The 4-loop slope of the Dirac form factor

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.

NEUTRON CHARGE RADIUS: RELATIVISTIC EFFECTS AND THE FOLDY TERM

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.