Lattice Calculation of the Proton Charge Radius

Abstract

The charge radius of the proton has been measured in scattering and spectroscopy experiments using both electronic and muonic probes. The electronic and muonic measurements are discrepant at $5\sigma$, giving rise to what is known as the proton radius puzzle. With the goal of resolving this, we introduce a novel method of using lattice QCD to determine the isovector charge radius -- defined as the slope of the electric form factor at zero four-momentum transfer -- by introducing a mass splitting between the up and down quarks. This allows us to access timelike four-momentum transfers as well as spacelike ones, leading to potentially higher accuracy in determining the form factor slope at $Q^2 = 0$ by interpolation. In this preliminary study, we find a Dirac isovector radius squared of $0.320 \pm 0.074$ fm$^2$ at quark masses corresponding to $m_\pi = 450$ MeV. We compare the feasibility of this method with other approaches of determining the proton charge radius from lattice QCD.