#
APS April Meeting 2011

## Volume 56, Number 4

##
Saturday–Tuesday, April 30–May 3 2011;
Anaheim, California

### Session C4: Proton Charge Radius and Precision QED

1:30 PM–3:18 PM,
Saturday, April 30, 2011

Room: Garden 4

Sponsoring
Unit:
GFB

Chair: Hossein Sadeghpour, Harvard-Smithsonian Center for Astrophysics

Abstract ID: BAPS.2011.APR.C4.1

### Abstract: C4.00001 : The size of the proton

1:30 PM–2:06 PM

Preview Abstract
Abstract

####
Author:

Randolf Pohl

(Max-Planck-Institute of Quantum Optics, Garching, Germany)

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).

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.APR.C4.1