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 phi residues. The former can be predicted using the respective pi pi rightarrow {{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 phi region in hadronic vacuum polarization (HVP). Our main results are: langle r^2rangle _text {c}=0.359(3),text {fm}^2, langle r^2rangle _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 ^{Ktext {-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_SK_L, le 1.05,text {GeV}]=118.3(1.5)times 10^{-11} for the HVP integrals around the phi resonance. The global fit to {{bar{K}}} K gives {{bar{M}}}_phi =1019.479(5),text {MeV}, {bar{ varGamma }}_phi =4.207(8),text {MeV} for the phi resonance parameters including vacuum-polarization effects.