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

TL;DR

This paper calculates relativistic corrections to the Bethe logarithm for helium's excited states, a crucial step toward precise QED contributions needed for determining the nuclear charge radius and testing fundamental physics.

Contribution

It provides the first detailed calculation of relativistic corrections to the Bethe logarithm for specific helium states, advancing the precision of QED calculations.

Findings

Relativistic corrections to the Bethe logarithm for $2^3S$ and $2^3P$ states are computed.

This work enhances the accuracy of helium transition energy predictions.

The results support future high-precision tests of the Standard Model.

Abstract

With this work we start a project of calculating the QED contribution of order $\alpha^7m$ to the $2^3P$-$2^3S$ 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 $2^3S$ and $2^3P$ states, which is the most numerically demanding part of the project.