scholarly journals Hadronic vacuum-polarization contribution to various QED observables

2021 ◽  
Vol 75 (2) ◽  
Author(s):  
Savely G. Karshenboim ◽  
Valery A. Shelyuto
Keyword(s):  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Vacuum Polarization ◽  
Muonic Hydrogen ◽  
New Physics ◽  
Order Effects ◽  
Indirect Determination ◽  
Standard Data ◽  
Conservative Estimation

Abstract Due to precision tests of quantum electrodynamics (QED), determination of accurate values of fundamental constants, and constraints on new physics, it is important in a consistent way to evaluate a number of QED observables such as the Lamb shift in hydrogen-like atomic systems. Even in a pure leptonic case, those QED variables are in fact not pure QED ones since hadronic effects are involved through intermediate states while accounting for higher-order effects. One of them is hadronic vacuum polarization (hVP). Complex evaluations often involve a number of QED quantities, for which treatment of hVP is not consistent. The highest accuracy for a calculation of the hVP term is required for the anomalous magnetic moment of a muon. However, a standard data-driven treatment of hVP, based on a dispersion integration of experimental data on electron-positron annihilation to hadrons and some other phenomena, leads to a contradiction with the experimental value of $$a_\mu $$ a μ . This experimental value can be considered as an indirect determination of the hVP contribution to $$a_\mu $$ a μ and the scatter of theory and experiment allows one to obtain a conservative estimation of the related hVP contribution. In this paper, we derive exact and approximate relations between the leading-order (LO) hVP contributions to various observables. Using those relations, we obtain for them a consistent set of the results, based on the scatter of $$a_\mu $$ a μ values. While calculating the LO hVP term, we have to remember that next-to-LO (NLO) hVP corrections are often comparable with the uncertainty of the LO term. Special attention is payed to hVP contribution to simple atoms. In particular, we discuss the NLO contribution to the Lamb shift in ordinary and muonic hydrogen and other two-body atoms for $$Z\le 10$$ Z ≤ 10 . We also consider the NLO contribution of the muonic vacuum polarization to the Lamb shift in hydrogen-like atoms. With the $$a_\mu $$ a μ puzzle unresolved, one may still require present-days values of the hVP contributions to various observable for comparison to experiment etc. the presence of contradicting values and a lack of consistency means an additional uncertainty for $$a_\mu $$ a μ and for key contributions to it, including the LO hVP one. We present here an estimation of such a propagated uncertainty in hVP contributions to different QED observables and recommend a consistent set of the related LO hVP contributions. Graphic Abstract

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

A precision determination of the Lamb shift in hydrogen

1979 ◽  
Vol 290 (1373) ◽  
pp. 373-404 ◽  
Keyword(s):  
Elementary Particle ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Lamb Shift ◽  
Ion Source ◽  
Interaction Region ◽  
Zero Magnetic Field ◽  
Zero Field ◽  
Hydrogen Atoms

For over 40 years, optical and microwave spectroscopists, and atomic, nuclear and elementary particle physicists have been engaged in measuring the 2 2 S ½ -2 2 P ½ energy level separation in atomic hydrogen (the Lamb shift) and attempting to predict the splitting theoretically. The discrepancies encountered have influenced the development of theoretical methods of calculation in the areas of atomic structure, quantum electrodynamics and elementary particle physics. In this paper we present the results of a precision microwave determination of the Lamb shift, using a fast atomic beam and a single microwave interaction region. The value obtained is in substantial agreement with the earlier determinations and with the recent calculation by Mohr but is in disagreement with the earlier calculation by Erickson. This disagreement is further accentuated if recent modifications to the size of the proton are included, whereas the agreement with Mohr’s calculation is not affected. The experimental method uses a 21 keV beam of metastable 2 s hydrogen atoms which are obtained by charge exchange of a proton beam extracted from a radio frequency (r.f.) ion source. The experiment is performed in essentially zero magnetic field and uses a precision transmission line interaction region to induce r.f. transitions at the Lamb shift frequency. The result for the 2 2 S ½ F = 0 to 2 2 P ½ F = 1 interval in zero field is 909.904 ± 0.020 MHz corresponding to a Lamb shift of 1057.862 ± 0.020 MHz. The paper discusses the method and the host of corrections for systematic effects which need to be applied to the line centre, many of which have not been sufficiently understood or controlled in previous experiments. The paper is introduced with a brief survey of significant landmarks in calculation and measurement of the Lamb shift and concludes with a comparison of the present theoretical and experimental positions.

Past, present and future of the muon g-2

2015 ◽  
Vol 39 ◽  
pp. 1560107
Author(s):  
A. E. Dorokhov ◽  
A. E. Radzhabov ◽  
A. S. Zhevlakov
Keyword(s):  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Relativistic Quantum ◽  
Magnetic Moments ◽  
Structure Constant ◽  
New Physics ◽  
Fine Structure Constant ◽  
Measured Quantity ◽  
The Standard Model

The electron and muon anomalous magnetic moments (AMM) are measured in experiments and studied in the Standard Model (SM) with the highest precision accessible in particle physics. The comparison of the measured quantity with the SM prediction for the electron AMM provides the best determination of the fine structure constant. The muon AMM is more sensitive to the appearance of New Physics effects and, at present, there appears to be a three- to four-standard deviation between the SM and experiment. The lepton AMMs are pure relativistic quantum correction effects and therefore test the foundations of relativistic quantum field theory in general, and of quantum electrodynamics (QED) and SM in particular, with highest sensitivity. Special attention is paid to the studies of the hadronic contributions to the muon AMM which constitute the main source of theoretical uncertainties of the SM.

The muonic hydrogen Lamb-shift experiment

2005 ◽  
Vol 83 (4) ◽  
pp. 339-349 ◽  
Author(s):  
R Pohl ◽  
A Antognini ◽  
F D Amaro ◽  
F Biraben ◽  
J MR Cardoso ◽  
...  
Keyword(s):  
Charge Radius ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Laser System ◽  
Bound State ◽  
Muonic Hydrogen ◽  
X Rays ◽  
Large Area ◽  
Proton Charge ◽  
Proton Charge Radius

The charge radius of the proton, the simplest nucleus, is known from electron-scattering experiments only with a surprisingly low precision of about 2%. The poor knowledge of the proton charge radius restricts tests of bound-state quantum electrodynamics (QED) to the precision level of about 6 × 10–6, although the experimental data themselves (1S Lamb shift in hydrogen) have reached a precision of 2 × 10–6. The determination of the proton charge radius with an accuracy of 10–3 is the main goal of our experiment, opening a way to check bound-state QED predictions to a level of 10–7. The principle is to measure the 2S–2P energy difference in muonic hydrogen (µ–p) by infrared laser spectroscopy. The first data were taken in the second half of 2003. Muons from our unique very-low-energy muon beam are stopped at a rate of ~100 s–1 in 0.6 mbar H2 gas where the lifetime of the formed µp(2S) atoms is about 1.3 µs. An incoming muon triggers a pulsed multistage laser system that delivers ~0.2 mJ at λ ≈ 6 µm. Following the laser excitation µp(2S) → µp(2P) we observe the 1.9 keV X-rays from 2P–1S transitions using large area avalanche photodiodes. The resonance frequency, and, hence, the Lamb shift and the proton radius, is determined by measuring the intensity of these X-rays as a function of the laser wavelength. A broad range of laser frequencies was scanned in 2003 and the analysis is currently under way. PACS Nos.: 36.10.Dr, 14.20.Dh, 42.62.Fi

scholarly journals CKM PARAMETERS AND RARE B DECAYS

2006 ◽  
Vol 21 (08n09) ◽  
pp. 1683-1696 ◽  
Author(s):  
FRANCESCO FORTI
Keyword(s):  
B Meson ◽  
New Physics ◽  
Precise Determination ◽  
Model Parameters ◽  
B Decays ◽  
Unitarity Triangle ◽  
Indirect Determination ◽  
Radiative Transitions ◽  
First Time

Measurements of the angles and sides of the unitarity triangle and of the rates of rare B meson decays are crucial for the precise determination of Standard Model parameters and are sensitive to the presence of new physics particles in the loop diagrams. In this paper the recent measurements performed in this area by BABAR and Belle will be presented. The direct measurement of the angle α is for the first time as precise as the indirect determination. The precision of the |Vub| determination has improved significantly with respect to previous measurement. New limits on B → τν decays are presented, as well as updated measurements on b → s radiative transitions and a new observation of b → dγ transition made by Belle.

Sign in / Sign up

Export Citation Format

Share Document