QCD中夸克1S能级的精确测量：mc和mb的质量更新

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"扰动QCD中夸克1 S能级中m c和m b的测定" 这篇文章是关于在扰动量子色动力学（QCD）框架下，通过对charm（c夸克）和bottom（b夸克）的1 S能级状态的研究来精确测定这两种重夸克的MS质量。QCD是描述强相互作用的基本理论，它解释了夸克如何通过胶子相互作用形成原子核。在QCD中，夸克的质量可以通过计算它们的能级来估算，而1 S能级是这类计算中的一个关键参考点，因为它对应于最简单的束缚态。文章在《Physics Letters B》上发表，是一个开放获取的资源，这意味着公众可以免费阅读和使用其研究成果。作者包括Y. Kiyo、G. Mishima和Y. Sumino，分别来自日本东京的骏台大学、东京大学和东北大学的物理系。论文的接收日期为2015年11月10日，接受日期为11月13日，并在11月17日在线发布，编辑为J. Hisano。研究的核心是通过ε展开进行的，这是一种在QCD中处理渐近自由度的技术，它允许研究人员在保留某些近似的情况下计算高能量过程。在ε展开中，计算通常被分为几个阶，每个阶代表了计算的精确度。在这项工作中，研究人员进行了至下一个至下一个至领先的顺序（N3LO）的计算，这是非常精确的，因为这涉及到包含所有可能的四阶效应。具体来说，对于charm quark（c），研究者通过比较实验观测到的charmonium（c夸克与c反夸克组成的束缚态，如J/ψ粒子）1 S能级的质量与其在QCD中的理论预测，得出了m_c = 1246 ± 2 (统计误差) ± 4 (α_s 误差) ± 23 (高阶效应误差) MeV的MS质量。这里的MS质量是在特定能量尺度上定义的，它考虑了量子电动力学（QED）和QCD修正。对于bottom quark（b），同样的方法用于bottomonium（b夸克与b反夸克的束缚态，如Υ粒子）1 S能级，得到m_b = 4197 ± 2 (统计误差) ± 6 (α_s 误差) ± 20 (高阶效应误差) ± 5 (m_c 误差) MeV。这里的最后一个误差项来自于 charm quark 质量的不确定性对 bottomonium 质量计算的影响。这个结果对粒子物理学和宇宙学具有重要意义，因为精确的夸克质量数据对于理解和预测高能物理过程，如粒子衰变、强相互作用的精确计算以及大爆炸宇宙学模型的构建都是至关重要的。此外，这些测量也有助于验证QCD理论本身，特别是在高阶扰动计算的可靠性方面。通过持续的实验和理论工作，科学家们能够不断提高这些基本粒子性质的估计精度，从而深化我们对自然界基本力的理解。

Physics Letters B 752 (2016) 122–127

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Determination of m

and m

from quarkonium 1S energy levels

in perturbative QCD

Y. Kiyo

, G. Mishima

b,∗

, Y. Sumino

Department of Physics, Juntendo University, Inzai, Chiba 270-1695, Japan

Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

Department of Physics, Tohoku University, Sendai 980-8578, Japan

a r t i c l e i n f o a b s t r a c t

Article history:

Received

10 November 2015

Accepted

13 November 2015

Available

online 17 November 2015

Editor:

J. Hisano

We update determination of the MS masses of the charm and bottom quarks, from comparisons of the

masses of the charmonium and bottomonium 1S states with their perturbative predictions up to next-

to-next-to-next-to-leading

order in ε expansion and using the MS masses. Effects of non-zero charm-

quark

mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain

= 1246 ± 2(d

) ± 4(α

) ± 23(h.o.) MeV and m

= 4197 ± 2(d

) ± 6(α

) ± 20(h.o.) ± 5(m

) MeV, which

agree with the current Particle Data Group values.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

The Standard Model (SM) of elementary particle physics has

been successfully completed by the discovery of the Higgs particle,

whereas no deﬁnite clue to physics beyond the SM has been found

yet. In such an era, necessity for precise understanding of the SM

is increasing more than ever. In particular, to meet demands for ac-

curate

measurements required in the LHC experiments as well as

those for high-precision ﬂavor physics, etc., there has been remark-

able

progress in the predictability of perturbative QCD in recent

years. The masses of the c- and b-quarks are among the important

fundamental parameters of perturbative QCD. They play crucial

roles, for instance, in testing predictions of the SM for the Yukawa

coupling constants of the Higgs particle, and also as the input pa-

rameters

for predicting various observables in ﬂavor physics.

The

masses of the c- and b-quarks have been determined in

many ways. Even referring only to works published after the lat-

est

version of Review of Particle Physics [1] by Particle Data Group

(PDG) Collaboration, there are analyses based on non-relativistic

QCD sum rule [2,3], relativistic QCD sum rule [4], deep inelas-

tic

scattering [5], heavy quarkonium spectroscopy [6], and lattice

computation [7]. (See [1] for earlier studies.) Their physics ingre-

dients

vary substantially, and also they probe different kinematical

regions of QCD. Therefore, consistency of the determined values

provides a non-trivial test of QCD, and of the SM more generally.

Corresponding author.

E-mail

address: mishima@hep-th.phys.s.u-tokyo.ac.jp (G. Mishima).

In this paper we determine the masses of the c- and b-quarks

from comparisons of the energy levels of the charmonium and

bottomonium 1S states with their perturbative predictions. This

is an update of the mass determination performed as part of the

analyses in [8,9], which included perturbative expansion up to the

next-to-next-to-leading order (NNLO). We include one more order,

namely up to NNNLO. Recently, the four-loop relation to the pole

and MS quark masses has been computed [10]. The present study

is the ﬁrst full analysis using the MS mass up to NNNLO. We also

include non-zero charm-quark mass effects in the computation of

the bottomonium energy levels, up to the highest order of the cur-

rently

available computations (up to two loops of internal c-quark)

[11]. On the experimental side, accurate data on the η

(1S) and

(1S) masses are available today, which we include in our anal-

ysis,

in addition to the J/ψ(1S) and ϒ(1S) masses used in the

NNLO analyses.

The purpose of the present study is to provide another ac-

curate

determination of these quark masses, and also there is a

different aspect. The heavy quarkonium states are unique among

various hadrons, in that properties of individual hadronic states

can be predicted purely within perturbative QCD. Hence, if we ob-

serve

consistency with the masses determined by other methods

with high accuracy, that can be an evidence that pure perturbative

QCD is indeed capable of predicting properties of these individual

hadrons with high precision, with only α

and the quark masses

as the input parameters of the theory.

Since

the study at the previous order, our understanding based

on perturbative QCD has developed considerably. On the one hand,

http://dx.doi.org/10.1016/j.physletb.2015.11.040

0370-2693/

SCOAP

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