Muonic hydrogen indicating a smaller proton

Muons are conceived as point-like elementary particles living a few microseconds (shall live longer when it moves fast) under lab conditions. They are heavier counterparts (200 times heavier) of electrons. When they are caught by a proton, a muonic hydrogen forms. Now they are used to investigate some fundamental questions concerning QED.

1. Muonic hydrogen is an exotic hydrogen atom, where a muon (instead of an electron) orbits the proton. Because the muon is 200 times heavier than the electron, the muon's orbit is 200 times closer to the proton in muonic hydrogen than that of the electron in regular hydrogen. This 200 times smaller orbit means that the muon "feels" the size of the proton: certain muon orbits are significantly perturbed by the size of the positive charge distribution of the proton. By measuring the perturbation of the muon orbit using a laser, it is possible to determine the size of the proton.
(https://muhy.web.psi.ch/wiki/index.php/Main/Introduction)
2. Our measurement of the muonic hydrogen Lamb shift has to be conceived as a progress in the investigation of the hydrogen atom. In fact, when combined with the the measured transition frequencies in hydrogen, the proton radius inferred from the measurement of the muonic hydrogen Lamb shift will provide the most precise test of bound-state QED in the hydrogen atom to this date. Our measurement is thus likely to spur additional investigations of the fundamental theory of the electromagnetic interaction (quantum electrodynamics), a theory that links charged particles and photons (and hence light), which are some of the most important building blocks of our universe. (https://muhy.web.psi.ch/wiki/index.php/Main/Introduction)
3. The μp Lamb shift, ΔE(2P-2S) ≈ 0.2 eV, is dominated by vacuum polarization which shifts the 2S binding energy towards more negative values (see figure). The μp fine- and hyperfine splittings are an order of magnitude smaller than the Lamb shift. The relative contribution of the proton size to ΔE(2P-2S) is as much as 1.8%, two orders of magnitude more than for normal hydrogen atoms. The muonic Lamb shift ΔE(2P-2S) was recalculated recently by several authors [6-8] considering all QED contributions on the ppm level, including three-loop vacuum polarization, hadronic vacuum polarization, light-by-light scattering, and recoil corrections to the order α6. The uncertainty in the calculated proton polarization shift will ultimately limit the calculated ΔE(2P-2S)-value to the 0.3 ppm precision level (disregarding terms which depend on the proton radius). The theoretical prediction of the muonic hydrogen Lamb shift is

ΔE(2P^F=2 - 2S^F=1)=205.952 (3)(4)(137) meV

where the first error is the uncertainty of the calculated QED-terms, the second one the uncertainty from the proton polarization, and the third one the uncertainty given by the poor knowledge of the proton radius. A measurement of the muonic Lamb shift with 30 ppm precision will hence determine the proton radius with 0.1% precision.(https://muhy.web.psi.ch/wiki/index.php/Main/Motivation)

4. The aim of our laser spectroscopy experiment is to measure the Lamb shift in muonic hydrogen (μp):

ΔE(2P - 2S) (with 30 ppm precision)

and to deduce the rms proton charge radius r_p (with 1000 ppm, 10 times more precise than presently known):

ΔE(2P -2S) = 209.98 - 5.23 r_p² [meV]

where r_p is given in fm (r_p ≈ 0.9 fm).

The principle of the experiment is to irradiate μp atoms in the 2S state by a short pulse of infrared laser radiation whose wavelength (of about 6 micrometer) corresponds to the small energy difference of the binding energies of the 2S and 2P states. What can be measured is the number of 2P-1S transitions which occurs in time-coincidence with the laser pulse when its wavelength is tuned over the 2S-2P resonance.

• The PiE5 beam at the PSI proton accelerator provides 2 x 10⁸ s^-1 negative pions with a momentum of 100 MeV/c.
• Pions are injected into the cyclotron trap where they decay and produce negative muons of low kinetic energy.
• From the cyclotron trap the muons are axially extracted and transported to a solenoid with 5 T magnetic field where the hydrogen target is placed.
• Before entering the target, each muon is detected, and this is used to trigger the laser and the data acquisition system.
• About 500 s^-1 low energy muons (3 - 6 keV) enter the target and slow down in 1 mbar of hydrogen gas by ionization. When an electron from the hydrogen atom is replaced by the muon, a muonic atom μp is formed in a highly excited state (n ≈ 14).
• 99% of the muonic hydrogen atoms deexcite to the 1S state within 100 ns and produce "prompt" x-rays of 2 keV energy. The remaining 1% reach the metastable 2S state which has a lifetime of about ≈ 1 μs at 1 mbar.
• A laser pulse with a wavelength tunable around 6 μm is injected in the target and, when in resonance (hν = ΔE(2P - 2S)), induces a 2S to 2P transition.
• Atoms in the 2P state decay to the 1S ground state emitting 1.9 keV x-rays , which are delayed relative to the prompt x-rays, and occur in coincidence with the laser pulse.
• Detection of a delayed 1.9 keV x-ray followed by an electron (originated from the muon decay reaction) is a signature of the laser transition.
• By measuring the rate of delayed 1.9 keV x-rays as a function of the laser frequency, the resonance frequency (corresponding to ΔE(2P - 2S)), and hence the proton charge radius r_p can be determined.
  (https://muhy.web.psi.ch/wiki/index.php/Main/Experiment)