Timelike electromagnetic kaon form factor

Abstract

We compute the electromagnetic charged kaon form factor in the timelike region by employing a Poincar\'e covariant formalism of the Bethe-Salpeter equation to study quark-antiquark bound states in conjunction with the Schwinger-Dyson equation for the quark propagator. Following a recent kindred calculation of the timelike electromagnetic pion form factor, we include the most relevant intermediate composite particles permitted by their quantum numbers in the interaction kernel to allow for a decay mechanism for the resonances involved. This term augments the usual gluon mediated interaction between quarks. For a sufficiently low energy timelike probing photon, the electromagnetic form factor is saturated by the $\ensuremath{\rho}(770)$ and $\ensuremath{\phi}(1020)$ resonances. We assume $SU(2)$ isospin symmetry throughout. Our results for the absolute value squared of the electromagnetic form factor agree qualitatively rather well and quantitatively moderately so with available experimental data.