{\mathrm{FMDC}}$ $<$ 5). We studied the effect of selecting the top 20% of the flow vector $q_{2}$ ($q_{3}$) on the magnitude of the flow $v_{2}$ ($v_{3}$). An enhancement of about 25% (15%) for $v_{2}$ ($v_{3}$) was observed for all centralities. Figure 4 shows the effect of large $q_{2}$ ($q_{3}$) selection on the relative amplitudes of the radii oscillations $R^{2}_{{\rm out},2}/R^{2}_{{\rm side},0}$ ($R^{2}_{{\rm out},3}/R^{2}_{{\rm side},0}$) and $R^{2}_{{\rm side},2}/R^{2}_{{\rm side},0}$ ( $R^{2}_{{\rm side},3}/R^{2}_{{\rm side},0}$). The large $q_{2}$ selection significantly enhances the relative amplitudes of the radius oscillations $R^{2}_{{\rm out},2}/R^{2}_{{\rm side},0}$ and slightly enhanced  $R^{2}_{{\rm side},2}/R^{2}_{{\rm side},0}$, possibly selecting more elliptic initial source. However, the large $q_{3}$ selection doesn’t affect the relative amplitudes of the radius oscillations.

3 Summary

We have performed a measurement of two-pion azimuthally differential femtoscopy relative to the second and third harmonic flow plane in Pb–Pb collisions at $\sqrt{s_{{}_{\rm NN}}}$ = 2.76 TeV. The final-state source eccentricity, estimated via side-radius oscillations relative to the second harmonic flow plane, is noticeably smaller than at lower collisions energies, but still exhibits an out-of-plane elongated source at freeze-out even after a stronger in-plane expansion. The negative signs of the relative amplitudes of radii oscillation, $R_{\mathrm{o}ut}$ and $R_{\mathrm{s}ide}$, measured relative to the third harmonic flow plane, are an indication that the initial triangularity is washed-out or even reversed according to the 3+1D hydrodynamic calculations. The azimuthally differential HBT combined with ESE measurements were performed. The large $q_{2}$ selection has significant enhancement on the HBT radii relative to the second harmonic flow plane, whereas large $q_{3}$ selection has no effect on the HBT radii relative to the third harmonic flow plane.

Acknowledgement

This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Nuclear Physics under Award Number DE-FG02-92ER-40713.