Kaon electromagnetic form factors in dispersion theory

Abstract

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: $⟨r^2{⟩}_{\text{c}}=0.359(3){\text{fm}}^2$, $⟨r^2{⟩}_{\text{n}}=-0.060(4){\text{fm}}^2$ for the charged and neutral radii, $\epsilon =0.63(40)$ 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 $a_{\mu }^{\text{HVP}}[K^{+}{K}^{-},\le 1.05\text{GeV}]=184.5(2.0)\times 10^{-11}$, $a_{\mu }^{\text{HVP}}[K_S{K}_L,\le 1.05\text{GeV}]=118.3(1.5)\times 10^{-11}$ for the HVP integrals around the $\varphi$ resonance. The global fit to $\bar{K}K$ gives ${\bar{M}}_{\varphi }=1019.479(5)\text{MeV}$, ${\bar{\Gamma }}_{\varphi }=4.207(8)\text{MeV}$ for the $\varphi$ resonance parameters including vacuum-polarization effects.

18 pages, 10 figures; v2 as published in EPJC

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