Is the proton radius a player in the redefinition of the International System of Units?
Authors: Nez F. , Antognini A. , Amaro F. D. , Biraben F. , Cardoso J. M. R. , Covita D. , Dax A. , Dhawan S. , Fernandes L. , Giesen A. , Graf T. , Hänsch T. W. , Indelicato P. , Julien L. , Kao C.-Y. , Knowles P. E. , Le Bigot E. , Liu Y.-W. , Lopes J. A. M. , Ludhova L. , Monteiro C. M. B. , Mulhauser F. , Nebel T. , Rabinowitz P. , Dos Santos J. M. F. , Schaller L. , Schuhmann K. , Schwob C. , Taqqu D. , Veloso J. F. C. A. , Kottmann F. , Pohl R. 
Published: September 2011

It is now recognized that the International System of Units (SI units) will be redefined in terms of fundamental constants, even if the date when this will occur is still under debate. Actually, the best estimate of fundamental constant values is given by a least-squares adjustment, carried out under the auspices of the Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants. This adjustment provides a significant measure of the correctness and overall consistency of the basic theories and experimental methods of physics using the values of the constants obtained from widely differing experiments. The physical theories that underlie this adjustment are assumed to be valid, such as quantum electrodynamics (QED). Testing QED, one of the most precise theories is the aim of many accurate experiments. The calculations and the corresponding experiments can be carried out either on a boundless system, such as the electron magnetic moment anomaly, or on a bound system, such as atomic hydrogen. The value of fundamental constants can be deduced from the comparison of theory and experiment. For example, using QED calculations, the value of the fine structure constant given by the CODATA is mainly inferred from the measurement of the electron magnetic moment anomaly carried out by Gabrielse's group. (Hanneke
et al.
2008
Phys. Rev. Lett.
100
, 120801) The value of the Rydberg constant is known from two-photon spectroscopy of hydrogen combined with accurate theoretical quantities. The Rydberg constant, determined by the comparison of theory and experiment using atomic hydrogen, is known with a relative uncertainty of 6.6×10
−12
. It is one of the most accurate fundamental constants to date. A careful analysis shows that knowledge of the electrical size of the proton is nowadays a limitation in this comparison. The aim of muonic hydrogen spectroscopy was to obtain an accurate value of the proton charge radius. However, the value deduced from this experiment contradicts other less accurate determinations. This problem is known as the proton radius puzzle. This new determination of the proton radius may affect the value of the Rydberg constant

. This constant is related to many fundamental constants; in particular,

links the two possible ways proposed for the redefinition of the kilogram, the Avogadro constant
N
A
and the Planck constant
h
. However, the current relative uncertainty on the experimental determinations of
N
A
or
h
is three orders of magnitude larger than the ‘possible’ shift of the Rydberg constant, which may be shown by the new value of the size of the proton radius determined from muonic hydrogen. The proton radius puzzle will not interfere in the redefinition of the kilogram. After a short introduction to the properties of the proton, we will describe the muonic hydrogen experiment. There is intense theoretical activity as a result of our observation. A brief summary of possible theoretical explanations at the date of writing of the paper will be given. The contribution of the proton radius puzzle to the redefinition of SI-based units will then be examined.