The subtraction contribution to the muonic-hydrogen Lamb shift: a point for lattice QCD calculations of the polarizability effect

TL;DR

This paper proposes a new approach to calculate the proton-polarizability contribution to the muonic-hydrogen Lamb shift using lattice QCD, aiming to reduce theoretical uncertainties in proton radius measurements.

Contribution

It introduces a novel subtraction point that simplifies lattice calculations of the subtraction function, focusing on the dominant contribution to the Lamb shift.

Findings

The subtraction contribution is the main effect on the Lamb shift.

The new subtraction point suppresses structure function contributions, facilitating lattice calculations.

This approach could improve the precision of proton polarizability estimates.

Abstract

The proton-polarizability contribution to the muonic-hydrogen Lamb shift is a major source of theoretical uncertainty in the extraction of the proton charge radius. An empirical evaluation of this effect, based on the proton structure functions, requires a systematically improvable calculation of the "subtraction function", possibly using lattice QCD. We consider a different subtraction point, with the aim of accessing the subtraction function directly in lattice calculations. A useful feature of this subtraction point is that the corresponding contribution of the structure functions to the Lamb shift is suppressed. The whole effect is dominated by the subtraction contribution, calculable on the lattice.