Kaon electromagnetic form factors in dispersion theory

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of $ω$ and $ϕ$ residues. The former can be predicted using the respective $ππ\to\bar K K$ partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen's theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the $ϕ$ region in hadronic vacuum polarization (HVP). Our main results are: $\langle r^2\rangle_\text{c}=0.359(3)\,\text{fm}^2$, $\langle r^2\rangle_\text{n}=-0.060(4)\,\text{fm}^2$ for the charged and neutral radii, $ε=0.63(40)$ for the elastic contribution to the violation of Dashen's theorem, $a_μ^{K\text{-box}}=-0.48(1)\times 10^{-11}$ for the charged kaon box in HLbL scattering, and $a_μ^\text{HVP}[K^+K^-, \leq 1.05\,\text{GeV}]=184.5(2.0)\times 10^{-11}$, $a_μ^\text{HVP}[K_SK_L, \leq 1.05\,\text{GeV}]=118.3(1.5)\times 10^{-11}$ for the HVP integrals around the $ϕ$ resonance. The global fit to $\bar K K$ gives $\bar M_ϕ=1019.479(5)\,\text{MeV}$, $\bar Γ_ϕ=4.207(8)\,\text{MeV}$ for the $ϕ$ resonance parameters including vacuum-polarization effects.

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