CERN LHC CMS探测：PbPb碰撞中非高斯椭圆流波动的深度研究
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在《物理学快报B》(Physics Letters B, Vol. 789, 2019, pp. 643-665)的文章中，研究人员探讨了在CERN LHC上的CMS实验中，对PbPb碰撞（能量为√sNN = 5.02 TeV）中非高斯椭圆流波动的深入研究。这项研究聚焦于事件级别的椭圆流系数v2的波动性，v2是衡量核碰撞中物质在空间分布对称性的关键物理量。
研究者们分析了不同碰撞中心类别下，带电粒子的椭圆流概率分布p(v2)，这些粒子的横截面动量范围为0.3 < pT < 3.0 GeV/c，且在伪rapidity |η| < 1.0范围内。通过计算p(v2)分布的矩，他们利用2nd、4th、6th和8th阶累积量来估计v2系数，这些高阶累积量的结果表明了初始状态的非高斯性。
值得注意的是，研究发现p(v2)的分布并非简单的高斯形式，而是存在非零的标准化偏度值，这进一步证实了初始状态的非线性特性。偏度是一个统计学概念，它衡量了数据分布偏离对称程度的测量，偏度为0表示正态分布，而正值或负值则表示分布更尖锐或扁平。非零偏度意味着v2的波动可能受到非高斯初始条件的影响，这可能是由于量子色动力学(QCD)过程中的复杂相互作用或早期宇宙阶段的非平衡行为。
为了更好地理解这种非高斯性，文章还讨论了贝塞尔–高斯和椭圆幂拟合方法，这两种方法被用来描述初始状态的空间各向异性，即碰撞区域在不同方向上的不均匀性。这种分析对于揭示极端条件下的QCD相变和探索强子物质基本性质具有重要意义，因为它可以帮助科学家们深入理解在极高温和高压环境下，物质如何从普通质子-质子状态转变为可能的夸克-胶子等离子体。
这篇论文提供了关于PbPb碰撞中非高斯椭圆流波动的重要实验观测数据，这对理论模型的检验以及对强相互作用物质行为的理解构成了宝贵贡献。通过结合实验数据和理论模拟，研究者们正在逐步揭示高能核碰撞中复杂微观现象的深层次规律。
The CMS Collaboration / Physics Letters B 789 (2019) 643–665 647
Fig. 3. Ratios of higher order cumulant elliptic-flow harmonics with values obtained from the moments of the unfolded p(v
2
) distributions. Both statistical (lines) and
systematic (gray bands) uncertainties are shown. Hydrodynamic predictions for 2.76 TeV collisions from Ref. [33]are presented as a dark color band and are compared to
the measured v
2
{6}/v
2
{4} ratio. In addition, higher order cumulant ratios reported by the ATLAS Collaboration for 2.76TeV collisions [37]with 0.5 < p
T
< 20.0GeV/c and
|η| < 2.5are compared to the 5.02 TeV measurement. The error bars on the ATLAS measurement represent the quadratic sum of statistical and systematic uncertainties and
points are offset horizontally for clarity.
in Ref. [52]. The cumulant results exhibit the previously observed
v
2
{2} > v
2
{4} ≈ v
2
{6} ≈ v
2
{8} behavior. The centrality-dependent
ratios for the elliptic-flow coefficients obtained for different cumu-
lant
orders are shown in Fig. 3. For most centrality ranges, the
ratios indicate a rank ordering of the cumulants, with differences
on the order of a few percent and with v
2
{4} > v
2
{6} > v
2
{8},
that is qualitatively inconsistent with a pure Gaussian fluctuation
model of flow harmonics. The differences increase as the collisions
become more peripheral. The calculated v
2
{6}/v
2
{4} ratio based
on an event-by-event hydrodynamic calculation using Monte Carlo
Glauber initial conditions [53] and an η/s value of 0.08 is shown
by the shaded band. This simulation is for pions with 0.2 < p
T
<
3.0GeV/c in PbPb collisions at
√
s
NN
= 2.76 TeV [33]. Also shown
are results from the ATLAS Collaboration [37]for PbPb collisions
at 2.76 TeV and for charged particles with 0.5 < p
T
< 20.0GeV/c
and
|η| < 2.5. The calculation is consistent with the experimental
results found at both beam energies. The similarity between exper-
imental
results with 2.76 and 5.02 TeV is consistent with the small
changes in the initial-state eccentricities expected between these
energies [54] and the expectation that the cumulant flow harmonic
ratios follow those of the corresponding eccentricity ratios [33].
Fig. 4 shows the centrality dependence of the standardized
skewness γ
exp
1
. Finite values are found for the standardized skew-
ness
for collisions with centralities greater than ≈15%. The hy-
drodynamic
predictions for the γ
exp
1
values for PbPb collisions at
2.76 TeV from Ref. [33]are also shown and found to be consis-
tent
with the current measurements. Within the hydrodynamic
model and allowing for a finite skewness of the event-by-event v
2
distribution, the small splitting between the cumulant orders is ex-
pected
to follow the relationship (v
2
{6} −v
2
{8})/(v
2
{4} −v
2
{6}) =
0.091 [33]. Experimentally, we find a value for this splitting ra-
tio
of 0.143 ± 0.008 (stat) ± 0.014 (syst) for 20–25% central events,
with the ratio increasing to 0.185 ±0.005(stat) ±0.012(syst) as the
centrality increases to 55–60%. The observed values might suggest
higher order terms in a cumulant expansion of the v
2
distribu-
tion
are required to account for the skewness. This relationship
was recently examined by the ALICE collaboration in Ref. [55]us-
ing
a q-cumulant analysis, with results comparable to the findings
in this paper when considering systematic uncertainties and a dif-
ferent
kinematic range for the ALICE measurement.
Both
elliptic power and Bessel–Gaussian parametrizations used
for fits such as shown in Fig. 1 assume a linear response between
eccentricity and flow, but only the elliptic power law allows for a
finite skewness. For a Bessel–Gaussian distribution, the skewness
is equal to zero. This feature results in the elliptic power function
being in better agreement with the observed fluctuation behavior
Fig. 4. The skewness estimate with respect to the reaction plane determined using
the elliptic-flow harmonic based on different cumulant orders. Both statistical and
systematic uncertainties are shown, where statistical uncertainties are smaller than
the data points. Hydrodynamic model predictions for 2.76 TeV PbPb collisions from
Ref. [33]are shown as a colored band.
than the Bessel–Gaussian parametrization, yielding χ
2
/dof values
on the order of unity. To avoid bin-to-bin correlations introduced
by the unfolding procedure, goodness of fit values are obtained
by refolding the fitted distributions with the response matrix and
comparing to the measured distribution. The elliptic power χ
2
/dof
values
vary between 0.8 and 1.5 from central to peripheral col-
lisions,
while the Bessel–Gaussian χ
2
/dof values vary between 3
and 9. Point-by-point systematic uncertainties on the unfolded dis-
tributions
are correlated and are thus not considered in the fits.
The
fit parameters for the elliptic power function are shown in
Fig. 5 for the different centrality bins. As also found in Ref. [15],
the fits do not converge for central collisions where the distribu-
tions
become very close to a Bessel–Gaussian form. Consequently,
the parameters are shown for centralities >15%. The experimen-
tal
k
2
values show only a weak centrality dependence. Viscous
hydrodynamic calculations indicate that deviations from thermal
equilibrium should lead to a reduced correspondence between the
initial-state geometry and the flow signal in peripheral collisions
[27,28]. This effect is suggested in Fig. 5 by the decrease in the
k
2
value with increasing centrality, although the systematic uncer-
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