Fine and hyperfine structure of P-wave levels in muonic hydrogen

Abstract

Corrections of orders α 5 and α 6 are calculated in the fine structure interval ∆E f s = E(2P 3/2 ) − E(2P 1/2 ) and in the hyperfine structure of the energy levels 2P 1/2 and 2P 3/2 in muonic hydrogen. The obtained numerical values ∆E f s = 8352.08 µeV , ∆Ẽ hf s (2P 1/2 ) = 7964.36 µeV , ∆Ẽ hf s (2P 3/2 ) = 3392.59 µeV can be considered as a reliable estimate for the comparison with corresponding experimental data and for the extraction of the experimental value of the Lamb shift (2P − 2S) in muonic hydrogen.

Standard electroweak interactions in gravitational theory with chameleon field and torsion

“…According to Brax and Burrage [38], the contribution of the chameleon field may solve the so-called "the proton radius anomaly" [39][40][41][42]. As has been shown in [43]- [47] the Lamb shift ∆E 2s→2p of the muonic hydrogen, calculated in QED with the account for the nuclear effects, can be expressed in terms of the charge radius of the proton r p …”

Triply heavy baryons and heavy quark spin symmetry

“…Our predictions are also in a reasonable agreement with those obtained within the BM, RTQM and LO pNRQCD evaluations of Refs. [1], [6] and [11], respectively. The QCDSR masses calculated in [10] come out systematically much smaller than ours, while those obtained in the NRCQM of Ref.…”

“…Indeed, in Ref. [35] the lattice data were also fitted to the sum of the three quark-quark potentials 6 and it was found that a slightly larger value for the confinement coefficient (0.53 σ vs σ/2) was required. The ad-hoc factor of 1/2 introduced in quark potentials when going from the mesons to baryons is understood here as a geometrical effect rather than as a colour factor as it is usually presented.…”

“…More recently there has been other phenomenological mass determinations that include nonrelativistic constituent quark model (NRCQM) calculations [3][4][5], the relativistic three quark model (RTQM) evaluation of Ref. [6], or the Regge approach in Ref. [7].…”

The size of the proton from the Lamb shift in muonic hydrogen

“…A treatment of possible solutions to this puzzle can be found in [35]. Assuming the theory for the Lamb shift in μp [37][38][39][40][41][42] and for the H atom [37,43] to be correct, and using the precisely measured 1S-2S interval in H [6,8], the 1S-and 2S-Lamb shifts in H calculated with our r p value, and the most recent value for the fine structure constant α [44], we obtain a new value for the Rydberg constant R ∞ = 10,973,731.568160 (16) m −1 (relative accuracy 1.5 × 10 12 ). This result is 4.6 times more precise than the CODATA-value [36], but −110 kHz/c or 4.9 σ away.…”