13 TeV质子-质子碰撞中顶夸克极化和tt自旋相关性的Dilepton测量

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"这篇研究论文详细介绍了在质子-质子碰撞中，特别是在13 TeV能量条件下，利用双轻子（电子对、电子-μ子对或μ子对）最终态来测量顶夸克的极化和顶夸克对（tt）的自旋相关性的方法。CMS实验在2016年收集了这些数据，总集成光度达到了35.9 fb^-1。这是首次在13 TeV能量下对tt生产密度矩阵的自旋相关部分的独立系数进行部分级归一化微分截面的测量。实验结果与标准模型的预测进行了对比，这些预测基于量子色动力学（QCD）的NLO精度模拟以及包含电弱校正的NLO QCD计算。所有测量值都与标准模型的预测保持一致。此外，归一化微分截面还被用于限制顶夸克的异常色磁偶极矩和偶极矩矩，分别在-0.24 < C_tG/Λ^2 < 0.07 TeV^-2和-0.33 < C_{tGI}/Λ^2 < 0.20 TeV^-2的范围内，置信度为95%。" 这篇论文的要点包括： 1. **实验背景**：研究在大型强子对撞机（LHC）的CMS实验中进行，利用质子-质子碰撞产生的双轻子事件，探索高能物理中的顶夸克性质。碰撞能量为13 TeV，这是粒子物理学研究的重要能量范围。 2. **数据采集**：数据集覆盖2016年的整个运行周期，总集成光度为35.9 fb^-1，提供了大量的样本以进行精确的统计分析。 3. **测量方法**：首次测量了tt对生产密度矩阵的自旋相关部分的独立系数，这些系数对于理解顶夸克的自旋状态和自旋相关性至关重要。 4. **理论框架**：比较了实验结果与标准模型的预测，其中预测基于NLO QCD的计算，同时考虑了电弱效应。这有助于验证标准模型的准确性和完整性。 5. **物理参数限制**：通过拟合归一化微分截面，限制了顶夸克的两个关键参数——异常色磁偶极矩（C_tG/Λ^2）和偶极矩矩（C_{tGI}/Λ^2）。这些限制提供了对超出标准模型的新物理现象的可能性的约束。 6. **结果一致性**：所有测量值均未发现与标准模型的显著偏差，这表明在目前的能量尺度下，标准模型仍然是描述顶夸克物理的有效理论。这篇研究是粒子物理学领域的一个重要贡献，它加深了我们对顶夸克这一最重基本粒子的理解，并且对可能存在的新物理现象进行了严格的测试。通过这种方法，科学家们能够更全面地了解宇宙的基本构成和相互作用。

measurements are made using the combination of events

from the three channels, where the fraction of signal events

in the data sample, estimated from simulation, is 79%.

In Figs. 2 and 3, distributions of all the reconstructed

angular observables (defined in Sec. II) are shown. There is

reasonable agreement between the data and the sum of the

expected signal and background contributions given the

systematic uncertainties. In addition to the systematic

uncertainties discussed in Sec. VII, two uncertainties that

affect only the normalization of the measured differential

cross section are considered: the 2.5% uncertainty in the

integrated luminosity of the data sample [5] is applied to the

normalization of all simulated predictions, and a 1.5%

normalization uncertainty is applied to the t

t prediction to

account for the uncertainty in the dileptonic branching

fraction (BF) [1]. The shapes of the reconstructed distri-

butions differ substantially from the expected parton-level

functional forms of Eqs. (8)–(10) owing to the effects of bin

migration, detector acceptance and efficiency, and back-

ground events, which are described in Sec. VI.

VI. UNFOLDING THE DIFFERENTIAL

CROSS SECTIONS

The effects of detector acceptance and efficiency sculpt

the reconstructed distributions, and the smearing intro-

duced by the detector response, kinematic reconstruction

algorithm, PS, and hadronization leads to the migration of

events across bins. In order to measure the differential cross

sections at the parton level in the full phase space, these

effects are accounted for by using the TUnfold regularized

unfolding method [51]. The response matrix used in the

unfolding is calculated for each measured distribution using

the default t

t simulation, where the momenta of the parton-

level top quarks are defined after QCD radiation has been

simulated but before the top quark decays.

To keep the bin-to-bin migrations small (to avoid strong

bin-to-bin correlations in the unfolded distributions), the

widths of the measurement bins are chosen according to the

reconstruction resolution of the observable. This is quanti-

fied both directly by comparing the generator level and

detector level observables in simulation, and by measuring

the purity and stability. Purity is defined as the fraction of

events in a given bin at the detector level that originate from

the same bin at the generator level, and stability is defined

as the fraction of events in a given bin at the generator level

that are reconstructed in the same bin at the detector level.

For all observables measured in the top quark rest frame,

the use of six bins of uniform width is found to be well

matched to the reconstruction resolution. The purities and

stabilities are typically 40%. For the observables measured

in the laboratory frame (cos φ

lab

and jΔϕ

j), six uniform-

width bins are also used. These observables have excellent

experimental resolution, and the purities and stabilities

are >99%.

The presence of background events is accounted for prior

to performing the unfolding. After subtracting all other

background components, the background from dileptonic t

events with leptonically decaying τ leptons is subtracted as

a fraction of the total remaining events. The fraction is

evaluated per bin as the ratio of the background to the total

dileptonic t

t events in simulation. Thus, the shapes of the

distributions for dileptonic t

t events are taken from data,

and any dependence on the total cross section used in the

normalization of the simulated t

t sample is avoided.

In TUnfold, a procedure based on matrix inversion is

used to obtain an unfolded distribution from the measured

distribution by applying a χ

minimization technique. The

potential large statistical fluctuations and strong anticorre-

lations between adjacent bins arising from the matrix

inversion are suppressed by introducing a term in the χ

expression that smooths (regularizes) the shape of the

unfolded distribution [51]. The regularization term penal-

izes the curvature of a vector constructed from the product

of the difference between the unfolded and simulated bin

values and a factor calculated using the expected functional

form [Eqs. (8)–(10)] such that a deviation in the coefficient

corresponds to a linear change in the vector. Since linear

changes are unconstrained by regularization of the curva-

ture, and the functional forms at the parton level (which are

unaffected by BSM phenomena in t

t production) depend

only on the coefficient, this ensures that the regularization

cannot introduce a bias in the unfolded distribution. For the

laboratory-frame distributions there are no such simple

functional forms, and no factor is applied to the difference

vector. However, this choice is of little consequence

because the regularization is very weak owing to the low

level of bin migration.

The use of wide bins for the response matrix loses

information about its dependence inside each bin, meaning

the unfolding can be biased if the physical process density

differs from the simulation. Since the curvature regulari-

zation is unbiased, we make use of narrower bins in the

TUnfold χ

minimization; a factor 4 narrower is found to be

sufficient to reduce the bias from binning to a negligible

level. We have thus replaced the biased implicit regulari-

zation from binning with an unbiased regularization of the

curvature within each of the original bins.

The regularization level is determined for each distribu-

tion by minimizing the average global correlation coef-

ficient (ρ

avg

) [51], where ρ

avg

is determined after rebinning

to the original six bins.

For each measured bin, we perform tests using pseudo-

data to confirm a linear response of the method to variations

in the coefficient, and confirm that the distribution of the

difference between the nominal bin value and that mea-

sured in pseudodata, normalized to the measured uncer-

tainty, is consistent with having zero mean and unit width.

The data in the three channels are combined before

unfolding in order to model correlations between channels

MEASUREMENT OF THE TOP QUARK POLARIZATION AND t

t … PHYS. REV. D 100, 072002 (2019)

072002-7

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