Short-range potentials from QCD at orderg²

Abstract

We systematically compute the effective short-range potentials arising from second order QCDdiagrams related to bound states of quarks, antiquarks, and gluons. Our formalism relies on the assumption that the exchanged gluons are massless, while the constituent gluons as well as the lightest quarks acquire a nonvanishing constituent mass because of confinement. We recover the well-known Fermi-Breit interaction in the heavy quark limit. Such an effective potential has been proved in the past to be relevant for the building of accurate potential models describing usual hadrons (mesons and baryons). The general potentials we obtain in this work are also expected to be useful in the understanding of exotic hadrons like glueballs and qqg hybrids. In particular, we compute for the first time an effective short-range quark-gluon potential, and show the existence of a quadrupolar interaction term in this case. We also discuss the influence of a possible nonzero mass for the exchanged gluons.

Glueball phenomenology and the relativistic flux tube model

“…In the quark-antiquark case, one is led to the well-known Fermi-Breit interaction. Other cases such as gluon-gluon and quark-gluon potentials have been investigated for example in [62]. As expected, it appears that, at the dominant order, the short-range potential is always given by a Coulomb term scaled by some color factor depending on the considered color sources; in particular one is led to…”

Gluons in glueballs: Spin or helicity?

“…Their complete expression can be found in Ref. [31], and involves the usual contact (spin-spin), spin-orbit, and tensor interactions. For our purpose, it is sufficient just to list the global structure of all these additional terms.…”

Semirelativistic potential model for three-gluon glueballs

“…Let us note that the Coulomb gauge Hamiltonian is more complicated than ours. For instance, the annihilation diagram for two gluons is taken into account whereas it vanishes in a potential model [52]. It is not surprising that both approaches gives rather the same results since they used the same formalism (a (L, S)-basis).…”