Onset of scaling violation in pion and kaon elastic electromagnetic form factors

TL;DR

This paper predicts the behavior of pion and kaon electromagnetic form factors using a symmetry-preserving quantum field approach, highlighting the presence of scaling violations and locating the maximum of $Q^2 F_P(Q^2)$ around 5 GeV$^2$, which can be tested experimentally.

Contribution

It provides parameter-free, unified predictions for pion and kaon form factors using a symmetry-preserving truncation of quantum field equations, emphasizing the significance of scaling violations.

Findings

Predicted maximum of $Q^2 F_P(Q^2)$ near 5 GeV$^2$ for pions and kaons.

Scaling violations imply a single maximum in $Q^2 F_P(Q^2)$ for positive-charge states.

Experimental tests can confirm the presence and location of the maximum, informing QCD scaling behavior.

Abstract

Using a symmetry-preserving truncation of the quantum field equations describing hadron properties, parameter-free predictions are delivered for pion and kaon elastic electromagnetic form factors, $F_{P=\pi,K}$, thereby unifying them with kindred results for nucleon elastic electromagnetic form factors. Regarding positive-charge states, the analysis stresses that the presence of scaling violations in QCD entails that $Q^2 F_P(Q^2)$ should exhibit a single maximum on $Q^2>0$. Locating such a maximum is both necessary and sufficient to establish the existence of scaling violations. The study predicts that, for charged $\pi$, $K$ mesons, the $Q^2 F_P(Q^2)$ maximum lies in the neighbourhood $Q^2 \simeq 5\,$GeV$^2$. Foreseeable experiments will test these predictions and, providing their $Q^2$ reach meets expectations, potentially also provide details on the momentum dependence of meson form factor scaling violation.