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.

Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

We reassess the impact of short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude on the anomalous magnetic moment of the muon, a μ = ( g - 2 ) μ / 2 , by comparing different solutions that have recently appeared in the literature. In particular, we analyze the relevance of the exact axial anomaly and its impact on a μ and conclude that it remains rather limited. We show that all recently proposed solutions agree well within uncertainties on the numerical estimate of the impact of short-distance constraints on a μ , despite differences in the concrete implementation. We also take into account the recently calculated perturbative corrections to the massless quark loop to update our estimate and outline the path towards future improvements.

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-waveK 0 ∗ ( 1430 ) and the P-waveK ∗ ( 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 theK 0 ∗ ( 1430 ) andK 0 ∗ ( 1950 ) resonances via Padé approximants,s K 0 ∗ ( 1430 ) = [ 1408 ( 48 ) - i 180 ( 48 ) ] MeV ands 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 .

First Results on the Scalar WIMP-Pion Coupling, Using the XENON1T Experiment

We present first results on the scalar coupling of weakly interacting massive particles (WIMPs) to pions from 1  t yr of exposure with the XENON1T experiment. This interaction is generated when the WIMP couples to a virtual pion exchanged between the nucleons in a nucleus. In contrast to most nonrelativistic operators, these pion-exchange currents can be coherently enhanced by the total number of nucleons and therefore may dominate in scenarios where spin-independent WIMP-nucleon interactions are suppressed. Moreover, for natural values of the couplings, they dominate over the spin-dependent channel due to their coherence in the nucleus. Using the signal model of this new WIMP-pion channel, no significant excess is found, leading to an upper limit cross section of 6.4×10^{-46}  cm^{2} (90% confidence level) at 30  GeV/c^{2} WIMP mass.

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.

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.