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 $$\omega $$ ω and $$\phi $$ ϕ residues. The former can be predicted using the respective $$\pi \pi \rightarrow {{\bar{K}}} K$$ π π → 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 $$\phi $$ ϕ region in hadronic vacuum polarization (HVP). Our main results are: $$\langle r^2\rangle _\text {c}=0.359(3)\,\text {fm}^2$$ ⟨ r 2 ⟩ c = 0.359 ( 3 ) fm 2 , $$\langle r^2\rangle _\text {n}=-0.060(4)\,\text {fm}^2$$ ⟨ r 2 ⟩ n = - 0.060 ( 4 ) fm 2 for the charged and neutral radii, $$\epsilon =0.63(40)$$ ϵ = 0.63 ( 40 ) for the elastic contribution to the violation of Dashen’s theorem, $$a_\mu ^{K\text {-box}}=-0.48(1)\times 10^{-11}$$ a μ K -box = - 0.48 ( 1 ) × 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 μ HVP [ K + K - , ≤ 1.05 GeV ] = 184.5 ( 2.0 ) × 10 - 11 , $$a_\mu ^\text {HVP}[K_SK_L, \le 1.05\,\text {GeV}]=118.3(1.5)\times 10^{-11}$$ a μ HVP [ K S K L , ≤ 1.05 GeV ] = 118.3 ( 1.5 ) × 10 - 11 for the HVP integrals around the $$\phi $$ ϕ resonance. The global fit to $${{\bar{K}}} K$$ K ¯ K gives $${{\bar{M}}}_\phi =1019.479(5)\,\text {MeV}$$ M ¯ ϕ = 1019.479 ( 5 ) MeV , $${\bar{ \varGamma }}_\phi =4.207(8)\,\text {MeV}$$ Γ ¯ ϕ = 4.207 ( 8 ) MeV for the $$\phi $$ ϕ resonance parameters including vacuum-polarization effects.

Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections

“…The threshold region in the K𝐾 channel is dominated by the isoscalar form factor, and can thus be analyzed in terms of the 𝜙 resonance parameters [41]. The relevant IB effects arise from FSR, from IB in the kaon masses, and from IB in the 𝜙 residues…”

“…To define the kaon masses in the isospin limit, we use the charged-kaon self energy (𝑀 2 𝐾 ± ) EM = 2.12(18) × 10 −3 GeV 2 from the Cottingham formula [41], leading to…”

“…Using the 𝜙 spectral function from Ref. [41] and varying the kaon masses according to Eq. ( 6), we obtain…”

“…These have been estimated from phenomenology before [36,37], but with recent work on the dominant exclusive channels using dispersion relations and chiral perturbation theory (ChPT) [4,21,[38][39][40] several estimates can be improved, most notably the impact of the pion-mass difference on the 2𝜋 channel. In addition, we include the K𝐾 channel [41], in which case IB effects in the kaon mass are enhanced due to the proximity of the K𝐾 threshold and the 𝜙 resonance. All numbers will be given in units of 10 −10 .…”

Interplay of nuclear physics, effective field theories, phenomenology, and lattice QCD in neutrino physics

“…The basic idea amounts to starting from the amplitude T μν involving two external currents interacting with a hadronic system, and then closing the loop by connecting the currents. In the electromagnetic case, this strategy allows one to estimate self energies of mesons [68][69][70][71][72][73] and nucleons [74][75][76][77], with numerical results typically dominated by elastic intermediate states. In Refs.…”