Strange resonance poles from $$K\pi $$ K π scattering below 1.8 GeV

Abstract

In this work we present a determination of the mass, width, and coupling of the resonances that appear in kaon-pion scattering below 1.8 GeV. These are: the much debated scalar κ-meson, nowadays known as K * 0 (800), the scalar K * 0 (1430), the K * (892) and K * 1 (1410) vectors, the spin-two K * 2 (1430) as well as the spin-three K * 3 (1780). The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the K π scattering amplitudes obtained in a recent and precise data analysis constrained with dispersion relations, which were not well satisfied in previous analyses. This analytic continuation will be performed by means of Padé approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties.

The non-ordinary Regge behavior of the $$K^*_0(800)$$ K 0 ∗ ( 800 ) or $$\kappa $$ κ -meson versus the ordinary $$K^*_0(1430)$$ K 0 ∗ ( 1430 )

“…However, by means of a rigorous dispersive analysis in [23], based on Roy-Steiner partial wave dispersion relations, it has been confirmed that a pole associated to that state exists. This pole, below 800 MeV, is found by many other approaches based on chiral symmetry and/or dispersion relations [15][16][17][18][19]22,24], in analytic extractions of poles without model-dependent assumptions [25,26] or very recently on the lattice [27] (although given the high quark masses used in the calculation it appears as a virtual state, as suggested in [28] from dispersion theory and effective chiral Lagrangians).…”

“…Within the second approach we will use a recent pole determination [26] that does not assume a particular functional form or model for the pole, but uses a sequence of Padé approximants with powerful convergence properties in the complex plane. This sequence is calculated from the values of the amplitude and its derivatives at an energy point near the resonance.…”

“…Actually, the parameterizations in [29] do have several poles [26] and describe the data very accurately. However, if one tries to implement a dispersive formalism with more Regge poles, each one has three more functions to determine (Re α, Im α and β), but still just one elastic unitarity condition for the whole partial wave.…”

“…This is why we provided the curves in Fig. 1, just to show that the pole contribution (extracted in [26] from a parameterization that describes the data accurately) dominates the amplitude in that same region. One might be worried that the peak is somewhat displaced, but we will also make the calculation with a Breit-Wigner functional form, which by construction satisfies unitarity, and we will check that the results are compatible with those obtained from the pole extracted in [26].…”

“…First, we have also used the pole obtained in a recent work [26], which also used the constrained data analysis of [29], although the pole was not obtained from the conformal fit there, but from a sequence of Padé approximants. The pole parameters thus obtained were…”