Pion electromagnetic form factor from full lattice QCD

TL;DR

This paper presents the first lattice QCD calculation of the pion electromagnetic form factor at physical quark masses, providing insights into the pion's internal structure and comparing results with experimental data.

Contribution

The study performs a novel lattice QCD calculation of the pion form factor at physical quark masses using multiple lattice spacings, avoiding chiral extrapolation and including disconnected diagram contributions.

Findings

Shape of the vector form factor matches experimental data.

Extracted pion charge radius consistent with experimental values.

Analyzed scalar form factor and disconnected diagram contributions.

Abstract

We present the first calculation of the pion electromagnetic form factor at physical light quark masses. This form factor parameterises the deviations from the behaviour of a point-like particle when a photon hits the pion. These deviations result from the internal structure of the pion and can thus be calculated in QCD. We use three sets (different lattice spacings) of $n_f = 2+1+1$ lattice configurations generated by the MILC collaboration. The Highly Improved Staggered Quark formalism (HISQ) is used for all of the sea and valence quarks. Using lattice configurations with $u$/$d$ quark masses very close to the physical value is a big advantage, as we avoid the chiral extrapolation. We study the shape of the vector ($f_+$) form factor in the $q^2$ range from $0$ to $-0.15$~GeV$^2$ and extract the mean square radius, $\langle r^2_v\rangle$. The shape of the vector form factor and the resulting radius is compared with experiment. We also discuss the scalar form factor and radius extracted from that, which is not directly accessible to experiment. We have also calculated the contributions from the disconnected diagrams to the scalar form factor at small $q^2$ and discuss their impact on the scalar radius $\langle r^2_s\rangle$.