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首页顶夸克质量测量中的强子化不确定性分析
"顶夸克质量测量中强子观测物的碎片不确定度" 本文详细探讨了在顶夸克质量测量过程中,由强子化和喷淋建模所引入的不确定性问题。顶夸克作为最重的基本粒子,其质量的精确测量对于理解标准模型以及可能的新物理现象至关重要。研究集中于那些利用顶夸克衰变到特定强子态的观测值,如t→任何+ J/ψ或t→任何+ (B→ 带电轨道),其中B代表B强子。 作者们分析了HERWIG 6和PYTHIA 8这两个事件生成器中的参数对顶夸克质量测量的敏感性。他们发现,这些参数的微小变化可能会导致顶夸克质量的蒙特卡洛模拟结果出现O(1%-10%)的偏差,这超过了500 MeV的阈值。为了减小这种不确定性,研究人员评估了光谱特性,如EB、mB 3的峰值、终点和分布,以及一些mT2类变量来测量顶夸克质量的方法。他们发现,尽管选择接近终点的区域可以降低对建模参数的依赖,但这会增加统计不确定性。 为了解决这个问题,文章提出了利用大型强子对撞机(LHC)上的顶夸克生成和衰变数据来约束喷淋和强子化的可能性。通过对多个校准观测值的全球性探索,作者们发现这些观测值对蒙特卡洛参数敏感,但对顶夸克质量的影响较小。如果这些观测值的测量精度能达到1%,那么它们可以有效地约束模型参数,从而减少不确定性。 文章强调了精确测量和理解顶夸克质量的重要性,因为这不仅有助于验证标准模型的预测,还可以揭示潜在的新物理现象。通过更深入地研究强子化和喷淋过程,以及开发更精确的模拟技术,科学家们有望提高顶夸克质量测量的准确性和可靠性。这项工作为未来的顶夸克物理实验提供了重要的参考,并为优化测量策略提供了指导。
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492 G. Corcella et al. / Nuclear Physics B 929 (2018) 485–526
Table 1
Ranges
and central values of the parameters that we varied. Note that some values are not varied around the default values
of the Monash tuning. For instance we run r
B
around the mid-point between PYTHIA6.4 and PYTHIA8-MONASH values.
PYTHIA8 parameter Range Monash default
p
T,min
TIMESHOWER:PTMIN 0.25–1.00 GeV 0.5
α
s,FSR
TIMESHOWER:ALPHASVA L U E 0.1092–0.1638 0.1365
Recoil T
IMESHOWER:RECOILTOCOLOURED on and off on
b quark mass 5:
M0 3.8–5.8 GeV 4.8 GeV
Bowler’s r
B
STRINGZ:RFACTB 0.713–0.813 0.855
String model a S
TRINGZ:ANONSTANDARDB 0.54–0.82 0.68
String model b S
TRINGZ:BNONSTANDARDB 0.78–1.18 0.98
Here the z variable implies the fraction of E + p
z
taken by the B hadron under the assumption
that a b quark of energy E moves along the z-axis, while m
T
symbolizes the associated B-hadron
transverse mass.
As discussed in the introduction, hadronization models are specific to the sho
wering to which
they are attached, and therefore it is important to study the sensitivity of top-mass observables
to variations of the showering quantities. Parameters for which a sensitivity is expected include
p
T,min
which is the scale at which the parton shower is stopped and hadronization models take
over, the value of the strong coupling constant at the Z-boson mass that is used in the final-state
parton shower, and the value of the b quark mass. In addition, we also check the effect induced
by discrete choices in using the b-quark or the W boson as a recoiler to impose momentum
conserv
ation when we have splittings from the b quark in the shower.
4
It is important to remark that the chosen range of variation of these parameters has little
importance for the calculation of the sensitivity defined in eq. (2). In fact, the derivative of the
observables with respect to the Monte Carlo parameters is typically stable across large ranges,
and as will be sho
wn later on, even the sensitivity
(O)
θ
is largely independent of it. What mainly
leads to the choice of given ranges is to have sufficiently large differences between spectra for
different parametrizations, so that the derivatives can be computed accurately, without being
overwhelmed by the statistical errors due to the finite size of the Monte Carlo sample.
At the same time, we avo
id taking values too far from the default, since this might generate
unforeseen changes in the Monte Carlo predictions. For these reasons, we shall vary parameters
up and down by at most 20% of their central values and evaluate numerically the derivatives
in all available data points. Fo
r a summary of the PYTHIA parameters and the ranges of varia-
tion, we refer to Table 1. In principle, other parameters could be varied and tuned as they affect
the kinematics of top quark events. For instance the initial state α
s
parameter of PYTHIA8,
S
PACESHOWER:ALPHASVA L UE , could be considered. We choose to not investigate them, as
they can be fixed from specific measurements such as the jet multiplicity used in [54].
4
The choice between b quark and W boson as a recoiler is a discrete choice, hence it cannot be treated in the same
way as we treat other continuous parameters. The calibration or tuning procedure described below can be regarded as a
way either to find which recoil scheme should be adopted, or to make the recoil parameter become a continuous one and
choose the recoiler randomly in such a way that the b and the W act as a recoiler in a fraction of events suggested by the
tuning.
G. Corcella et al. / Nuclear Physics B 929 (2018) 485–526 493
2.2. Variation of HERWIG parameters
For the sake of comparison, we also investigate the impact of the HERWIG shower and
hadronization parameters on the top-quark mass measurement. In fact, HERWIG and PYTHIA
generators differ in several aspects: for example, the ordering variables of the showers are not the
same, matrix-element corrections are implemented according to different strate
gies and, above
all, models for hadronization and underlying events are different.
As fa
r as HERWIG is concerned, hadronization occurs according to the cluster model, which
is strictly related to the angular ordering of the parton shower, yielding color pre-confinement
even before the hadronization transition. In the following, we shall use the HERWIG 6 event gen-
erator, written in Fortran language. In fact, the object-oriented code HER
WIG 7 [55] presents a
number of improvements, especially when using the new dipole shower model with the modified
kinematics for massive quarks [56]. However, although the latest version HERWIG 7.1 exhibits
remarkable improvements for the purpose of bottom-quark fragmentation, the comparison with
the e
+
e
−
→b
¯
b data is still not optimal.
As for HER
WIG 6, in Ref. [57]the authors tried to tune it to LEP and SLD data, finding that
the comparison could be much improved with respect to the default parametrization, although
some discrepancy still persists and the prediction is only marginally consistent with the data. As
a whole, we decided to follo
w [57] and stick to using HERWIG 6 in the present paper. As done
in the case of PYTHIA, we identify the relevant shower and hadronization parameters and vary
them by at most 20% around their respective default values.
The relevant parameters of the cluster model are the following: CLMSR(2) which controls the
Gaussian smearing of a B-hadron with respect to the b-quark direction, PSPLT(2) which gov-
erns the mass distribution of the decays of b-flavored clusters, and CLMAX and CLPOW which
determine the highest allowed cluster masses. Their def
ault values and variation ranges are sum-
marized in Table 2. Furthermore, unlike Ref. [57] which just accounted for cluster-hadronization
parameters, we shall also explore the dependence of top-quark mass observables on the following
parameters: RMASS(5) and RMASS(13), the bottom and gluon effective masses, and the virtu-
ality cutoffs, VQCUT for quarks and VG
CUT for gluons, which are added to the parton masses
in the shower (see Table 2). We also investigate the impact of changing QCDLAM as it plays the
role of an effective
QCD
in the so-called Catani–Marchesini–Webber (CMW) definition of the
strong coupling constant α
S
in the parton shower (see Ref. [58]for the discussion on its relation
with respect to the standard
QCD
in the MS scheme). As well as for other parameters, we vary
QCDLAM around its default value, the range of variation is tabulated in Table 2.
3. Observables
In this section, we identify the observables that we employ to study their sensitivities to pa-
rameter variations. We first discuss the observables relevant to top quark mass measurements,
followed by our proposed variables for the tuning or the calibration of Monte Carlo parameters.
For the formulation of how to compute these observ
ables, we will follow the naming scheme for
t
¯
t final states that we illustrate in Fig. 1.
3.1. m
t
-Determination observables
We first list up the observables that we consider for the top-quark mass measurement.
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