On the Spectrum of Lattice Massive SU(2) Yang–Mills

Abstract

On the basis of extended simulations, we provide some results concerning the spectrum of Massive SU(2) Yang–Mills on the lattice. We study the “time” correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin I = 0,1 and internal spin J = 0,1 channels. No correlation is found in the I = 1, J = 0 channel. In the I = 1, J = 1 channel and far from the critical mass value m[subscript c], the energy gap roughly follows the bare value m (vector mesons). In approaching the critical value m[subscript c] at β fixed, there is a bifurcation of the energy gap: one branch follows the value m, while the new is much larger and it shows a more and more dominant weight. This phenomenon might be the sign of two important features: the long range correlation near the fixed point at β →∞ implied by the low energy gap and the screening (or confining) mechanisms across the m = m[subscript c] associated to the larger gap. The I = 0, J = 0,1 gaps are of the same order of magnitude, typically larger than the I = 1, J = 1 gap (for m ≫ m[subscript c]). For m ∼ m[subscript c], both I = 0 gaps have a dramatic drop with minima near the value m. This behavior might correspond to the formation of I = 0 bound states both in the J = 0 and J = 1 channels.