Relativistic corrections to the Bethe logarithm for the $2{}^{3}S$ and $2{}^{3}P$ states of He

With this work we start a project calculating the QED contribution of order ${\alpha }^{7}m$ to the $2{}^{3}P–2{}^{3}S$ transition energy in helium, aiming for an accurate determination of the nuclear charge radius $r_E$ from measurements of the corresponding transition frequency. Together with the complementary determination of $r_E$ from muonic helium, this project will provide a stringent test of universality of electromagnetic interactions of leptons in the Standard Model. We report a calculation of the relativistic corrections to the Bethe logarithm for the $2{}^{3}S$ and $2{}^{3}P$ states, which is the most numerically demanding part of the project.