μHe+ 3和μH3的Lamb位移核结构修正：揭示质子半径之谜

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在《物理学快报B》2016年755期的380-386页中，一篇名为“μHe+ 3和μH3中Lamb位移的核结构校正”的文章探讨了在类氢原子μHe+ 3和μH3中的2S-2P跃迁过程中，核结构修正的精确计算及其对测量质子电荷半径的影响。这篇研究的重要性在于，它能够通过精确测量这类原子的Lamb位移来提取核电荷半径，这是目前物理学中一个关键的参数，因为它的测量精度受到核结构修正不确定性的影响。 “质子半径难题”指的是，基于早期实验测量，质子的电荷半径与国际原子量委员会(CODATA)给出的标准值存在显著偏差，这一差异达到7σ。该问题引起了科学家们的广泛关注，因为它可能暗示着我们对基本粒子性质的理解存在误差。作者们通过从头算的方法，对μHe+ 3和μH3中的核极化校正进行了详尽的研究，这些同位素的核结构校正是决定质子半径提取精度的关键因素。他们的工作显著降低了核结构校正的不确定度，将之降低到了百分之一级别，这对于当前正在进行的μHe+ 3实验来说具有重要的指导意义。这不仅有助于提高测量结果的可靠性，而且可能为解决质子半径难题提供新的线索。此外，研究还推荐了μH3反射镜系统作为一种潜在的工具，用于进一步探测核子极化率，并通过精确测量释放更多的科学信息，以深化对基本粒子性质的理解。这篇论文的关键词包括“质子半径”，“μ子原子”，“核极化”，以及“两光子交换”，强调了核结构修正对于理解这些微小系统的量子行为至关重要的作用。通过这样的理论计算和实验验证，研究人员正在不断逼近物理学前沿，为我们揭示更深层次的自然界规律。

Physics Letters B 755 (2016) 380–386

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Nuclear structure corrections to the Lamb shift in μ

and μ

N. Nevo Dinur

a,∗

, C. Ji

b,c,d

, S. Bacca

b,e

, N. Barnea

Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel

TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada

ECT*, Villa Tambosi, 38123 Villazzano (Trento), Italy

INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy

Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

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

Article history:

Received

6 January 2016

Accepted

11 February 2016

Available

online 18 February 2016

Editor:

W. Haxton

Keywords:

Charge

radius

Muonic

atom

Nuclear

polarizability

Two-photon

exchange

Measuring the 2S–2P Lamb shift in a hydrogen-like muonic atom allows one to extract its nuclear charge

radius with a high precision that is limited by the uncertainty in the nuclear structure corrections. The

charge radius of the proton thus extracted was found to be 7σ away from the CODATA value, in what

has become the yet unsolved “proton radius puzzle”. Further experiments currently aim at the isotopes

of hydrogen and helium: the precise extraction of their radii may provide a hint at the solution of the

puzzle. We present the ﬁrst ab initio calculation of nuclear structure corrections, including the nuclear

polarization correction, to the 2S–2P transition in μ

and μ

H, and assess solid theoretical error

bars. Our predictions reduce the uncertainty in the nuclear structure corrections to the level of a few

percent and will be instrumental to the on-going μ

experiment. We also support the mirror μ

system

as a candidate for further probing of the nucleon polarizabilities and shedding more light on the

puzzle.

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

1. Introduction

The root-mean-square (RMS) charge radius of the proton r

≡



r

 was recently determined with unprecedented precision from

laser spectroscopy measurements of 2S–2P transitions in muonic

hydrogen μH, where the electron is replaced by a muon [1,2]. The

extracted r

differs by 7σ from the CODATA value [3], which is

based in turn on many measurements involving electron–proton

interactions. This discrepancy between the ‘muonic’ and ‘electron-

ic’

proton radii (r

(μ

−

) and r

−

), respectively) is known as the

“proton radius puzzle”, and has attracted much attention (see, e.g.,

Ref. [4] for an extensive review and Ref. [5] for a brief sum-

mary

of current results and ongoing experimental effort). In an

attempt to solve the puzzle, extractions of r

−

) from the am-

ple

electron–proton (ep) scattering data have been reanalyzed by,

e.g., Refs. [6–9], while several planned experiments aim to re-

measure

ep scattering in new kinematic regions relevant for the

Corresponding author.

E-mail

addresses: nir.nevo@mail.huji.ac.il (N. Nevo Dinur), ji@ectstar.eu (C. Ji),

bacca@triumf.ca (S. Bacca), nir@phys.huji.ac.il (N. Barnea).

puzzle [10,11]. r

extracted from electronic hydrogen is also being

reexamined, both theoretically [12] and experimentally [13–15], as

well as the Rydberg constant [15,16], which is relevant for sev-

eral

radius extraction methods. A few of the theoretical attempts

to account for the discrepancy between r

−

) and r

(μ

−

) include

new interactions that violate lepton universality [17–19] and novel

proton structures [20–24]. Yet the puzzle has not been solved. An-

swers

may be provided (see, e.g. Refs. [25,26]) by a planned experi-

ment

at PSI [27] to scatter electrons, muons, and their antiparticles

off the proton using the same experimental setup.

Alternatively,

it will be insightful to study whether the puzzle

also exists in other light nuclei, and whether it depends on the

atomic mass A, charge number Z , or the number of neutrons N. In

particular, the CREMA collaboration plans to extract high-precision

charge radii from Lamb shift measurements that were recently per-

formed

in several hydrogen-like muonic systems [5,28], namely,

μD, μ

, and μ

. These measurements may unveil a de-

pendence

of the discrepancy on the isospin of the measured nu-

cleus

and, in particular, probe whether the neutron exhibits a simi-

lar

effect as the puzzling proton. To obtain some control over these

issues, it is advisable that nuclei with different N/Z ratios will be

mapped out. It is the purpose of this Letter to perform an ab initio

calculation

of nuclear structure corrections (including nuclear po-

http://dx.doi.org/10.1016/j.physletb.2016.02.023

0370-2693/

SCOAP

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