Kaon electromagnetic form factors in dispersion theory

Abstract

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their lowenergy singularities, in the isovector part from twopion intermediate states and in the isoscalar contribution in terms of ω and φ residues. The former can be predicted using the respective ππ → KK partialwave 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: r 2 c = 0.359(3) fm 2 , r 2 n = −0.060(4) fm 2 for the charged and neutral radii, = 0.63( 40) for the elastic contribution to the violation of Dashen's theorem, a K-box µ = −0.48(1) × 10 −11 for the charged kaon box in HLbL scattering, and a HVP µ [K + K − , ≤ 1.05 GeV] = 184.5(2.0) × 10 −11 , a HVP µ [K S K L , ≤ 1.05 GeV] = 118.3(1.5) × 10 −11 for the HVP integrals around the φ resonance. The global fit to KK gives Mφ = 1019.479(5) MeV, Γφ = 4.207(8) MeV for the φ resonance parameters including vacuumpolarization effects.

A dispersive analysis of $$\varvec{\eta '\rightarrow \pi ^+\pi ^-\gamma }$$ and $$\varvec{\eta '\rightarrow \ell ^+\ell ^-\gamma }$$

“…The quoted numbers for M ω , Γ ω are VP subtracted, to ensure consistency with the bookkeeping as defined in the appendix. We also show the analog quantities for the φ, which enter the isoscalar part of the TFF (and are consistent with analogous determinations from e + e − → K K[104]).…”

Prospects for precise predictions of $a_μ$ in the Standard Model

“…[6] include the crucial 2π channel (new data from SND [151] and covariance matrix from BESIII [88]) as well as new data for e + e − → 3π [152,153], the second-largest channel both in absolute value and error, see Table 2. Moreover, unitarity and analyticity constraints have been analyzed for the π 0 γ [154] and KK channels [155]. However, as of now, none of these developments indicate significant changes compared to the situation described in Ref.…”

“…In this part of the evaluation, ongoing work thus mainly concerns a consolidation of the η, η poles, both using dispersion relations [176,177] and lattice QCD [178,179] (see Refs. [155,180] for recent work on the box contributions).…”

The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region

“…More recently, a new parameterization of the kaon EMFFs was presented based on dispersion theory in Ref. [34], where the kaon EMFFs are divided into the isoscalar and isovector parts with the former one expressed in terms of ω and φ residues and the latter saturated by the two-pion intermediate states. For simplicity, we approximate the isovector kaon form factor by a single effective Breit-Wigner term that is related to the ρ meson contribution and fit it to the unconstrained fit to data (UFD) parameterization from Ref.…”