New results on collectivity with ATLAS

TL;DR

This paper presents recent ATLAS measurements of collective phenomena across various collision systems, revealing insights into particle emission sources, flow characteristics, and fluctuations in high-energy nuclear collisions.

Contribution

It provides new experimental results on collectivity in small and large collision systems, including HBT measurements, flow analysis, and fluctuation studies, expanding understanding of collective effects.

Findings

Particle emission source measured via HBT in p+Pb collisions

Elliptic flow of charged hadrons and muons analyzed in p+Pb

Longitudinal flow fluctuations studied in Pb+Pb collisions

Abstract

The collective phenomena are observed not only in heavy ion collisions, but also in the proton-nucleus and in high-multiplicity $pp$ collisions. The latest results from this area obtained in ATLAS are presented. In $p$+Pb collisions the emission source of particles is measured using the HBT method. The analysis of $p$+Pb data collected in 2016 provides information on the elliptic flow of charged hadrons and muons. Low multiplicity events from $pp$, $p$+Pb and peripheral Pb+Pb collisions are studied with the cumulant methods. A deeper understanding of Pb+Pb collisions is provided by the analysis of longitudinal fluctuations of the collective flow parameters.

Equations

$$C_{\mathrm{BE}}(\mathbf{q})=1+e^{\Vert \mathbf{Rq}\Vert },$$

$$\frac{\mathrm{d}{N}_{\mathrm{ch}}}{\mathrm{d}\varphi }\sim 1+2\sum _{n=1}^{\infty }{v}_n(p_{\mathrm{T}},\eta )\cos (n(\varphi -{\Psi }_n)).$$

$$v_n\{2\}=\sqrt{c_n\{2\}},v_n\{4\}=\sqrt[4]{-c_n\{4\}},v_n\{6\}=\sqrt[6]{-c_n\{6\}/4},v_n\{8\}=\sqrt[8]{-c_n\{8\}/33}.$$

$$\frac{v_2\{4\}}{v_2\{2\}}={\left(\frac{4}{3+N_s}\right)}^{1/4}.$$

$$r_{n|n;k}\approx 1-4k{F}_{n;k}^{\mathrm{r}}\eta \mathrm{and}{R}_{n,n|n,n}\approx 1-4F_{n;n}^{\mathrm{twi}}\eta ,$$

Full text

Proceedings of the Fifth Annual LHCP

ATL-PHYS-PROC-2017-064

June 9, 2017

NEW RESULTS ON COLLECTIVITY WITH ATLAS

KRZYSZTOF W. WOŹNIAK 111Work supported in part by the National Science Centre, Poland, grant 2015/18/M/ST2/00087 and by PL-Grid Infrastructure.

*On behalf of the ATLAS Experiment,

Institute of Nuclear Physics, Polish Academy of Sciences

Krakow, Poland*

ABSTRACT

The collective phenomena are observed not only in heavy ion collisions, but also in the proton-nucleus and in high-multiplicity $pp$ collisions. The latest results from this area obtained in ATLAS are presented. In $p$+Pb collisions the emission source of particles is measured using the HBT method. The analysis of $p$+Pb data collected in 2016 provides information on the elliptic flow of charged hadrons and muons. Low multiplicity events from $pp$, $p$+Pb and peripheral Pb+Pb collisions are studied with the cumulant methods. A deeper understanding of Pb+Pb collisions is provided by the analysis of longitudinal fluctuations of the collective flow parameters.

PRESENTED AT

The Fifth Annual Conference

on Large Hadron Collider Physics

Shanghai Jiao Tong University, Shanghai, China

May 15-20, 2017

1 Introduction

Strong collective effects were first found in heavy ion collisions, where they indicate a creation of the Quark-Gluon Plasma. This phase of matter manifests azimuthal correlations among produced particles, referred to as collective particle flow. However, similar effects are observed in proton-nucleus and even in high-multiplicity proton-proton collisions. The measurements of Pb+Pb, $p$+Pb and $pp$ collisions at energies available from the Large Hadron Collider (LHC) and performed using the ATLAS detector [1] allow to study collective phenomena in detail. The obtained results are important for understanding the particle production at LHC energies.

2 Results

One of the questions, which can be answered by analysing correlations among produced particles is the size of their emission source. The Bose-Einstein correlations of identical bosons, as a function of the difference of their momenta, ${\mathrm{\bf q}}={\mathrm{\bf p^{a}}}-{\mathrm{\bf p^{b}}}$, can be parameterized as:

[TABLE]

where the diagonal elements of the matrix ${\bf R}$ are $R_{\mathrm{out}}$, $R_{\mathrm{side}}$ and $R_{\mathrm{long}}$. These parameters were studied for $p$+Pb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV [2] as a function of $k_{\mathrm{T}}$ (where $\mathrm{\bf k}=0.5(\mathrm{\bf p^{a}}-\mathrm{\bf p^{b}})$) and the number of nucleons participating in collisions, $N_{\mathrm{part}}$. Especially interesting is the ratio $R_{\mathrm{out}}/R_{\mathrm{side}}$ which represents asymmetry of the source. In Figure 1 (left) one can see that this ratio depends on $k_{\mathrm{T}}$, which indicates radial expansion of the source of particles [2]. This ratio depends also on the orientation of the correlated pairs (represented by $\phi_{k}$, azimuthal angle of $k_{\mathrm{T}}$) with respect to the event plane, $\Psi_{2}$, as shown in Figure 1 (right). The $R_{\mathrm{out}}/R_{\mathrm{side}}$ ratio is larger out of plane than in plane ($\phi_{k}\approx\Psi_{2}$) as $R_{\mathrm{out}}$ is enhanced out of plane and $R_{\mathrm{side}}$ does not change much with $\phi_{k}-\Psi_{2}$ [3].

In the studies of azimuthal correlations among charged particles the Fourier decomposition is used:

[TABLE]

The flow harmonics $v_{n}$ can be obtained also from two-particle correlations. In $pp$ and $p$+Pb collisions these correlations contain large contributions from other sources (non-flow), which have to be subtracted. ATLAS applies a template method [4] to remove them. In Figure 3 the elliptic flow $v_{2}$ in $p$+Pb collisions at 5.02 TeV and 8.16 TeV for all hadrons ($h$-$h$) and for hadron-muon ($h$-$\mu$) correlations (at 8.16 TeV) is shown as a function of charged-particle multiplicity, $N_{\mathrm{ch}}^{\mathrm{rec}}$ [5]. There is no dependence of $v_{2}$ on the energy of collisions and a very weak increase with multiplicity. The values of $v_{2}^{h-\mu}$ reach only about $0.6\,v_{2}^{h-h}$.

The non-flow effects are most pronounced in low-multiplicity events as they usually involve relatively small number of particles in limited kinematical range (resonance decays, jets) and are thus suppressed in multi-particle correlations. Such correlation can be used to calculate cumulants, $c_{n}\{2k\}$ [6], closely related to flow harmonics:

[TABLE]

In the case of $c_{n}\{2\}$ a separation of particles in pseudorapidity ($|\Delta\eta|>2$) is required in calculations of $v_{n}\{2,|\Delta\eta|>2\}$ to suppress short-range correlations. In Figure 3 elliptic flow $v_{2}$ values obtained for $p$+Pb, Pb+Pb and $pp$ collisions using different multi-particle cumulants are compared [6]. While the $v_{2}\{2k\}$ values are similar (for k=2, 3, 4), those for $k=1$ with $|\Delta\eta|>2$ requirement are larger. Comparison of $v_{2}\{2,|\Delta\eta|>2\}$ for different systems shows an increase with the size of colliding projectiles for events with the same number of produced particles. The $v_{2}\{2k\}$ harmonics do not change with the multiplicity and the energy for $pp$ collisions while are increasing with multiplicity for $p$+Pb and Pb+Pb collisions.

Further suppression of short range correlations can be achieved if in the calculations of correlations, used to obtain cumulants, particles from different ranges of pseudorapidity (i.e. subevents) are used [7]. For $c_{2}\{4\}$ negative values are expected, as otherwise $v_{2}\{4\}$ can not be calculated using Eq. 3. In Figure 6 one can see that positive $c_{2}\{4\}$ are obtained at low multiplicities, but are reduced in two- and especially three-subevent cumulant methods. The $v_{2}\{4\}$ values from three-subevent method are lower than $v_{2}\{2\}$ from peripheral subtraction or template fit method (Figure 6). This difference can be interpreted as a result of event-by-event flow fluctuations, which are closely related to the effective number of sources, $N_{s}$, for particle production:

[TABLE]

The number of sources shown in Figure 6 is similar for $pp$ and $p$+Pb collisions and for the latter it increases from 10 to 20 in the full available event-multiplicity range.

For events with large multiplicities, such as measured in Pb+Pb collisions at 5.02 TeV, standard methods of calculation of flow harmonics are sufficiently robust against non-flow effects. In Figure 8 (left) $v_{n}$, for $n=2-7$, as a function of $p_{\mathrm{T}}$ in 20-30% centrality interval are shown [8]. Flow harmonics up to $v_{7}$ are non-zero. The $v_{2}$ is 0.05 even for $p_{\mathrm{T}}>20$ GeV. Relatively large $v_{2}$ for particles with high transverse momenta means that also very energetic partons are interacting in the QGP. This observation is consistent with the measured suppression of high-$p_{\mathrm{T}}$ charged hadrons as quantified by the nuclear modification factor, $R_{\mathrm{AA}}$ [9]. In Figure 8 (right) one can see that $R_{\mathrm{AA}}<1$ in the same centrality and $p_{{}_{\mathrm{T}}}$ range.

A deeper understanding of flow phenomena may provide study of the dependence of flow fluctuations on position in pseudorapidity using correlators $r_{n|n;k}$ and $R_{n,n|n,n}$ (see Ref. [10] for definitions). Assuming that their dependence on pseudorapidity is linear it can be parameterized as:

[TABLE]

where $F_{n;k}^{\mathrm{r}}=F_{n;n}^{\mathrm{asy}}+F_{n;n}^{\mathrm{twi}}$, $F_{n;n}^{\mathrm{asy}}$ and $F_{n;n}^{\mathrm{twi}}$ are decorrelation parameters connected with magnitude (asymmetry) and twist fluctuations, respectively. In Pb+Pb collisions the decorrelation parameters $F_{n;k}^{\mathrm{r}}$ are similar for all centralities but depend on the energy of the collision and are 10-16% larger at 2.76 TeV than at 5.02 TeV (see Figure 8 (left)). On the other hand the magnitude and twist decorrelation parameters, shown in Figure 8 (right), are approximately constant for $N_{\mathrm{part}}>100$. In the whole multiplicity range $F_{n;2}^{\mathrm{asy}}\approx F_{n;2}^{\mathrm{twi}}$ for the same $n$ [10].

3 Conclusions

Studies of correlations among particles produced in different types of collisions available at LHC provide valuable information on properties of their source. In $p$+Pb collisions the volume from which particles are emitted has an elongated shape and undergoes a radial expansion. The flow of muons originating from $b$ or $c$ quarks is much smaller than that of charged hadrons. Results on flow harmonics obtained using cumulant methods clearly show that the non-flow contributions are very important in low-multiplicity events and need to be properly subtracted. In new detailed studies of Pb+Pb collisions non-zero flow harmonics up to $v_{7}$ were measured. Analysis of longitudinal fluctuations of flow harmonics reveals decorrelation effects which are stronger at lower collision energy, but similar when decomposed into magnitude and twist contributions.