We evaluate a Laurent expansion in dimensional regularization parameter $epsilon=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using a recently developed method of one of the present co
authors (R.L.) and extending thereby results by Baikov and Chetyrkin obtained at transcendentality weight seven. We observe only multiple zeta values in our results. Therefore, we conclude that all the four-loop massless propagator integrals, with any integer powers of numerators and propagators, have only multiple zeta values in their epsilon expansions up to transcendentality weight twelve.
We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present
coauthors (R.L.). We observe only multiple zeta values in our results.
We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g-2 in QED up to the transc
endentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm.
The quasiclassical correction to the Molieres formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not sph
erically symmetric potential. Unlike the leading term, the correction to the Molieres formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Molieres formula.
The excessiveness of integration-by-part (IBP) identities is discussed. The Lie-algebraic structure of the IBP identities is used to reduce the number of the IBP equations to be considered. It is shown that Lorentz-invariance (LI) identities do not b
ring any information additional to that contained in the IBP identities, and therefore, can be discarded.
The correction to the wave function of the ground state in a hydrogen-like atom due to an external homogenous magnetic field is found exactly in the parameter $Zalpha$. The $j=1/2$ projection of the correction to the wave function of the $ns_{1/2}$ s
tate due to the external homogeneous magnetic field is found for arbitrary $n$. The $j=3/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the nuclear magnetic moment is also found for arbitrary $n$. Using these results, we have calculated the shielding of the nuclear magnetic moment by the $ns_{1/2}$ electron.
