Erratum: f_{0}(1370) Controversy from Dispersive Meson-Meson Scattering Data Analyses [Phys. Rev. Lett. 130, 051902 (2023)].

This corrects the article DOI: 10.1103/PhysRevLett.130.051902.

Dispersive ππ→KK[over ¯] Amplitude and Giant CP Violation in B to Three Light-Meson Decays at LHCb.

The LHCb collaboration has recently reported the largest CP violation effect from a single amplitude, as well as other giant CP asymmetries in several B-meson decays into three charmless light mesons. It is also claimed that this is predominantly due to ππ→KK[over ¯] rescattering in the final state, particularly in the 1 to 1.5 GeV region. In these analyses the ππ→KK[over ¯] amplitude is by default estimated from the ππ elastic scattering amplitude and does not describe the existing ππ→KK[over ¯] scattering data. Here we show how the recent model-independent dispersive analysis of ππ→KK[over ¯] data can be easily implemented in the LHCb formalism. This leads to a more accurate description of the asymmetry, while being consistent with the measured scattering amplitude and confirming the prominent role of hadronic final state interactions, paving the way for more elaborated analyses.

f_{0}(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±40)-i(300_{-70}^{+30}) MeV in ππ 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_{-60}^{+70})-i(220_{-70}^{+80}) MeV also appears in the ππ→KK[over ¯] 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 ππ and KK[over ¯] channels that should be attributed to data.

Determination of the Lightest Strange Resonance K_{0}

In this work we present a precise and model-independent dispersive determination from data of the existence and parameters of the lightest strange resonance κ/K_{0}^{*}(700). We use both subtracted and unsubtracted partial-wave hyperbolic and fixed-t dispersion relations as constraints on combined fits to πK→πK and ππ→KK[over ¯] data. We then use the hyperbolic equations for the analytic continuation of the isospin I=1/2 scalar partial wave to the complex plane, in order to determine the κ/K_{0}^{*}(700) and K^{*}(892) associated pole parameters and residues.

Global parameterization of π π scattering up to 2 GeV.

We provide global parameterizations of π π → π π scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of π π → π π , both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 GeV . Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the σ / f 0 ( 500 ) , f 0 ( 980 ) and ρ ( 770 ) pole parameters.

Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis.

We use our latest dispersive analysis of ππ scattering data and the very recent K(ℓ4) experimental results to obtain the mass, width, and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model-independent way by means of once- and twice-subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the f(0)(600) pole at (457(-13))+14))-i(279(-7)(+11)) MeV and that of the f(0)(980) at (996 ± 7)-i(25(-6)(+10)) MeV, whereas their respective couplings to two pions are 3.59(-0.13)(+0.11) and 2.3 ± 0.2 GeV.

Quark-mass dependence of the rho and sigma mesons from dispersion relations and chiral perturbation theory.

We use the one-loop chiral perturbation theory pipi-scattering amplitude and dispersion theory in the form of the inverse amplitude method to study the quark-mass dependence of the two lightest resonances of the strong interactions, the f(0)(600) (sigma) and the rho meson. As the main results, we find that the rhopipi coupling constant is almost quark mass independent and that the rho mass shows a smooth quark-mass dependence while that of the sigma shows a strong nonanalyticity. These findings are important for studies of the meson spectrum on the lattice.

Nature of the f0(600) scalar meson from its Nc dependence at two loops in unitarized chiral perturbation theory.

By using unitarized two-loop chiral perturbation theory partial waves to describe pion-pion scattering we find that the dominant component of the lightest scalar meson does not follow the qq dependence on the number of colors that, in contrast, is obeyed by the lightest vectors. The method suggests that a subdominant qq component of the f0(600) possibly originates around 1 GeV.

Nature of light scalar mesons from their large-Nc behavior.

We show how to obtain information about the states of an effective field theory in terms of the underlying fundamental theory. In particular, we analyze the spectroscopic nature of meson resonances from the meson-meson scattering amplitudes of the QCD low energy effective theory, combined with the expansion in the large number of colors. The vectors follow a qq behavior, whereas the sigma, kappa, and f0(980) scalars disappear for large Nc, in support of a q q qq-like nature. The a0 shows a similar pattern, but the uncertainties are large enough to accommodate both interpretations.

Towards a neural network based therapy for hallucinatory disorders.

Pattern completion in a neural network model of the thalamus and a biologically plausible model of synaptic plasticity are the key concepts used in this paper for analyzing some cognitive disorders that involve hallucinations of several kinds: visual hallucinations in the Charles Bonnet syndrome and psychedelic drugs consumption, somatic hallucination in phantom limbs, cognitive hallucinations in schizophrenia and even in multiple personality disorders. All these types of hallucinations are proposed to be the result of a pattern completion dynamics performed in thalamic deafferented areas. Effective treatments of some of these disorders involve peripheral stimulation jointly with a central inhibition so that the neural circuits generating the disorders are depressed according to the proposed model of synaptic plasticity.