Determination of the Lightest Strange Resonance 
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 or 
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, from a Dispersive Data Analysis

Peláez, J. R.; Rodas, A.

doi:10.1103/physrevlett.124.172001

“…For the latter, the uncertainties are computed from the propagation in quadrature of the LEC errors. These results are perfectly consistent with the most precise dispersive calculations [58][59][60]. The χ κ,U S results for both unitarization methods, including their uncertainties, are plotted in Fig.…”

Section: Theoretical Analysis From Effective Theoriessupporting

confidence: 85%

The role of strangeness in chiral and $$U(1)_A$$ restoration

Nicola

¹

,

Elvira

²

,

Vioque-Rodríguez

³

et al. 2021

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We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ($$\chi _S^\kappa $$ χ S κ , $$\chi _P^K$$ χ P K ) in the isospin 1/2 channel. We show that $$\chi _S^\kappa $$ χ S κ develops a maximum above the QCD chiral transition, after which it degenerates with $$\chi _P^K$$ χ P K . We also obtain $$\chi _S^\kappa $$ χ S κ within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $$K_0^*(700)$$ K 0 ∗ ( 700 ) (or $$\kappa $$ κ ) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $$\pi K$$ π K scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $$\chi _S^\kappa $$ χ S κ dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $$m_l/m_s$$ m l / m s ratio that allows one studying $$K-\kappa $$ K - κ degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for $$O(4)\times U(1)_A$$ O ( 4 ) × U ( 1 ) A restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $$U(1)_A$$ U ( 1 ) A restoration.

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“…Since we cannot give preference to any particular fit variant, we quote the average over all four versions as central value and assign the spread as systematic uncertainty BR(τ → K S πν τ ) = 4.35 (6) 10 −3 at the level of 1.5σ . We thus conclude that the branching fraction extracted by combining the shape as measured in the Belle spectrum with the normalization from K 3 decays comes out consistent with the direct measurement in τ decays.…”

Section: Fit Resultsmentioning

confidence: 99%

“…At low energies, the π K S-wave of isospin 1/2 is characterized by the interplay of low-energy theorems induced by the chiral structure of QCD [1,2] and a relatively close-by pole located deep in the complex plane called the κ or K * (700) [3][4][5][6][7][8]. The properties of the κ cannot be described by a sima e-mail: noel@itp.unibe.ch (corresponding author) ple Breit-Wigner (BW) model, but require the proper consideration of the analytic structure, most conveniently implemented in the framework of dispersion relations.…”

Section: Introductionmentioning

confidence: 99%

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

Detten

¹

,

Noël

²

,

Hanhart

³

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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“…The same data fitted with naive models lacking the minimum fundamental requirements can yield a pole, or not, and the parameters of that pole can vary wildly. This was illustrated nicely in [107] but as we will see is even more shocking for the κ [54,55]. In particular, the incorrect use of Breit-Wigner shapes, often with some ad-hoc modifications that violate the well-known analytic structure of partial waves, and sometimes even unitarity, was very frequent, both in scattering and production.…”

Section: The Model-dependence Problemmentioning

confidence: 85%

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

Peláez

¹

,

Rodas

²

,

Elvira

³

2021

Eur. Phys. J. Spec. Top.

Self Cite

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For several decades, the σ/f0(500) and κ/K * 0 (700) resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons σ/f0(500) and κ/K * 0 (700). Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats.

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Determination of the Lightest Strange Resonance K0*(700) or κ , from a Dispersive Data Analysis

Cited by 30 publications

References 68 publications

The role of strangeness in chiral and $$U(1)_A$$ restoration

The role of strangeness in chiral and $$U(1)_A$$ restoration

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

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

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