Related papers: Self-consistent statistical error analysis of $\pi…
Nucleon-Nucleon potentials are commonplace in nuclear physics and are determined from a finite number of experimental data with limited precision sampling the scattering process. We study the statistical assumptions implicit in the standard…
Simulation Based Inference (SBI) is shown to yield more accurate resonance parameter estimates than traditional chi-squared minimization in certain cases of model misspecification, demonstrated through a case study of pi-pi scattering and…
The S and P wave $\pi \pi$ phase shifts are recalculated in terms of two phenomenological parameters using the one loop CPTh and the elastic unitarity condition. Using these phase shifts, the vector and scalar form factors are calculated…
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…
We provide new global parametrizations of $\pi\pi \to \pi\pi$ scattering for the S2, P, D, F, and G partial waves up to at least 1.8 GeV, easy to implement for phenomenological use. With earlier S0-wave parametrizations, slightly updated…
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…
Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a…
The master formula approach to chiral symmetry breaking is used to analyze the phase shifts for $\pi\pi$ scattering in the elastic region. The results are in excellent agreement with the data for the phase shifts up to the K-K bar…
We demonstrate that, together with the available experimental information, chiral symmetry determines the low energy behaviour of the $\pi\pi$ scattering amplitude to within very small uncertainties. In particular, the threshold parameters…
We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of…
Analytical solutions of the S-and P-wave subsystem in pi(-)p->pi(-)pi(+)n and pi(+)p->pi(+)pi(-)p measured on polarized targets at CERN reveal evidence for rho^0(770)-f_0(980) spin mixing. We study the response of these analytical solutions…
We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a…
A family of threshold parameters which probe the stability of chiral predictions is considered. The relevant criteria for the choice of threshold parameters are discussed. Sum rules for these quantities are derived from dispersion relations…
A combined analysis of data on isoscalar S-wave processes $\pi\pi\to\pi\pi,K\overline{K},\eta\eta$ and on decays $J/\psi\to\phi\pi\pi,\phi K\overline{K}$ from the DM2, Mark III and BESIII collaborations is performed to study $f_0$ mesons.…
We discuss $\pi\pi$ scattering in the framework of chiral perturbation theory. In particular, we recall the predictions made some time ago for the threshold parameters and for the phase shift difference $\delta_0^0-\delta_1^1$.
We consider the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$, in the chiral limit. At $T=0$ this formulation provides a good description of scattering data in the…
We carry out an analysis of $\pi\pi$ scattering in the $IJ=00$, $11$ and $20$ channels in configuration space up to a maximal center-of-mass energy $\sqrt{s}=1.4$ GeV. We separate the interaction into two regions marked by an elementarity…
This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the…
We study the scattering for the energy-subcritical stochastic nonlinear Schr\"odinger equation (SNLS) with additive noise. In particular, we examine the long-time behavior of solutions associated with the noise…
Residuals in regression models are often spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on…