The time-like electromagnetic kaon form factor

TL;DR

This paper calculates the electromagnetic charged kaon form factor in the time-like region using a covariant Bethe-Salpeter and Schwinger-Dyson formalism, including resonance decay mechanisms, and compares results with experimental data.

Contribution

It introduces a covariant formalism incorporating resonance decay channels into the calculation of the kaon form factor, extending previous pion form factor studies.

Findings

Qualitative agreement with experimental data

Resonance contributions from $ ho(770)$ and $\phi(1020)$

Moderate quantitative accuracy

Abstract

We compute the electromagnetic charged kaon form factor in the time-like 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 time-like 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 time-like probing photon, the electromagnetic form factor is saturated by the $\rho(770)$ and $\phi(1020)$ 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.