The Inverse Amplitude Method in ππ\pi\pi Scattering in Chiral Perturbation Theory to Two Loops

The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6}$ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.Comment: (Latex, epsfig) 30 pages, 13 figures, 8 table

Rough Sets: a Bibliometric Analysis from 2014 to 2018

Along almost forty years, considerable research has been undertaken on rough set theory to deal with vague information. Rough sets have proven to be extremely helpful for a diversity of computer-science problems (e.g., knowledge discovery, computational logic, machine learning, etc.), and numerous application domains (e.g., business economics, telecommunications, neurosciences, etc.). Accordingly, the literature on rough sets has grown without ceasing, and nowadays it is immense. This paper provides a comprehensive overview of the research published for the last five years. To do so, it analyzes 4,038 records retrieved from the Clarivate Web of Science database, identifying (i) the most prolific authors and their collaboration networks, (ii) the countries and organizations that are leading research on rough sets, (iii) the journals that are publishing most papers, (iv) the topics that are being most researched, and (v) the principal application domains

πK\pi K Scattering in Three Flavour ChPT

We present the scattering lengths for the $\pi K$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include analytical results for the dependence on the low-energy constants (LECs) at NNLO due to the size of the expressions. These results, together with resonance estimates of the NNLO LECs are used to obtain constraints on the Zweig rule suppressed LECs at NLO, $L_4^r$ and $L_6^r$. Contrary to expectations from NLO order calculations we find them to be compatible with zero. We do a preliminary study of combining the results from $\pi\pi$ scattering, $\pi K$ scattering and the scalar form-factors and find only a marginal compatibility with all experimental/dispersive input data.Comment: 23 page

Scalar meson dynamics in Chiral Perturbation Theory

A comparison of the linear sigma model (L$\sigma$M) and Chiral Perturbation Theory (ChPT) predictions for pion and kaon dynamics is presented. Lowest and next-to-leading order terms in the ChPT amplitudes are reproduced if one restricts to scalar resonance exchange. Some low energy constants of the order $p^4$ ChPT Lagrangian are fixed in terms of scalar meson masses. Present values of these low energy constants are compatible with the L$\sigma$M dynamics. We conclude that more accurate values would be most useful either to falsify the L$\sigma$M or to show its capability to shed some light on the controversial scalar physics.Comment: 9 pages, REVTeX 4.0. Final version accepted for publicatio

Meson resonances, large N_c and chiral symmetry

We investigate the implications of large N_c and chiral symmetry for the mass spectra of meson resonances. Unlike for most other mesons, the mass matrix of the light scalars deviates strongly from its large-N_c limit. We discuss the possible assignments for the lightest scalar nonet that survives in the large-N_c limit.Comment: 14 page

Splitting Strong and Electromagnetic Interactions in K(L4) Decays

We recently considered $K_{\ell 4}$ decays in the framework of chiral perturbation theory based on the effective Lagrangian including mesons, photons, and leptons. There, we published analytic one-loop-level expressions for form factors $f$ and $g$ corresponding to the mixed process, $K^0\to\pi^0\pi^-\ell^+\nu_{\ell}$. We propose here a possible splitting between strong and electromagnetic parts allowing analytic (and numerical) evaluation of Isospin breaking corrections. The latter are sensitive to the infrared divergence subtraction scheme and are sizeable near the $\pi\pi$ production threshold. Our results should be used for the extraction of the $P$-wave iso-vector $\pi\pi$ phase shift from the outgoing data of the currently running KTeV experiment at FNAL.Comment: 47 pages, LaTeX, 6 postscript figure

Pion mass dependence of the Kl3K_{l3} semileptonic scalar form factor within finite volume

We calculate the scalar semileptonic kaon decay in finite volume at the momentum transfer $t_{m} = (m_{K} - m_{\pi})^2$, using chiral perturbation theory. At first we obtain the hadronic matrix element to be calculated in finite volume. We then evaluate the finite size effects for two volumes with $L = 1.83 fm$ and $L= 2.73 fm$ and find that the difference between the finite volume corrections of the two volumes are larger than the difference as quoted in \cite{Boyle2007a}. It appears then that the pion masses used for the scalar form factor in ChPT are large which result in large finite volume corrections. If appropriate values for pion mass are used, we believe that the finite size effects estimated in this paper can be useful for Lattice data to extrapolate at large lattice size.Comment: 19 pages, 5 figures, accepted for publication in EPJ

Chiral Extrapolation of the Strangeness Changing K pi Form Factor

We perform a chiral extrapolation of lattice data on the scalar K pi form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.Comment: few minor change