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 ω and ϕ residues. The former can be predicted using the respective 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 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, ϵ = 0.63 ( 40 ) for the elastic contribution to the violation of Dashen's theorem, a µ K -box = - 0.48 ( 1 ) × 10 - 11 for the charged kaon box in HLbL scattering, and a µ HVP [ K + K - , ≤ 1.05 GeV ] = 184.5 ( 2.0 ) × 10 - 11 , a µ HVP [ 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 K ¯ K gives M ¯ ϕ = 1019.479 ( 5 ) MeV , Γ ¯ ϕ = 4.207 ( 8 ) MeV for the ϕ resonance parameters including vacuum-polarization effects.

On the scalar π K form factor beyond the elastic region.

Pion-kaon ( π K ) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of π K scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of π K scattering in a given partial wave are related to the phases of the respective π K form factors by Watson's theorem. Going beyond that, we here construct a representation of the scalar π K form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from π K scattering and maintaining the correct analytic structure. As a first application, we consider the decay τ → K S π ν τ , in particular, we study to which extent the S-wave K 0 ∗ ( 1430 ) and the P-wave K ∗ ( 1410 ) resonances can be differentiated and provide an improved estimate of the CP asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the K 0 ∗ ( 1430 ) and K 0 ∗ ( 1950 ) resonances via Padé approximants, s K 0 ∗ ( 1430 ) = [ 1408 ( 48 ) - i 180 ( 48 ) ] MeV and s K 0 ∗ ( 1950 ) = [ 1863 ( 12 ) - i 136 ( 20 ) ] MeV , as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for τ → K 0 ∗ ( 1430 ) ν τ in terms of the corresponding residue, leading to the upper limit BR ( τ → K 0 ∗ ( 1430 ) ν τ ) < 1.6 × 10 - 4 .

Dispersive analysis of the pion transition form factor.

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the [Formula: see text] cross section, generalizing previous studies on [Formula: see text] decays and [Formula: see text] scattering, and verify our result by comparing to [Formula: see text] data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below [Formula: see text], and extract the slope of the form factor at vanishing momentum transfer [Formula: see text]. We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

Constraints on the [Formula: see text] form factor from analyticity and unitarity.

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic [Formula: see text] form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds. We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the [Formula: see text] form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around [Formula: see text].

Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor.

In order to isolate the contribution of the nucleon strange electric form factor to the parity-violating asymmetry measured in 4He(e-->],e')4He experiments, it is crucial to have a reliable estimate of the magnitude of isospin-symmetry-breaking (ISB) corrections in both the nucleon and 4He. We examine this issue in the present Letter. Isospin admixtures in the nucleon are determined in chiral perturbation theory, while those in 4He are derived from nuclear interactions, including explicit ISB terms. A careful analysis of the model dependence in the resulting predictions for the nucleon and nuclear ISB contributions to the asymmetry is carried out. We conclude that, at the low momentum transfers of interest in recent measurements reported by the HAPPEX Collaboration at Jefferson Lab, these contributions are of comparable magnitude to those associated with strangeness components in the nucleon electric form factor.