ATLAS实验：5.02TeV铅铅和质子铅碰撞中的平均横向动量与流谐波关联测量

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"这篇论文是ATLAS合作组在Eur.Phys.J.C期刊上发表的一篇开放访问文章，探讨了在5.02 TeV的铅-铅和质子-铅碰撞中平均横向动量与流谐波的相关性。通过在大型强子对撞机(LHC)上的实验，研究了夸克-胶子等离子体的特性。" 在高能物理学领域，尤其是在超相对论性离子碰撞研究中，夸克-胶子等离子体（Quark-Gluon Plasma, QGP）是一种非常重要的研究对象。ATLAS探测器是LHC的一个关键组件，用于检测这些高能碰撞产生的粒子，以理解基本粒子交互的极端条件。在这项研究中，ATLAS团队利用了5.02 TeV的铅-铅碰撞数据样本（总集成亮度为22μb^-1）和质子-铅碰撞数据样本（总集成亮度为28nb^-1），对流动谐波进行了详细分析。流动谐波是描述高能碰撞中粒子集体运动的一种方式，它反映了系统在碰撞后形成的不均匀性。这个分析主要关注的是二次、三次和四次流动谐波，它们分别对应于椭圆流（v2）、三角流（v3）和四次流（v4）。通过修改过的皮尔逊相关系数，研究了这些流动谐波与单个事件中带电粒子平均横向动量的关联。在铅-铅碰撞中，观察到随着事件中心度的增加，所有研究的流动谐波的相关系数都有显著的变化，这表明QGP的形成和演化受参与碰撞的核子数量的影响。而这些变化在不同带电粒子动量范围内表现得相当一致，这为理解QGP的动力学提供了线索。在质子-铅碰撞中，只观察到了二阶流动谐波的微弱中心依赖性，这可能暗示了在这些碰撞中集体流动的形成机制有所不同。通过将实验结果与基于流体动力学模型的预测进行比较，可以定性地描述铅-铅数据，这有助于进一步理解等离子体的行为以及QGP的性质。这些发现对于推动我们对强相互作用的理解以及早期宇宙状态的模拟具有重要意义。 ATLAS实验的这项研究揭示了在5.02 TeV能级下的铅-铅和质子-铅碰撞中，平均横向动量与流动谐波的复杂关系，提供了有关夸克-胶子等离子体特性的宝贵信息，并为今后的理论建模和实验研究奠定了基础。

985 Page 6 of 29 Eur. Phys. J. C (2019) 79 :985

gitudinal impact parameters of the track to 0.5 mm. For the

p+Pb analysis, the loose selection relaxes the requirements

on the transverse and longitudinal impact parameters of the

track to 2 mm and on the impact parameter signiﬁcances

to less than 4. In the tight selection, the impact parame-

ter values and their signiﬁcances must be less than 1 mm

and 2, respectively. For each of the two track selections the

absolute difference is calculated with respect to the baseline

measurement: |ρ(v

{2}

, [p

])

base

−ρ(v

{2}

, [p

])

loose

|or

|ρ(v

{2}

, [p

])

base

− ρ(v

{2}

, [p

])

tight

|. The largest dif-

ference is taken as a systematic uncertainty.

Detector material Since the tracks that are used in the cal-

culation of ρ(v

{2}

, [p

]) are weighted by the inverse of

the tracking efﬁciency, a bias in its estimation due to inac-

curate modelling of the material in the detector may change

the balance between low- and high-p

tracks in the sums.

Based on simulations, the estimated uncertainty in the detec-

tor description is obtained [43,44]. The resulting p

- and

η-dependent uncertainties in the track efﬁciency of up to 4%

are used to determine the systematic uncertainty.

Tracking azimuthal uniformity In this analysis, the weight-

ing factors w correct for any non-uniformity in the azimuthal

angle distribution of reconstructed tracks. The weights are

obtained from the data by requiring azimuthal uniformity

over the two-dimensional distribution of reconstructed tracks

in the η–φ plane. The effect of that correction on the result

is conservatively estimated by comparing the baseline mea-

surement and the measurement obtained without applying

this weight. The uncertainty is small, and it envelopes poten-

tial effects of imperfections in the weighting factors determi-

nation, including their dependence on the transverse momen-

tum, collision centrality, run-by-run differences, on dead

module maps or the vertex position.

Residual pile-up events The selection criteria discussed in

Sect. 3 suppress the fraction of pile-up events accepted for

analysis to almost zero in central Pb+Pb collisions. To esti-

mate the systematic uncertainty related to pile-up, the mea-

surement is conservatively repeated without this event rejec-

tion, resulting in at most a 1% difference in the most central

Pb+Pb events for the ρ(v

{2}

, [p

]) coefﬁcient. The p +Pb

data were taken with higher pile-up than the Pb+Pb data.

To estimate the impact of contamination by residual pile-up

events, p+Pb results were obtained with only the vertex crite-

ria applied. The variation covers the estimated residual pile-

up fraction in events of the highest track multiplicity [36].

Centrality selection The minimum-bias trigger is fully efﬁ-

cient for the 0–85% centrality interval. However, the total

fraction of inelastic Pb+Pb events selected is known only to

1% accuracy due to trigger inefﬁciency and possible sample

contamination in more peripheral interactions. The central-

ity is estimated using the  E

FCal

distribution [6,10] and the

Glauber model [38] to obtain the mapping from the observed

 E

FCal

to the number of nucleons participating in the col-

lision, N

part

. The modiﬁed PCC uncertainty is evaluated by

repeating the analysis with the altered centrality selections on

the  E

FCal

distribution, which results in ±1% uncertainty

in the total fraction of inelastic Pb+Pb events. The centrality

selection contributes mainly to uncertainties for peripheral

collisions.

Figure 1 shows the magnitude of the systematic uncer-

tainties δρ(v

{2}

, [p

]) for n = 2 − 4 in Pb+Pb collisions

as a function of N

. In Pb+Pb collisions, the systematic

uncertainty of the measured correlation coefﬁcients across

different order harmonics and centralities is not dominated

by a single source. One of the largest uncertainties comes

from restoring the azimuthal uniformity, and dominates for

the second order harmonic in the most central collisions and

for the third and fourth order harmonics almost over the full

centrality range.Asizeable contributionto the uncertainty for

all three harmonics is due to the track selection. The impact

of the detector material is rather small except for a signiﬁcant

contribution for the forth order harmonic in the most central

events. The residual pile-up in Pb+Pb collisions gives a negli-

gible contribution. Figure 1d shows systematic uncertainties

for ρ(v

{2}

, [p

]) coefﬁcients in p+Pb collisions for the

main interval of 0.3 < p

< 2 GeV as a function of event

activity. In p+Pb interactions the largest uncertainty in the

most active collisions (N

> 150) originates from pile-up.

The track selection is a source of sizeable uncertainty for this

collision system, while the azimuthal uniformity correction

procedure and the detector material have a small impact.

Details on the contributions to systematic uncertainties

from different sources of c

,Var



{2}



dyn

and

cov(v

{2}

, [p

]) are included in the Appendix.

6 Results

6.1 The constituents of the modiﬁed PCC

The constituents of the modiﬁed PCC, c

,Var



{2}



dyn

and cov(v

{2}

, [p

]) and are combined, using Eq. (4), to

obtain ρ. Figure 2 shows the dynamical p

ﬂuctuation coef-

ﬁcient c

as a function of charged-particle multiplicity in

Pb+Pb and p+Pb collision systems for tracks in three dif-

ferent p

intervals. A strong decrease of c

with increasing

is observed in all measured results. A similar decrease

was seen for c

in Au+Au and Pb+Pb data at lower centre-

of-mass energies [28,29], evaluated for lower p

range,

0.15 < p

< 2 GeV, not accessible with the ATLAS detec-

tor. For the same N

,thec

values differ by an order of

magnitude for different p

ranges of tracks used in the anal-

ysis. For the intervals with the same lower p

limit, the c

123

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ATLAS实验：5.02TeV铅铅和质子铅碰撞中的平均横向动量与流谐波关联测量

pp冲突中$$ \ sqrt {s} = 7 \\ hbox {TeV} $$ s = 7TeV和p–Pb冲突中$$ \ sqrt {s_ { \ mathrm {NN}}} = 5.02 \ \ hbox {TeV} $$ sNN = 5.02TeV

由s = 7 $$ \ sqrt {\ mathrm {s}} = 7 $$ TeV pp和s NN = 5.02 $$ \ sqrt {s _ {\ mathrm {NN}}}中的双强子相关的射流碎片横向动量测量 = 5.02 $$ TeV p–Pb碰撞

$$ \ sqrt {s_ {NN}} = 5.02 $$ sNN = 5.02 TeV的p–Pb碰撞的热模型描述

在sNN = 5.02 $$ \ sqrt {s _ {\ mathrm {NN}}} = 5.02 $$和8.16 TeV的质子-铅碰撞中带电强子的伪快速分布

ATLAS的$$ \ sqrt {s _ {_ \ text {NN}}} = 5.02 $$ sNN = 5.02 Tev时，Pb + Pb碰撞中的及时和非及时$$ J / \ psi $$ J /ψ椭圆流 探测器

在$$ \ sqrt {s _ {\ mathrm {NN}}} = 5.02〜\ text {Te} \ text {V} $$ sNN的Pb + Pb碰撞中测量$$ W ^ \ pm $$ W±玻色子产生量 ATLAS探测器的= 5.02Te

勘误至：用ATLAS探测器测量在$$ \ sqrt {s} = 5.02 $$ s = 5.02 TeV pp碰撞中W和Z玻色子的产生

$$ \ text {Pb--Pb} $$ Pb--Pb碰撞在$$ \ sqrt {s_ \ mathrm {{NN}}} = 2.76 \ hbox {TeV} $$ sNN = 2.76TeV

在$$ \ sqrt {s _ {\ mathrm {NN}}} $$ sNN = 5.02 TeV的p–Pb碰撞中产生中性介子和$$ \ eta $$η介子

来自美强子衰变的电子的椭圆流是从$$ \ sqrt {s_ \ mathrm {NN}} = 2.76 \ \ hbox {TeV} $$ sNN = 2.76TeV的Pb–Pb碰撞数据中提取的

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ATLAS的$$ \ sqrt {s _ {_ \ text {NN}}} = 5.02 $$ sNN = 5.02 Tev时，Pb + Pb碰撞中的及时和非及时$$ J / \ psi $$ J /ψ椭圆流探测器