Heavy-light quarks interactions in QCD vacuum

TL;DR

This paper investigates how QCD vacuum instantons induce strong interactions between light and heavy quarks, leading to dynamical mass generation and effective interactions relevant for heavy-light meson systems.

Contribution

It derives a fermionized representation of the light quark determinant in the presence of heavy quarks and calculates the heavy-light quark interaction terms within the instanton model.

Findings

Dynamical light quark mass M = 570 MeV

Instanton contribution to heavy quark mass ΔM = 148 MeV

Derived heavy-light quark interaction terms

Abstract

QCD vacuum instantons induce very strong interactions between light quarks, which generate large dynamical light quark mass M for initially almost massless quarks and can bound these quarks to produce almost massless pions in accordance with the spontaneous breaking of chiral symmetry (S\chiSB). On the other hand, the QCD vacuum instantons generate heavy-light quark interactions terms, which are responsible for the effects of S\chiSB in a heavy-light quark system. Summing the re-scattering series that lead to the total light quark propagator and making few further steps, we get the fermionized representation of low-frequencies light quark determinant in the presence of the quark sources, which is relevant for our problems. The next important step in the line of this strategy is to derive the equation and calculate the heavy quark propagator in the instanton media and in the presence of light quarks. This one provide finally the heavy and N_f light quarks interaction term. As an example, we derive heavy quark-light mesons interaction term for the N_f=2 case. If we take the average instanton size \rho=0.35 fm, and average inter-instanton distance R=0.856 fm from our previous estimates, we obtain at LO on 1/N_c expansion dynamical light quark mass M = 570 MeV and instanton media contribution to heavy quark mass \Delta M=148 MeV. These factors define the coupling between heavy and light quarks and, certainly, between heavy quarks and light mesons. We will apply this approach to heavy quark and heavy-light quark systems.