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Register a new userOne-loop vacuum polarization at $malpha^7$ order for the two center problem
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Added by
Vladimir I. Korobov
Publication date
2014
fields
Physics
and research's language is
English
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We present calculations of the one-loop vacuum polarization contribution (Uehling potential) for the two-center problem in the NRQED formalism. The cases of hydrogen molecular ions ($Z_1=Z_2=1$) as well as antiprotonic helium ($Z_1=2$, $Z_2=-1$) are considered. Numerical results of the vacuum polarization contribution at $malpha^7$ order for the fundamental transitions $(v=0,L=0)to(v=1,L=0)$ in H$_2^+$ and HD$^+$ are presented.
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We present calculations of the one-loop vacuum polarization correction (Uehling potential) for the three-body problem in the NRQED formalism. The case of one-electron molecular systems is considered. Numerical results of the vacuum polarization contribution at m$alpha$7 and higher orders for the fundamental transitions (v = 0, L = 0) $rightarrow$ (v = 1, L = 0) in the H2+ and HD+ molecular ions are presented and compared with calculations performed in the adiabatic approximation. The residual uncertainty from this contribution on the transition frequencies is shown to be of a few tens of Hz.
A complete effective Hamiltonian for relativistic corrections at orders $malpha^6$ and $malpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest.
NRQED approach to the fine and hyperfine structure corrections of order m$alpha$ 6 and m$alpha$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$alpha$ 6 and m$alpha$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used in the literature.
The malpha^6(m/M) order corrections to the hyperfine splitting in the H_2^+ ion are calculated. That allows to reduce uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about 10 ppm. Results are in good agreement with the high precision experiment carried out by Jefferts in 1969.
We present a detailed analysis of $e^+e^-topi^+pi^-$ data up to $sqrt{s}=1,text{GeV}$ in the framework of dispersion relations. Starting from a family of $pipi$ $P$-wave phase shifts, as derived from a previous Roy-equation analysis of $pipi$ scattering, we write down an extended Omn`es representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the $omega$ meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find $a_mu^{pipi}|_{leq 1,text{GeV}}=495.0(1.5)(2.1)times 10^{-10}$ and $a_mu^{pipi}|_{leq 0.63,text{GeV}}=132.8(0.4)(1.0)times 10^{-10}$. While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the $pipi$ $P$-wave, valuable input for future global analyses of low-energy $pipi$ scattering, as well as a determination of the pion charge radius, $langle r_pi^2 rangle = 0.429(1)(4),text{fm}^2$.
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