Comment on "Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution"

Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution

We quantify a limitation in the usual accounting of the finite-size effects, where the leading $[(Zα)^4]$ and subleading $[(Zα)^5]$ contributions to the Lamb shift are given by the mean-square radius and the third Zemach moment of the charge distribution. In the presence of any non-smooth behaviour of the nuclear form factor at scales comparable to the inverse Bohr radius, the expansion of the Lamb shift in the moments breaks down. This is relevant for some of the explanations of the "proton size puzzle". We find, for instance, that the de Rújula toy model of the proton form factor does not re…

Reply to "Comment on `Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution'"

To comply with the critique of the Comment [J. Arrington, arXiv:1602.01461], we consider another modification of the proton electric form factor, which resolves the "proton-radius puzzle". The proposed modification satisfies all the consistency criteria put forward in the Comment, and yet has a similar impact on the puzzle as that of the original paper. Contrary to the concluding statement of the Comment, it is not difficult to find an ad hoc modification of the form factor at low $Q$ that resolves the discrepancy and is consistent with analyticity constraints. We emphasize once again that we …

评“兰姆位移与超高能宇宙射线“和“高能宇宙射线的真空极化能损“

Comment on "The Lamb Shift and Ultra High Energy Cosmic Rays" and Comment on "Vacuum Polarization Energy Losses of High Energy Cosmic Rays"

宇宙射线的光谱已被证明远远超过10 ^20 eV。在过去的40年里观察到了近20个事件，现在已经确定能量接近或超过10^21 eV的粒子。没有任何附近的天体物理物体被证明与最高能量事件的到达方向相关，然而，人们期望在远源的情况下看到的光谱高能端的指数截止是不可见的。最近有人指出，量子电动力学的真空对粒子传播的影响可以定性地解释这个谜。本说明是对这些想法的批评。

Comment on "The third Zemach moment of the proton", by Cloet and Miller

Cloet and Miller, in arXiv:1008.4345, state that "existing data rule out a value of the third Zemach moment large enough to explain the current puzzle with the proton charge radius determined from the Lamb shift in muonic Hydrogen. This is in contrast with the recent claim of De Rújula [arXiv:1008.3861]". To be more precise: it is not. It is, however, contrary to what they claim that I claim. Cloet and Miller have simply misinterpreted my claims.

Comment on "Nucleon spin-averaged forward virtual Compton tensor at large Q^2"

In recent work, Hill and Paz apply the operator product expansion to forward doubly virtual Compton scattering. The resulting large-$Q^2$ form of the amplitude $W_1(0,Q^2)$ is compatible with the one we obtain by extrapolation of low-$Q^2$ results from a chiral effective field theory, providing support for our approach. That paper also presents a result for the two-photon contribution to the Lamb shift in muonic hydrogen that has a much larger uncertainty than in previous work. We show that this an overestimate arising from the inclusion of the proton pole term in the subtracted dispersion rel…

Proton form-factor dependence of the finite-size correction to the Lamb shift in muonic hydrogen

The measurement of the 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition in muonic hydrogen by Pohl et al. and subsequent analysis has led to the conclusion that the rms radius of the proton differs from the accepted (CODATA) value by approximately 4%, corresponding to a 4.9 sigma discrepancy. We investigate the finite-size effects - in particular the dependence on the shape of the proton electric form-factor - relevant to this transition using bound-state QED with nonperturbative, relativistic Dirac wave-functions for a wide range of idealised charge-distributions and a parameterization of experime…