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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 ππ→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: ⟨r2⟩c=0.359(3)fm2, ⟨r2⟩n=-0.060(4)fm2 for the charged and neutral radii, ϵ=0.63(40) for the elastic contribution to the violation of Dashen’s theorem, aμK-box=-0.48(1)×10-11 for the charged kaon box in HLbL scattering, and aμHVP[K+K-,≤1.05GeV]=184.5(2.0)×10-11, aμHVP[KSKL,≤1.05GeV]=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.

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, aμ=(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 aμ 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 aμ, 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.

A bstract Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from ππ intermediate states to the partial waves for the process γ * γ * → ππ . All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

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 e + e - → 3 π cross section, generalizing previous studies on ω , ϕ → 3 π decays and γ π → π π scattering, and verify our result by comparing to e + e - → π 0 γ data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1 GeV , and extract the slope of the form factor at vanishing momentum transfer a π = ( 30.7 ± 0.6 ) × 10 - 3 . 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.

Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching fractions of resonances determined as ratios of count rates. To make contact between these quantities it is necessary to connect line shapes and resonance parameters. In this work we propose such a connection and illustrate the formalism with detailed studies of the ρ ( 770 ) and f 0 ( 500 ) resonances. Based on the line shapes inferred from the resonance parameters along these lines, expressions for partial widths and branching ratios are derived and compared to other approaches in the literature.

The difference between the electromagnetic self-energies of proton and neutron can be calculated with the Cottingham formula, which expresses the self-energies as an integral over the electroproduction cross sections – provided the nucleon matrix elements of the current commutator do not contain a fixed pole. We show that, under the same proviso, the subtraction function occurring in the dispersive representation of the virtual Compton forward scattering amplitude is determined by the cross sections. The representation in particular leads to a parameter-free sum rule for the nucleon polarisabilities. We evaluate the sum rule for the difference between the electric polarisabilities of proton and neutron by means of the available parameterisations of the data and compare the result with experiment.

Pion–kaon (πK) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of πK 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 πK scattering in a given partial wave are related to the phases of the respective πK form factors by Watson’s theorem. Going beyond that, we here construct a representation of the scalar πK form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from πK scattering and maintaining the correct analytic structure. As a first application, we consider the decay τ→KSπντ, in particular, we study to which extent the S-wave K0∗(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 K0∗(1430) and K0∗(1950) resonances via Padé approximants, sK0∗(1430)=[1408(48)-i180(48)]MeV and sK0∗(1950)=[1863(12)-i136(20)]MeV, as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for τ→K0∗(1430)ντ in terms of the corresponding residue, leading to the upper limit BR(τ→K0∗(1430)ντ)<1.6×10-4.

Kaon physics is at a turning point – while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop, held in September 2023 at CERN.

Electric dipole moments (EDM) of fundamental particles inherently violate time-reversal (T) and the combined charge-conjugation and parity symmetry (CP). We aim to measure the EDM of the muon using the frozen-spin technique within a compact storage trap. This method exploits the high effective electric field, E ≈ 165 MV / m , experienced in the rest frame of the muon with a momentum of about 23 MeV / c when it passes through a solenoidal magnetic field of | B → | = 2.5 T . In this paper, we outline the fundamental considerations for a muon EDM search and present a conceptual design for a demonstration experiment to be conducted at secondary muon beamlines of the Paul Scherrer Institute in Switzerland. In Phase I, with an anticipated data acquisition period of 200 days, the expected sensitivity to a muon EDM is σ ( d ) ≤ 4 E - 21 e · cm . In a subsequent phase, Phase II, we propose to improve the sensitivity to σ ( d ) ≤ 6 E - 23 e · cm using a dedicated instrument installed on a different beamline that produces muons of momentum 125  MeV / c .

A bstract Based on the recently proposed Roy-Steiner equations for pion-nucleon ( πN ) scattering [1], we derive a system of coupled integral equations for the and S -waves. These equations take the form of a two-channel Muskhelishvili-Omnès problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including intermediate states. In particular, we determine the correction , which is needed for the extraction of the pion-nucleon σ term from πN scattering, as a function of pion-nucleon subthreshold parameters and the πN coupling constant.