Baryonic form factors of light pseudoscalar mesons

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.