QCD vacuum: nuclear forces, nucleons, pions [ellipsis (horizontal)

Abstract

This contribution contains six sections, namely:1. from QCD to chiral perturbation theory ‐ QCD is widely accepted as the theory of strong interactions, but direct applications to low‐energy hadronic processes are difficult. In this regime, the light quarks u and d prevail, and one can employ a rigorously equivalent effective theory, known a chiral perturbation theory, based on hadronic degrees of freedom.2. strong vacuum and the pion ‐ Chiral symmetry is not exact in the real world. Nevertheless, the absence of of parity multiplets and the smallness of the pion mass suggest that it is a good approximate symmetry, realized in the Nambu‐Goldstone mode. Its ground state, the vacuum, is filled with a condensate, made of quark‐antiquark pairs. In sections 1–3, instances are presented of observables strongly influenced by the QCD vacuum.3. nuclear forces ‐ In the last few years, chiral perturbation theory has produced a very reliable picture of both two‐ and three‐nucleon forces. In particular, the important isospin independent central potential VC+ is well understood and known to be dominated by the scalar form factor of the nucleon, a function that describes the disturbance it produces over the vacuum.4. nucleon scalar form factor ‐ The spatial integration of the nucleon scalar form factor gives rise to σN, the nucleon σ‐term. The value of this quantity can be extracted from experiment and the empirical value accepted presently is 45±8 MeV. A simple model, based on the idea that the pion cloud of the nucleon is constructed at the expenses of the surrounding condensate, produces a σN in the range 43–49 MeV, with no free parameters.5. scalar radius of the pion ‐ The value of this radius can be extracted from pion‐pion scattering data and the most reliable estimate is 〈r2〉Sπ = 0.61±0.04 fm2. The extension of the model described in section 4 to the pion gives rise to a picture in which it is embedded into the condensate. As one moves towards its center, the condensate is gradually replaced by a mesonic cloud. When this process is completed, a phase transition occurs, at a distance R≃0.6 fm. A version of the model, including scalar resonances, yields 〈r2〉Sπ = 0.59 fm2.6. conclusion ‐ The QCD vacuum is an active component of low‐energy hadronic processes, essential to a consistent description of Nuclear Physics.