解析三环计算揭示：次强子对μ子磁矩贡献达到NNLO精度
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本文主要探讨了"光子真空极化对介子异常磁矩的次次至强次强子贡献"这一关键主题，针对的是物理学家们关注的高精度实验测量——即缪子的异常磁矩。异常磁矩是指粒子（如电子或缪子）在静止时磁场中的磁性与其固有磁矩的偏差，这对于理解基本粒子物理学和标准模型的精细结构常数非常重要。
作者们，Alexander Kurza、Tao Liu、Peter Marquard和Matthias Steinhauser，来自德国卡尔斯鲁厄理工学院（KIT）和德累斯顿电子同步加速器（DESY），他们在《物理快报B》734期（2014年）的144-147页上发表了他们的研究成果。他们采用先进的渐近展开技术来计算三环核心函数，这是一种复杂的量子场论方法，用于处理多圈图的高阶效应。
他们的工作主要集中在计算次次至强次强子贡献（NNLO）对μ子异常磁矩的影响，这是对之前研究的进一步精细化，特别是对主导的强子贡献的不确定性达到了相似的量级。这项计算的结果是aμhad, NNLO = 1.24±0.01×10^-10，这个数值表明，尽管它是更高阶的计算，但其不确定性仍与目前主导的强子贡献相匹配，因此在未来的精确测量和理论分析中具有重要意义。
这篇论文的发表过程显示了严谨的科学态度，从最初的接收日期到修订并接受，再到在线发布的日期，都遵循了标准的时间线。编辑A.Ringwald也参与了整个审稿和发表过程。这项研究的结果不仅有助于提高对基本物理现象的理解，还可能影响对新物理的搜索，因为它可能会揭示超出标准模型的新效应或理论的局限性。
本文是粒子物理学领域的一个重要贡献，它深化了我们对μ子异常磁矩的理解，并为未来的实验测量提供了更为精确的理论预测，对于检验基础物理学理论和探索粒子物理的细微之处具有重要意义。
Physics Letters B 734 (2014) 144–147
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Hadronic contribution to the muon anomalous magnetic moment to
next-to-next-to-leading order
Alexander Kurz
a,b
, Tao Liu
a
, Peter Marquard
b
, Matthias Steinhauser
a,∗
a
Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany
b
Deutsches Elektronen Synchrotron (DESY), 15738 Zeuthen, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
26 March 2014
Received
in revised form 5 May 2014
Accepted
7 May 2014
Available
online 20 May 2014
Editor:
A. Ringwald
We compute the next-to-next-to-leading order hadronic contribution to the muon anomalous magnetic
moment originating from the photon vacuum polarization. The corresponding three-loop kernel functions
are calculated using asymptotic expansion techniques which lead to analytic expressions. Our final result,
a
had,NNLO
μ
= 1.24 ± 0.01 × 10
−10
, has the same order of magnitude as the current uncertainty of the
leading order hadronic contribution and should thus be included in future analyses.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
The anomalous magnetic moment of the electron and the muon
is measured with high precision and at the same time also ac-
curately
predicted including high-order quantum corrections (see,
e.g., Refs. [1–4] for reviews on this topic). Notable recent achieve-
ments
in this context are the five-loop QED corrections obtained
in Refs. [5,6].
In
the case of the muon the largest input to the uncer-
tainty
comes from hadronic contributions which to a large ex-
tent rely
on experimental measurements of the cross section
σ (e
+
e
−
→ hadrons). Several groups have performed the leading
order (LO) [7–10] and next-to-leading order (NLO) [8,11–13] anal-
ysis.
In this paper we compute the next-to-next-to-leading order
(NNLO) hadronic corrections to the anomalous magnetic moment
of the electron and the muon. We evaluate the three-loop kernels
in the limit M
μ
m
π
and show that four expansion terms are
sufficient to obtain a precision far below the per cent level. Note
that we do not consider the light-by-light contribution where the
external photon couples to the hadronic loop (see, e.g., Ref. [14])
but only the contributions involving the hadronic vacuum polar-
izations.
In
the next section we briefly mention some technical details
of our calculation and discuss the NLO contribution. Section 3 con-
tains
the results of the various NNLO contributions for the muon
anomalous magnetic moment and in Section 4 we apply our re-
sults
to the anomalous magnetic moment of the electron. We con-
clude
in Section 5.
*
Corresponding author.
2. Technicalities and NLO result
The LO hadronic contribution to the anomalous magnetic mo-
ment
of the muon (see Fig. 1) can be computed via
a
(1)
μ
=
1
3
α
π
2
∞
m
2
π
ds
R
(s)
s
K
(1)
(s), (1)
where α is the fine structure constant and R(s) is given by
the properly normalized total hadronic cross section in electron
positron collisions
R(s) =
σ (e
+
e
−
→ hadrons)
σ
pt
, (2)
with σ
pt
= 4πα
2
/(3s). A convenient integral representation for
K
(1)
(s) is given by
K
(1)
(s) =
1
0
dx
x
2
(1 − x)
x
2
+(1 − x)
s
M
2
μ
, (3)
analytic results can be found in Refs. [15,16].
A
crucial input for the evaluation of a
had
μ
is a compilation of
the experimental data for R(s) as obtained by various experiments.
In our analysis we use a FORTRAN code which is provided to us
by the authors of Ref. [8]. This gives us access to both the cen-
tral
values and the upper and lower limit of R(s). However, the
use of the latter leads to a vast overestimation of the final un-
certainty
since we have no information about the correlations of
http://dx.doi.org/10.1016/j.physletb.2014.05.043
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.
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