The muonic hydrogen Lamb shift and the proton radius

Abstract

We obtain a model independent expression for the muonic hydrogen Lamb shift up to O(m µ α 6 , m µ α 5 m 2 µ m 2 ρ ). The hadronic effects are controlled by the chiral theory, which allows for their model independent determination. We give their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radius: r p =0.8412(15) fm. This number is at 6.8σ variance with respect to the CODATA value. The parametric control of the uncertainties allows us to obtain a model independent determination of the error, which is dominated by hadronic effects.

On proton charge radius definition

“…The relation (1) derives from our description of the neutron decay and yields r p = 0.841235641 (10) fm based on the experimental proton mass m p [8] inserted via λ p in (1) and it is in striking agreement with the result using muons. In particular we note the result r p = 0.8412(15) fm using a higher-order determination of the muonic hydrogen Lamb shift [22]. Further experimental establishment of (1) would confirm the working of the Higgs mechanism in the neutron transformation to the proton [23].…”

“…Second consider the exchange of one quantum of action h during the time τ , thus Λτ = h or Λcτ = hc where we introduce hc as a quantum of space action to get αϕ 0 a = hc for the quantum exchange with the Higgs field. Equating the two space quanta within the full period leads to(22) 4. Here we use mu = 0.0022 GeV and m d = 0.0047 GeV and so on from[8] for sliding from α(m Z ) to α(m W ).…”