Related papers: Precise determination of the sigma pole location f…
Studies on the IJ=00 $\pi\pi$ and $K\bar K$ coupled--channel system are made using newly derived dispersion relations between the phase shifts and poles and cuts. It is found that the $\sigma$ resonance must be introduced to explain the…
Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real…
We review the use of new and precise dispersive equations, which also implement crossing symmetry, in order to shed further light on the long-standing puzzle in the parameters of the f0(500), as well as the f0(980). This puzzle is finally…
We complete and improve the fits to experimental $\pi\pi$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity…
The naive use of higher order perturbation theory leads the left--hand cut integrals in $\pi\pi$ dispersion relations~\cite{hjy,Xiao01} divergent. This problem is discussed and solved. Also we point out that the Adler zero condition imposes…
The $\sigma$ resonance was observed as a conspicuous $\pi^+\pi^-$ peak in hadronic decays like $J/\psi\to \pi^+\pi^-\omega$ or $D^+\to\pi^+\pi^-\pi^+$. The phase of the $\sigma\to\pi^+\pi^-$ amplitude, extracted from production data within…
We report here our results on how to obtain the Regge trajectory of a resonance from its pole in a scattering process by imposing analytic constraints in the complex angular momentum plane. The method, suited for resonances that dominate an…
We present a data-driven analysis of the resonant S-wave $\pi\pi \to \pi\pi$ and $\pi K \to \pi K$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
We improve previous results on dispersive decay for 1D Klein- Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken the assumption on the potential.
Magnetic guiding fields in combination with energy dispersive semiconductor detectors have been employed already more than 50 years ago for in-beam internal conversion electron spectroscopy. Even then it was recognized that efficiency…
We give some estimates for the light-quark mass dependence of the pole position of the sigma ($f_{0}(500)$) resonance in the complex energy plane, with the help of a chiral Lagrangian for the resonance field and some input from hadronic…
In this talk I briefly review the recent developments on light scalar meson spectroscopy, paying particular attention to the causes of major revision of the $\sigma$ or $f_0(500)$ meson in the Review of Particle Phsycis. This resonance,…
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…
Using dispersion theory with an improved description of the two-pion continuum based on the precise Roy-Steiner analysis of pion-nucleon scattering, we analyze recent data from electron-proton scattering. This allows for a high-precision…
Exact calculations of the radiative corrections to the single spin asymmetry in the exclusive pion electroproduction below $\Delta(1232)$ resonance are performed by employing the EXCLURAD code. The analysis of the dependence of the obtained…
In this paper the solutions of the zero-sound dispersion equation in the random phase approximation (RPA) are considered. The calculation of the damped zero-sound modes \omega_s(k) (complex frequency of excitation) in the nuclear matter is…
Scalar mesons are a key expression of the infrared regime of QCD. The lightest of these is the $\sigma$. Now that its pole in the complex energy plane has been precisely located, we can ask whether this state is transiently ${\bar q}q$ or…
An extended Roy equation including a bound state pole is used to study $\pi\pi$ scatterings at unphysical large pion masses when $\sigma$ becomes a bound state in one situation and stays as a broad resonance in the other case. The coupled…
We review results of an analysis of pipi interactions in S, P and D waves for two-pion effective mass from threshold to about 1.4 GeV. In particular we show a recent improvement of this analysis above the K anti-K threshold using more data…