B→D(*)ℓνℓ衰变中|V_cb|的提取与R(D(*))的标准模型预测
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更新于2024-07-16
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"这篇研究论文详细探讨了在B介子衰变到D或D*轻子νℓ过程中提取V cb 矩阵元的过程。研究人员使用了B→D*衰变中四个动力学变量（包括q2能区）的差分衰变率，并在CLN和BGL形状因子参数化中进行了分析。通过对所有可用数据的组合拟合，他们分别得到了V cb 的值为（39.77±0.89）×10^-3和（40.90±0.94）×10^-3。在这些拟合中，研究者结合了晶格量子色动力学（Lattice QCD）和光锥求和规则（Light Cone Sum Rules, LCSR）的数据。"
在这项研究中，科学家们关注的是弱相互作用中 CKM 矩阵元V cb 的精确测定，这是标准模型中描述夸克之间混合的关键参数。B介子衰变到D或D*轻子νℓ是理解这一矩阵元的重要途径，因为它涉及到b和c夸克之间的转变。通过使用CLN和BGL两种不同的形状因子参数化方法，研究者可以更全面地理解衰变过程的动力学。
CLN参数化是基于Heavy Quark Expansion (HQET) 的理论框架，它考虑了重夸克的质量在无限大时的行为。而BGL参数化则提供了一种更为灵活的描述，适合处理更复杂的形状因子结构。对这两个模型进行的拟合都考虑了数据的相关性和不确定性，以提高结果的可靠性。
除了形状因子的计算，研究者还利用了HQET关系来推导R(D*)和R(D*), 这两个比率衡量了B介子衰变到D*轻子与D轻子的比例，是检验新物理现象的重要指标。在考虑已知校正和对未知高阶校正的保守估计后，他们得到了R(D*) = 0.259±0.006（CLN）和R(D*) = 0.257±0.005（BGL）的结果。
这个研究的重要性在于，它提供了对标准模型预测的精确度量，有助于寻找可能存在的超出标准模型的新物理效应。通过细致的数据分析和理论计算，这些结果可以作为未来实验和理论研究的基础，进一步推动我们对基本粒子相互作用的理解。
JHEP12(2017)060
Source G(1)
Fermilab/MILC [17] 1.0541(83)
HPQCD [18] 1.035(40)
HQE(BPS Expansion) [25] 1.04(2)
Table 2. Different values of G(1) used in B → D`ν
`
fits.
this establishes approximate relations between the slope and the higher power coefficients
of the form factors (valid within ≈ 2%). Other than |V
cb
|, only two parameters parametrize
the form factors under this scenario: ρ
2
D
and G(1). The form factor normalization G(1)
is predicted by both HPQCD and Fermilab/MILC. There is one HQE result based on
Bogomol’nyi-Prasad-Sommerfield (BPS) symmetry (partially) [25] as well. These are listed
in table 2 and G(1) is used as a nuisance parameter in some of our fits.
In our analysis, for the B → D
∗
`ν
`
data, we mainly depend on the unfolded binned
differential decay rates by Belle. For four kinematic variables w, cos θ
v
, cos θ
l
and χ, with
10 bins each, this amounts to a total of 40 data points, their uncertainties and the full
correlation matrix [13]. Other than these, we make use of the zero-recoil value of the form
factor h
A
1
(w) from unquenched Fermilab/MILC lattice data [26]:
h
A
1
(1) = 0.906 ± 0.013 . (2.1)
In addition to these, we have used, in few cases, the inputs from light cone sum rule
(LCSR) [27]:
h
A
1
(w
max
) = 0.65(18), R
1
(w
max
) = 1.32(4), R
2
(w
max
) = 0.91(17), (2.2)
and the following inputs throughout our analysis:
¯m
b
( ¯m
b
) = 4.163 ± 0.016 GeV, m
c
(3 GeV) = 0.986 ±0.013 GeV,
α
S
( ¯m
b
( ¯m
b
)) = 0.2268 ± 0.0023. (2.3)
3 CLN parameterization: fit results
3.1 Fit from B → D`ν
`
data
As shown in table 3, when we fit the available data using CLN parameterization for the
form factors, we use different combinations of the predicted values of G(1). The best results
are obtained when all the inputs are combined together, and the corresponding extracted
values of |V
cb
| and R(D) are shown in table 3. To do a preliminary cross-check of the
validity of the fits, we have completely reproduced the table V of ref. [23], except the last
column, where the authors quote the fit results after averaging the separate samples. We
have instead used the whole 40-data-point-long sample with the full correlation matrix and
have considered values of m
e
and m
µ
to incorporate the correct values of w
max
consistent
with experimental results. The reason for doing this is two-fold: (a) The increased number
– 4 –
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