多实验射流截面数据驱动强耦合常数αs(M_Z)精确测定
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本文主要探讨了利用来自多个实验的包括ATLAS、CDF、CMS、D0、H1、STAR和ZEUS的射流截面测量数据来确定强耦合常数$$ \alpha _{\text {s}}(M_{\text {Z}}) $$(在质子-反质子对撞机上运行时的标准模型基本相互作用强度)的方法。射流截面是高能物理实验中一种重要的研究工具，它反映了粒子束碰撞后产生的辐射分布。
文章首先回顾了这些实验的数据收集过程和分析方法，强调了射流截面测量对于理解量子色动力学(QCD)中的强相互作用的重要性。作者对各个实验的测量结果进行了详尽的比较，以确保数据的一致性和可靠性。通过统计分析和理论建模，他们考虑了可能影响测量结果的各种系统误差和理论不确定性。
在确定$$ \alpha _{\text {s}}(M_{\text {Z}}) $$的过程中，作者采用了先进的数据分析技术，如全球最佳拟合方法，将不同实验的测量结果综合起来，以减小个体数据的随机误差对最终结果的影响。这种多实验数据融合的方法有助于提高精度和置信度，因为多个独立实验的结果可以相互校验和补充。
研究结果显示，通过结合所有实验的射流截面数据，可以得到比单个实验更为精确且稳定的$$ \alpha _{\text {s}}(M_{\text {Z}}) $$值。这不仅提升了强耦合常数测量的准确度，也展示了在现代高能物理学中，国际合作和数据共享对于深化基础物理理解的关键作用。
这篇文章不仅提供了关于如何利用多实验数据优化强耦合常数测定的实用方法，还展示了理论物理与实验测量之间紧密的联系，以及大型国际合作项目在推动科技进步中的核心地位。这项工作对于粒子物理学标准模型的验证以及未来高能物理实验的设计具有重要意义。
68 Page 4 of 16 Eur. Phys. J. C (2019) 79 :68
ing PDFs, scales μ
r
and μ
f
, and assumptions on α
s
(M
Z
).
Jet algorithms are taken either from the FastJet software
library [78] or, for jet cross sections in DIS, from NLO-
Jet++. The PDFs are evaluated via the LHAPDF interface
[79,80] at version 6. The running of α
s
(μ
r
) is performed at
2-loop order using the package CRunDec with five mass-
less quark flavours [81,82]. The minimal subtraction (
MS)
scheme [83–85] has been adopted for the renormalisation
procedure in these calculations.
For the computation of the inclusive jet cross section in
hadron-hadron collisions, the renormalisation and factorisa-
tion scales, μ
r
and μ
f
, are identified with each jet’s p
T
, i.e.
μ
r
= μ
f
= p
jet
T
. In neutral current (NC) DIS, the scales
are chosen to be μ
r
2
=
1
2
Q
2
+ ( p
jet
T
)
2
and μ
f
2
= Q
2
as used by the H1 Collaboration [27]. Alternative scale
choices have been discussed with respect to NNLO predic-
tions [5,7,86,87], but are beyond the scope of this article.
The EW corrections, c
EW
, relevant for the LHC data
are provided by the experimental collaborations together
with the data, based on Ref. [71]. These are considered
to have negligible uncertainties. Due to restrictions of the
scale choices in this calculation, the leading jet’s transverse
momentum, p
max
T
, is used to define the scales μ
r
and μ
f
.
The NP correction factors c
NP
, except for the STAR data
[88], are also provided by the experimental collaborations,
together with an estimate of the corresponding uncertainty
[16,20,27,32,33,41,46,61,62].
4 Comparison of three extraction methods for α
s
(M
Z
)
Commonly, the value of α
s
(M
Z
) is determined from inclu-
sive jet cross sections in a comparison of pQCD predictions
to the measurements. These α
s
(M
Z
) results therefore depend
on details of the extraction method such as the treatment of
uncertainties in the characterisation of differences between
theory and data, or the evaluation and propagation of theoret-
ical uncertainties to the final result. An overview of previous
determinations of α
s
(M
Z
) from fits to inclusive jet cross sec-
tion data is provided in Table 1. We choose the three α
s
(M
Z
)
determinations performed by the CMS [62], D0 [61], and
H1 [27] collaborations listed in the upper part of Table 1 for
further study.
The three extraction methods differ in the following aspects:
• the definition of the χ
2
function to quantify the agreement
between theory and data,
• the uncertainties considered in the χ
2
function,
• the strategy to determine the central result for α
s
(M
Z
),
• the propagation of the uncertainties to the value of
α
s
(M
Z
),
• the choice of PDF sets,
• the consideration of the α
s
(M
Z
) dependence of the PDFs,
and
• the treatment of further theoretical uncertainties.
To study the impact of these differences, we have imple-
mented the three methods in our computational framework
and will refer to them as “CMS-type”, “D0-type”, and “H1-
type”, respectively. As an integral part of these methods and
to reproduce as precisely as possible the respective published
results, we restrict ourselves in this section to the use of
the original somewhat older PDF sets. The CMS result was
obtained with the CT10 PDF set [89], and the D0 and H1
results with MSTW2008 PDFs [90]. The CMS-type and D0-
type methods use the entire α
PDF
s
(M
Z
) series available for the
PDF set, whereas the H1-type method uses a PDF determined
with a value of α
PDF
s
(M
Z
) = 0.1180.
Each method is then employed to extract α
s
(M
Z
) from
each of the individual data sets selected in Sect. 2,cf.also
Table 2. The experimental uncertainties and their correla-
tions are treated according to the respective prescriptions by
the experiments. The resulting α
s
(M
Z
) values are listed in
Table 3.
In a first step, these results are compared to the ones
obtained by the CMS [62], D0 [61], and H1 [27] collab-
orations as listed in Table 1. All three central results are
reproduced, the H1 result exactly, and the CMS and D0
results within +0.0003 and +0.0001. Such small differences
can easily be caused already by using different versions of
LHAPDF (e.g. changes from version 5 to version 6). The
experimental uncertainties of the CMS and H1 analyses are
exactly reproduced.
1
In a second step, the α
s
(M
Z
) results and their experi-
mental uncertainties are compared to each other and their
dependencies on the extraction method and PDFs are stud-
ied. The α
s
(M
Z
) results determined for each data set are
displayed in Fig. 1 (top row) for the three different extrac-
tion methods using CT10 PDFs (left) and MSTW2008 PDFs
(right). For the STAR data, α
s
(M
Z
) results cannot be deter-
mined in case of the CMS-type and D0-type methods with
MSTW2008 PDFs, since no local χ
2
minima are found. In
all other cases the α
s
(M
Z
) results obtained with MSTW2008
PDFs are rather independent of the extraction method for all
data sets. This is different when using CT10 PDFs: While
in this case the extraction method has little impact on the
α
s
(M
Z
) results from HERA data (H1 and ZEUS), it notably
affects the results for the LHC data (ATLAS and CMS), and
has large effects for the Tevatron data (CDF and D0). In the
1
For the D0 analysis, the decomposition of uncertainties has been pub-
lished only for their central result based on approximate NNLO pQCD
and hence a comparison of the experimental uncertainty on α
s
(M
Z
) for
the NLO result is not possible.
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