On the scalar $$\varvec{\pi K}$$ form factor beyond the elastic region

Abstract

Pion–kaon ($$\pi K$$ π K ) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $$\pi K$$ 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 $$\pi K$$ π K scattering in a given partial wave are related to the phases of the respective $$\pi K$$ π K form factors by Watson’s theorem. Going beyond that, we here construct a representation of the scalar $$\pi K$$ π K form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $$\pi K$$ π K scattering and maintaining the correct analytic structure. As a first application, we consider the decay $${\tau \rightarrow K_S\pi \nu _\tau }$$ τ → K S π ν τ , in particular, we study to which extent the S-wave $$K_0^*(1430)$$ K 0 ∗ ( 1430 ) and the P-wave $$K^*(1410)$$ 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 $$K_0^*(1430)$$ K 0 ∗ ( 1430 ) and $$K_0^*(1950)$$ K 0 ∗ ( 1950 ) resonances via Padé approximants, $$\sqrt{s_{K_0^*(1430)}}=[1408(48)-i\, 180(48)]\,\text {MeV}$$ s K 0 ∗ ( 1430 ) = [ 1408 ( 48 ) - i 180 ( 48 ) ] MeV and $$\sqrt{s_{K_0^*(1950)}}=[1863(12)-i\,136(20)]\,\text {MeV}$$ 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 $${\tau \rightarrow K_0^*(1430)\nu _\tau }$$ τ → K 0 ∗ ( 1430 ) ν τ in terms of the corresponding residue, leading to the upper limit $${\text {BR}(\tau \rightarrow K_0^*(1430)\nu _\tau )<1.6 \times 10^{-4}}$$ BR ( τ → K 0 ∗ ( 1430 ) ν τ ) < 1.6 × 10 - 4 .

Probing violation of CP & T invariance in the transitions of τ leptons

“…'We' have listened a nice talk by Noel at the TAU2021 Workshop; one can read it in the Proceedungs [3] 3 . It is based on his article [4]. His talk was clearer (in my view) than in his article about finding CP violation there, but also a sign of ND.…”

“…My main question is the title: "On the scalar πK form factor beyond the elastic region" both in his talk & his article[4]. First he discussed the tools for analyzing data.…”

CP asymmetry in the angular distributions of τ → KSπντ decays. Part II. General effective field theory analysis

“…For recent discussions about the two-hadron tensor form factors, the readers are also referred to refs. [41,118,121,122].…”

“…After the initial null results from CLEO [28,29] and Belle [30], a non-zero CP asymmetry was reported for the first time by the BaBar collaboration [31], by measuring the decay-rate difference between τ + and τ − decays. However, such a measurement is in conflict with the SM prediction [27,[32][33][34] at the level of 2.8σ, which has motivated many NP explanations by including the extra contribution from non-standard tensor interactions [34][35][36][37][38][39][40][41]. Unfortunately, the suppression of the relative phase between the Kπ vector and tensor form factors as well as the combined constraints from other relevant observables have already excluded such a possibility [34][35][36].…”

Novel approaches in Hadron Spectroscopy

“…Most of the recent data on XYZ states come from electroweak processes, as heavy meson/baryon decays or e + e − annihilation. Matrix elements can most often be studied in terms of form factors [178,482,483].…”