N/D Method for πK Scattering as Part of MISP 2020 Proceeding

Noël, Frederic; Detten, Leon von; Hanhart, C.

doi:10.3103/s106833562011007x

Cited by 2 publications

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References 8 publications

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“…For the P -wave, inelastic effects are typically included in resonance chiral theory (RChT) [28] via the K * (1410), providing an extended parameterization of the phase shift to be used in the Omnès factor or by feeding the corresponding amplitudes into a unitarization scheme such as the N/D method [29,30]. The latter is hard to handle, however, since it is difficult to prevent its high-order polynomials from generating unphysical poles [31]. Moreover, for the S-wave, the effect of inelasticities in τ → K S πν τ is usually neglected apart from a generous variation of the unknown phase of the form factor, leading to an Omnès representation that, besides constraints from the Callan-Treiman low-energy theorem [32][33][34][35][36], essentially involves a subtracted version of the elastic solution.…”

Section: Introductionmentioning

confidence: 99%

On the scalar $πK$ form factor beyond the elastic region

von Detten,

Noël,

Hanhart

et al. 2021

Preprint

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Section: Introductionmentioning

confidence: 99%

On the scalar $πK$ form factor beyond the elastic region

von Detten,

Noël,

Hanhart

et al. 2021

Preprint

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

et al. 2021

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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 .

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N/D Method for πK Scattering as Part of MISP 2020 Proceeding

Cited by 2 publications

References 8 publications

On the scalar $πK$ form factor beyond the elastic region

On the scalar $πK$ form factor beyond the elastic region

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

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