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 $\omega$ and $\varphi$ residues. The former can be predicted using the respective $\pi \pi \to \bar{K}K$ 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 $\varphi$ 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}$^2$forthechargedandneutralradii,$\epsilon=0.63(40)$ for the elastic contribution to the violation of Dashen’s theorem, $a_{\mu }^{K\text{-box}}=-0.48(1)\times {10}^{-11}$ for the charged kaon box in HLbL scattering, and $a_\mu^$\text{HVP}$[K^+K^-, \leq 1.05,$\text{GeV}$]=184.5(2.0)\times 10^{-11}$,$a_\mu^$\text{HVP}$[K_SK_L, \leq 1.05,$\text{GeV}$]=118.3(1.5)\times 10^{-11}$fortheHVPintegralsaroundthe$\phi$resonance\mathrm{.}Theglobalfitto$\bar K K$gives$\bar M_\phi=1019.479(5),$\text{MeV}$$,$\bar \Gamma_\phi=4.207(8),$\text{MeV}$$ for the $\varphi$ resonance parameters including vacuum-polarization effects.