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Register a new userTwo-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
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Authors
Oleksandr Tomalak
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We evaluate the two-photon exchange corrections to the Lamb shift and hyperfine splitting of S states in electronic hydrogen relying on modern experimental data and present the two-photon exchange on a neutron inside the electronic and muonic atoms. These results are relevant for the precise extraction of the isotope shift as well as in the analysis of the ground state hyperfine splitting in usual and muonic hydrogen.
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We calculate the contribution from the two-photon exchange on the neutron to the hyperfine splitting of S energy levels. We update the value of the neutron Zemach radius, estimate total recoil and polarizability corrections. The resulting two-photon exchange in electronic atoms exceeds by an order of magnitude the leading Zemach term and has different sign both in electronic and muonic hydrogen.
In this work, the two-photon-exchange (TPE) effects in $e^+e^- rightarrow pi^+ pi^-$ at small $sqrt{s}$ are discussed within a hadronic model. In the limit $m_erightarrow 0$, the TPE contribution to the amplitude can be described by one scalar function $overline{c}_{1}^{(2gamma)}$. The ratio between this function and the corresponding contribution in one-photon exchange $c_{1}^{(1gamma)}$ reflects all the information of the TPE corrections. The numerical results on this ratio are presented and an artificial function is used to fit the numerical results. The latter can be used conveniently in the further experimental data analysis. The numerical results show the asymmetry of the differential cross sections in $e^+e^- rightarrow pi^+ pi^-$ is about $-4%$ at $sqrt{s}sim 0.7$ GeV.
Electroweak second order shifts of muonium ($mu^+e^-$ bound state) energy levels are calculated for the first time. Calculation starts from on-shell one-loop elastic $mu^+ e^-$ scattering amplitudes in the center of mass frame, proceed to renormalization and to derivation of muonium matrix elements by using the momentum space wave functions. This is a reliable method unlike the unjustified four-Fermi approximation in the literature. Corrections of order $alpha G_F$ (with $alpha sim 1/137$ the fine structure constant and $G_F$ the Fermi constant) and of order $alpha G_F /(m_Z a_B)$ (with $m_Z$ the Z boson mass and $a_B$ the Bohr radius) are derived from three classes of Feynman diagrams, Z self-energy, vertex and box diagrams. The ground state muonium hyperfine splitting is given in terms of the only experimentally unknown parameter, the smallest neutrino mass. It is however found that the neutrino mass dependence is very weak, making its detection difficult.
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 experimental data in order to comment on the extent to which the perturbation-theory analysis which leads to the above conclusion can be confirmed. We find no statistically significant dependence of this correction on the shape of the proton form-factor.
In this work, the two-photon-exchange (TPE) effects in $eprightarrow enpi^+$ at small $-t$ are discussed within a hadronic model. The TPE contributions to the amplitude and the unpolarized differential cross section are both estimated and we find that the TPE corrections to the unpolarized differential cross section are about $-4%sim-15%$ at $Q^2=1$GeV$^2sim1.6$GeV$^2$. After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyse the TPE corrections to the separated cross sections $sigma_{textrm{L,T,LT,TT}}$. We find that the TPE corrections (at $Q^2=1$GeV$^2sim1.6$GeV$^2$) to $sigma_{textrm{L}}$ are about $-10%sim -20%$, to $sigma_{textrm{T}}$ are about $20%$ and to $sigma_{textrm{LT,TT}}$ are much larger. By these analysis, we conclude that the TPE contributions in $eprightarrow enpi^+$ at small $-t$ are important to extract the separated cross sections $sigma_{textrm{L,T,LT,TT}}$ and the electromagnetic magnetic form factor of $pi^+$ in the experimental analysis.
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