Calculation of regge trajectories of strange resonances and identification of the k-0*(800) as a non-ordinary meson

We review how the Regge trajectory of an elastic resonance can be obtained just from its pole position and coupling, using a dispersive formalism. This allows us to deal correctly with the finite widths of resonances in Regge trajectories. In this way, we can calculate the Regge trajectories for the K* (892), K_1(1400) and K_(0)^(*)(1430), obtaining ordinary linear Regge trajectories, expected for qq resonances. In contrast, for the K_(0)^(*)(800) meson, the resulting Regge trajectory is non-linear and with much smaller slope, strongly supporting its non-ordinary nature

Estudio dispersivo de mesones ligeros

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica, leída el 18-10-2019Quantum Chromodynamics (QCD) is the fundamental theory that explains the strong interactions between quarks and gluons. Unfortunately, the fact that QCD is asymptotically free at short distances produces the confinement of quarks at low energies, creating the well known hadrons, which are then appropriate the degrees of freedom to extract information from. In order to overcome this difficulty, Weinberg introduced in 1979 [1] Chiral Perturbation Theory (ChPT). This is an effective field theory that considers the octet of pseudo-goldstone bosons (pions, kaons and eta) produced by the chiral symmetry breaking as the degrees of freedom and provides a systematiclow-energy expansion for the observables. Nevertheless, ChPT is not able to determine with high accuracy the low energy parameters of the meson-meson interactions, besides, its series expansion does not respect unitarity, and hence can only be applied very close to threshold...La Cromodinámica Cuántica (QCD) es la teoría fundamental que explica la interacción fuerte entre quarks y gluones. Sin embargo, el hecho de que (QCD) muestra una libertad asintótica a distancias muy pequeñas también implica que quarks y gluones se encuentran confinados a baja energía, formando los conocidos hadrones, por tanto estos pasan a ser los grados de libertad a traves de los cuales extraer información. Es por esto que Weinberg introdujo en 1979 [1] la Teoría de Perturbaciones Quiral (ChPT). Esta es una teoría efectiva que considera el octete de pseudo-bosones goldstone (piones, kaones y eta) producidos por la ruptura espontánea de la simetría Qiral como grados de libertad y proporciona una expansión sistemática de los observables a baja energía. Sin embargo, esta no puede determinar con la precisión necesaria las constantes de baja energía, a parte de no respetar principios fundamentales como la unitariedad, por lo que en principio sólo puede ser aplicada a energías en torno al umbral de interacción...Depto. de Física TeóricaFac. de Ciencias FísicasTRUEunpu

The non-ordinary Regge behavior of the K_(0)^(*)(800) or κ-meson versus the ordinary K_(0)^(*) (1430)

The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the K_(0)^(*)(1430) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q (q) over bar resonances. In contrast, for the K_(0)^(*)(800) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the f_(0)(500) or σ meson. The slope of these unusual Regge trajectories seems to scale with themeson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non- ordinary, predominantly meson-meson- like, interpretation for the lightest strange and non-strange resonances

Quark mass dependence of ππ\pi \pi scattering in isospin 0, 1, and 2 from lattice QCD

Using lattice QCD we extract $\pi\pi$ scattering amplitudes with isospin--0,1,2 in low partial-waves at two values of the light quark mass corresponding to $m_\pi \sim 283$ and $330$ MeV. We confirm expectations of weak repulsion in isospin--2, and the presence of a narrow $\rho$ resonance in isospin--1, and study the pion mass dependence of these channels. In isospin--0 we find that the two pion masses considered straddle the point at which the $\sigma$ transitions from being a stable bound-state to being either a virtual bound-state or a subthreshold resonance. We discuss the ability of lattice calculations like these to precisely determine the $\sigma$ pole location when it is a resonance, and propose an approach in which the full complement of amplitudes computed in this paper can be used simultaneously to provide more constraint.Comment: 18 pages, 17 figures, 1 table, corresponds to version published in PR

The f0(1370) controversy from dispersive meson-meson scattering data analyses

We establish the existence of the long-debated $f_0(1370)$ resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at $(1245\pm 40)- i\,(300^{+30}_{-70})$ MeV in $\pi\pi$ scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at $(1380^{+70}_{-60})-i\,(220^{+80}_{-70})$ MeV also appears in the $\pi\pi\to K\bar K$ data analysis with partial-wave dispersion relations. Despite settling its existence, our model-independent dispersive and analytic methods still show a lingering tension between pole parameters from the $\pi\pi$ and $K\bar K$ channels that should be attributed to data.Comment: 14 pages, 7 figure

Prospects For ** → Via Lattice QCD

The ** → scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where 3 states can go on shell, and is exact up to exponentially small corrections that scale like (e−mL), where L is the spatial extent of the cubic volume and m is the pion mass. In order to implement this formalism and remove all power-law finite volume errors, it is necessary to first obtain →, ⋆→, ⋆→, and ⋆→ amplitudes; all of which can be determined via lattice quantum chromodynamic calculations

Strange resonance poles from K π scattering below 1.8 GeV

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 ĸ- meson, nowadays known as K(_1)(*) (800), the scalar K(_1)(*) (1430), the K*(892) and K(_1)(*) (1410) vectors, the spin-two K(_1)(*) (1430) as well as the spin-three K(_1)(*) (1780). The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the Kπ 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 Pade approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances sigma/f(0)(500) and kappa/K*(0)(700)

For several decades, the sigma/f(0)(500) and kappa/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 sigma/f(0)(500) and kappa/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