scholarly journals The three loop slope of the Dirac form factor and the S Lamb shift in hydrogen

1999 ◽  
Author(s):  
K Melnikov
Keyword(s):  
Form Factor ◽  
Lamb Shift ◽  
Dirac Form Factor

scholarly journals Three-Loop Slope of the Dirac Form Factor and the1SLamb Shift in Hydrogen

2000 ◽  
Vol 84 (8) ◽  
pp. 1673-1676 ◽  
Author(s):  
Kirill Melnikov ◽  
Timo van Ritbergen
Keyword(s):  
Form Factor ◽  
Dirac Form Factor

scholarly journals The 4-loop slope of the Dirac form factor

2020 ◽  
Vol 234 ◽  
pp. 01009
Author(s):  
Stefano Laporta
Keyword(s):  
Form Factor ◽  
Hydrogen Atom ◽  
Energy Levels ◽  
Elliptic Integrals ◽  
Loop Contribution ◽  
One Dimensional ◽  
Dirac Form Factor ◽  
Complete Elliptic Integrals

The 4-loop contribution to the slope of the Dirac form factor in QED has been evaluated with 1100 digits of precision. The value is $ {m^2}F_1^{(4)'}(0) = {\rm{0}}{\rm{.886545673946443145836821730610315359390424032660064745}} \cdots {\left( {{\alpha \over \pi }} \right)^4} $. We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogiπ2iπ iπ arithms of argument $ {e^{{{i\pi } \over 3}}},{e^{{{2i\pi } \over 3}}},{e^{{{i\pi } \over 2}}} $, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope.

scholarly journals Effects of light-by-light scattering in the Lamb shift and hyperfine structure of muonic hydrogen

2019 ◽  
Vol 222 ◽  
pp. 03010 ◽  
Author(s):  
A. E. Dorokhov ◽  
A. P. Martynenko ◽  
F. A. Martynenko ◽  
A. E. Radzhabov
Keyword(s):  
Experimental Data ◽  
Form Factor ◽  
Lamb Shift ◽  
Axial Vector ◽  
Muonic Hydrogen ◽  
Meson Exchange ◽  
Interaction Operator ◽  
Two Photon ◽  
Meson Coupling ◽  
Precise Experimental Data

We calculate the meson exchange contribution to the interaction operator of muon and proton, which is determined by the meson coupling with two photon state. For the construction of transition form factor Meson → γγ we use the existing parametrizations based on experimental data including the monopole parametrization over photon four-momenta. For an estimate of the form factor value atzero photon four-momenta squared we use experimental data on the decay width ΓMeson→γγ. It is shown that scalar, pseudoscalar, axial vector and tensor mesons exchanges give significant contribution to the Lamb shift (LS) and hyperfine splitting (HFS) in muonic hydrogen which should be taken into account for a comparison with precise experimental data.

scholarly journals NEUTRON CHARGE RADIUS: RELATIVISTIC EFFECTS AND THE FOLDY TERM

2003 ◽  
Vol 18 (31) ◽  
pp. 5767-5779 ◽  
Author(s):  
W. R. B. DE ARAÚJO ◽  
T. FREDERICO ◽  
M. BEYER ◽  
H. J. WEBER
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Charge Radius ◽  
Relativistic Effects ◽  
Spin Coupling ◽  
Coupling Scheme ◽  
Neutron Radius ◽  
Quark Spin ◽  
Dirac Form Factor ◽  
Front Model

The neutron charge radius is studied within a light-front model with different spin coupling schemes and wave functions. The cancellation of the contributions from the Foldy term and Dirac form factor to the neutron charge form factor is verified for large nucleon sizes and it is independent of the detailed form of quark spin coupling and wave function. For the physical nucleon our results for the contribution of the Dirac form factor to the neutron radius are insensitive to the form of the wave function while they strongly depend on the quark spin coupling scheme.

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