On the non-perturbative gluon mass and heavy quark physics

Abstract We study a recently proposed gauge invariant, non-local pure gauge observable, which is equivalent to the gluon propagator in a certain gauge. The correlator describes a gluon coupled to static sources and decays with eigenvalues of the Hamiltonian, permitting a non-perturbative definition of a gluonic parton mass. Detailed numerical tests of the observable are performed in SU(2) gauge theories in 2+1 dimensions. In a Higgs model it reproduces the physical W-boson mass, while in a confining theory its non-local nature results in almost exclusive projection onto torelonic states. However, the gluon mass can also be related to the mass difference between the lowest gluelumps, i.e., gluon configurations bound to adjoint sources. Its value is computed in SU(2) pure gauge theory in 2+1 dimensions to be m A =0.360(19) g 2 , which plays an important role as “magnetic mass” of the four-dimensional theory at high temperatures. The same quantity is found to determine the mass splitting between vector and scalar mesons in the three-dimensional theory. In SU(3) pure gauge theory in 3+1 dimensions the corresponding gluelump splitting yields m A ≈370 MeV. Possible relations of this quantity with the QCD heavy meson spectrum are discussed.