Baryonic form factors of light pseudoscalar mesons

TL;DR

This paper calculates the space-like baryonic form factors of pions and kaons using the Bethe-Salpeter formalism, providing insights into quark mass differences and meson structure.

Contribution

It introduces a novel computation of baryonic form factors for light pseudoscalar mesons employing a fully dressed quark approach within the Bethe-Salpeter framework.

Findings

The pion baryonic radius is 0.043(2) fm, consistent with dispersive data.

Kaon baryonic radii are approximately 0.265(7) fm and 0.262(7) fm, larger than the pion.

Results align with chiral QCD models and provide new predictions without dispersive counterparts.

Abstract

Employing the Bethe-Salpeter formalism, we present a computation of the space-like baryonic form factor for the pion and kaon. In the exact isospin-symmetric limit this observable is forbidden by $G$-parity, so that any nonzero signal constitutes a direct probe of the quark mass difference $m_d - m_u$. The form factors are evaluated in the impulse approximation using fully dressed quark propagators, meson Bethe-Salpeter amplitudes, and a dressed baryon-current vertex constrained by the vector Ward-Takahashi identity. The baryonic radius computed with this method for the pion is given by $\langle r_{\! B}^2\rangle_{\pi^+}^{1/2} = 0.043(2)$ fm, and is consistent with the available dispersive benchmarks. Our predictions for the kaons, namely $\langle r_{\!B}^2\rangle_{K^+}^{1/2} = 0.265(7)$ fm and $\langle r_{\!B}^2\rangle_{K^0}^{1/2} = 0.262(7)$ fm, indicate a larger spatial extent than in the pion case; these results have no dispersive counterparts, and are compatible with chiral QCD models.