原文已发表在CPL Express Letters栏目

Received 7 September 2021; 

online 13 November 2021

Sophisticated statistical techniques combined with rigorous mathematics enable the first unbiased extraction of the proton’s magnetic radius from electron scattering experiments: rM=0.817(27) fm.

Figure 1 Lepton scattering from the proton provides access to its electric and magnetic radii. Controversies exist over the values of both. A novel mathematical approach applied to the analysis of scattering data is enabling a resolution of both puzzles.

The Universe is 14-billion years old. In all that time, proton decay has not been observed. This extraordinary fact makes the proton Nature’s most fundamental bound state. It is also a fermion; hence, the proton is an essentially quantum field theoretical composite object because, as noted by Wolfgang Pauli: “...the connection between spin and statistics is one of the most important applications of the special relativity theory ...”; and subsequently by Steven Weinberg: “… quantum field theory is the only known means of unifying quantum mechanics with special relativity …”. An interacting proton is also characterized by two radii: electric, rE, and magnetic, rM. For a simply structured composite fermion, they are the same; and until the beginning of this millennium, extant data suggested rE=rM. However, much has changed in the past decade. A controversy over the value of rE, born in muonic hydrogen spectroscopy measurements, seems to have been resolved, in favour of a lower value of 0.8409(4)fm than originally determined using electron-proton (ep) scattering. Now, the value of rM is the focus. In this case, ep scattering is the only viable approach to measurement; and existing experiments and analyses disagree by as much as 3.5σ, as shown in Fig. 1.

An international team, joining the Institute for Nonperturbative Physics in the School of Physics at Nanjing University, Nanjing, China, the European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Trento, Italy, and Helmholtz-Zentrum Dresden-Rossendorf, Germany, adapted a novel mathematical technique to the challenge of extracting the proton’s magnetic radius. This method, developed by the team specifically for use in the interpolation and extrapolation of precise data, is mathematically guaranteed to capture both local and global features of the curve that underlies the physical measurement. The global quality is vital because it justifies use of the interpolations outside the domain of available data and thus enables and legitimizes evaluation of the curve’s slope at the origin, i.e., calculation of the radius. Within empirical uncertainties, as shown in Fig. 1, the proton magnetic and electric radii are equal. 

Equality between the proton’s magnetic and electric radii is readily understood if the proton is a point particle or, at least, a simply structured bound state. However, modern experiment and theory indicate that the proton is a very complex system. In fact, within the Standard Model of particle physics, proton structure is explained by remarkable nonperturbative features of quantum chromodynamics (QCD), the relativistic quantum field theory describing interactions between gluons and quarks. These extraordinary features relate to the emergence of nuclear size mass-scales in a domain where the Higgs boson has almost no impact. Moreover, any discussion of proton radii leads immediately to considerations of confinement, which is the fact that gluons and quarks have never been isolated in a detector. Solving the puzzle of confinement is one of the $1-million Millennium Challenges. Thus, the analysis completed by this team, with the result rM≈rE, imposes tight constraints on any attempt to understand proton structure. Truly comprehending the result will deliver insights into the phenomena that underlie the emergence of mass and length scales in Nature.