Session C4: Proton Charge Radius and Precision QED

 Saturday, April 30, 2011 1:30PM - 2:06PM C4.00001: The size of the proton Invited Speaker: Randolf Pohl 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). Saturday, April 30, 2011 2:06PM - 2:42PM C4.00002: The Mainz high-precision proton form factor measurement Invited Speaker: Jan Bernauer Form factors offer a direct approach to fundamental properties of the nucleons like the radius and charge distribution. Renewed interest was stirred up by the 5 sigma discrepancy between a recent determination of the proton radius from the Lamb shift in muonic hydrogen and preceding electron scattering results. The low-q shape of the form factors might also contain a direct signal of a pion cloud around the nucleus and is a strong test of hadron models. In my talk, I will discuss the electron scattering experiment performed with the 3-spectrometer-facility of the A1 collaboration at MAMI in Mainz, Germany. The data set covers the $Q^2$-range from 0.004 to 1\,$(\mathrm{GeV}/c)^2$ and includes about 1400 separate cross section measurements, spanning the range of scattering angles from below 20$^\circ$ to above 120$^\circ$ at six beam energies between 180 and 855\,MeV, with statistical uncertainties below 0.4\%. The 3-spectrometer-setup allowed for a simultaneous monitoring of the luminosity and overlapping and redundant measurements of the cross section to achieve stringent control over systematic uncertainties. Beam stabilization systems and redundant current measurements further limit systematic effects. The measured cross sections were analyzed with the standard Rosenbluth separation technique and by employing direct fits of a large set of form factor models. The high redundancy of the data set allowed us to extract the form factors up to 0.6\,$(\mathrm{GeV}/c)^2$ with very small uncertainties and to give a new, precise value for the proton radius from electron scattering. From the form factors, the charge distribution and Zemach moments were calculated. The latter constitute important input for the theoretical corrections of the muonic Lamb shift experiment. However, the revised values can not explain the discrepancy. Further possible explanations include higher order QED-corrections, vacuum effects or even physics beyond the standard model. Saturday, April 30, 2011 2:42PM - 3:18PM C4.00003: Theory of the Lamb shift in muonic hydrogen Invited Speaker: Savely Karshenboim Recently a successful measurement of the Lamb shift in muonic hydrogen was performed at PSI. According to the claimed accuracy, the most accurate value of the proton charge radius came from comparison of the PSI experiment and related theory. Unfortunately, the result disagrees with those from the hydrogen spectroscopy and electron-proton scattering experiments. To resolve discrepancy one has to revisit theory and measurements in each of three mentioned areas, namely, in spectroscopy of ordinary and muonic hydrogen and in the scattering. The present talk is on the state of the art of theory of the Lamb shift in muonic hydrogen.