Glueball spectrum and hadronic processes in low-energy QCD

Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the $\sigma$ and $\eta -{\eta }^{\mathrm{\prime }}$ mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant $\mathrm{\Lambda }$ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.