Narrow Results

In this paper, we describe our studies of the sigma meson, $f_0(500)$, using two-pion correlation functions. We use lattice quantum chromodynamics in the quenched approximation with so-called clover fermions. By working at unphysical pion masses we are able to identify a would-be resonance with mass less than $2m_{\pi }$, and then extrapolate to the physical point. We include the most important annihilation diagram, which is “partially disconnected” or “single annihilation”. Because this diagram is quite expensive to compute, we introduce a somewhat novel technique for the computation of all-to-all diagrams, based on momentum sources and a truncation in momentum space. In practice, we use only $p=0$ modes, so the method reduces to wall sources. At the point where the mass of the pion takes its physical value, we find a resonance in the $0^{++}$ two-pion channel with a mass of approximately $609\pm 80$ MeV, consistent with the expected properties of the sigma meson, given the approximations we are making.

The results of an extensive campaign of measurements of the π→ππ process in the nucleon and nuclei at intermediate energies are presented. Several differential cross-sections were measured following the detection of multiparticle (π⁺,π⁺π^±) and (π⁺,π⁺π^-p) events, which allowed to understand the general properties of the pion production reaction inside the nucleus. Particular attention was devoted to the study of the effects of nuclear matter on the π-π scalar-isoscalar system. The most relevant results are reviewed and compared to theories as well as to other recent experimental results.

Flavor symmetric sea quarks could contribute to the ratio of in the proton, as well as flavor asymmetric sea quarks. We clarify the isoscalar mesonic contribution, especially σ meson cloud effects in the meson cloud model. We also provide the meson numbers in the proton with different meson cutoff values. Our calculations show that a physical proton picture favors smaller cutoff of the examined range 1.0<Λ_ω<1.5GeV.

The main experimental works, where dipole polarizabilities of charged pions have been determined, are considered. Possible reasons for the differences between the experimental data are discussed. In particular, it is shown that the account of the $\sigma$-meson gives a significant correction to the value of the polarizability obtained in the latest experiment of the COMPASS collaboration. We present also new fit results for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ reaction.

The dipole and quadrupole polarizabilities of the charged pion have been found from the analyses of γγ → π⁺π⁻ reaction using dispersion relations with subtractions.