Existence of mesons and mass splitting in strong coupling lattice quantum chromodynamics.

Abstract

We consider one flavor lattice quantum chromodynamics in the imaginary time functional integral formulation for space dimensions d52, 3 with 434 Dirac spin matrices, small hopping parameter k, 0,k!1, and zero plaquette coupling. We determine the energy-momentum spectrum associated with four-component gauge invariant local meson fields which are composites of a quark and an antiquark field. For the associated correlation functions, we establish a Feynman–Kac formula and a spectral representation. Using this representation, we show that the mass spectrum consists of two distinct masses ma and mb , given by mc 522 lnk1rc(k), c5a,b, where rc is real analytic. For d52, ma and mb have multiplicity two and the mass splitting is k 41O(k 6); for d53, one mass has multiplicity one and the other three, with mass splitting 2k 41O(k 6). In the subspace of the Hilbert space generated by an even number of fermion fields the dispersion curves are isolated ~upper gap property! up to near the two-meson threshold of asymptotic mass 24 lnk.