The size of the proton

A measurement of the Lamb shift (2S--2P energy difference) in muonic hydrogen ($\mu$p, the exotic hydrogen atom made from a proton and a negative muon $\mu^-$) has been on the physicists' wish list for more than 40 years. Due to its 200 times larger mass, the muon's Bohr radius in $\mu$p is only 1/200 of the electron's Bohr radius in regular hydrogen (H). This enhances finite size effects by about $200^3$ in $\mu$p, compared to H. The proton's finite size $r_p$ affects the 2S Lamb shift in $\mu$p by as much as 2\%, making $\mu$p a unique, clean, atomic system to study $r_p$ using laser spectroscopy. We have recently observed the first transitions in muonic hydrogen~[1] and muonic deuterium~[2]. The $2S_{1/2}^{F=1}$ to $2P_{3/2}^{F=2}$ transition in $\mu$p was found at 49881.88(76)\,GHz [1]. Even with this - by laser spectroscopy standards - very moderate accuracy of 760\,MHz (4\% of the natural line width) we can deduce $r_p$ 10 times more accurately than the CODATA world average [3]. We obtain $r_p\,=\,0.84184(67)$\,fm~[1]. The accuracy of $r_p$ is limited by the uncertainty of the proton polarizability which is enters the theory relating the measured frequency to $r_p$. We have also measured a second transition in $\mu$p ( $2S_{1/2}^{F=0}$ to $2P_{3/2}^{F=1}$ ) [2]. It confirms our value~[1] of $r_p$, and provides the first determination of the 2S hyperfine splitting (HFS) in $\mu$p. The HFS reveals the Zemach radius, i.e. the radius of the magnetization distribution inside the proton. Now there is a ``proton size puzzle.'' We found the resonance~[1] 75\,GHz (i.e. 4 natural line widths) away from the expected position. Our $r_p$ is 10 times more accurate, but 4\% ($5 \sigma$) smaller than the CODATA value~[3]. There are still surprises in physics.\\[4pt] [1] R. Pohl et al. (CREMA collaboration), Nature 466, 213 (July 2010).\\[0pt] [2] CREMA collaboration, to be published.\\[0pt] [3] P.J.~Mohr, B.N.~Taylor and D.B.~Newell, Rev.~Mod.~Phys. 80, 633 (2008).