Vacuum polarization corrections to low energy quark effective couplings

Abstract

In this work corrections to low energy punctual effective quark couplings up to the eighth order are calculated by considering vacuum polarization effects with the scalar quark-antiquark condensate. The departing point is a QCD-based NJL model. By separating the quark field into two components, one that condenses and another one for interacting quarks, the former is integrated out with the help of usual auxiliary fields and an effective action in terms for interacting quark fields is found. The scalar auxiliary field reduces to the quark-antiquark condensate in the vacuum and the determinant is expanded in powers of the quark-antiquark bilinears generating chiral invariant effective 2N-quark interactions (N = 2, 3...). The corresponding coupling constants and effective masses are estimated, and the general trend is that for increasing the effective gluon mass the values of the effective coupling constants decrease. All the values are in good agreement with phenomenological fits.

SU(2) low energy quark effective couplings in weak external magnetic field

“…This splitting of the field can be made by means of the bilinearsψΓψ where Γ stands for Dirac, color or flavor operators, such that the resulting determinant corresponds basically to the one loop BFM results. The splitting can be written as [35,36]…”

“…G for massless and massive gluons [35,49,50]. The quark field will be split according to the Background Field Method (BFM) [51,52].…”

“…The one loop background field method for quarks, as employed in Refs. [35][36][37], will be considered in the presence of a constant weak magnetic field.…”

Flavor-dependent U(3) Nambu Jona Lasinio coupling constant

“…Furthermore, the approach considered here provides a natural path to Schwinger-Dyson and Bethe-Salpeter equations for the detailed investigation of hadron structure and interactions [20,21]. The method extends previous works for u-d-s non-degenerate or u-d degenerate quarks [7,22]. In the next section the logics of the calculation is only outlined because it has been shown with details in previous works of the author [7,22,23,24].…”

“…In addition to the explicit chiral and flavor symmetry breakings due to the non-degenerate current quark mass, the couplings to electromagnetic fields also break these symmetries contributing to masses [2,4] and coupling constant [5]. NJL can be obtained from QCD calculations in a variety of ways, for example [6,7,8,9,10,11] being that gluon exchange between quarks is currently believed to be the main fundamental process. Lately, an effective gluon mass was found to be appropriated to parameterize the deep infrared behavior of an gluon propagator and quark-NJL coupling constant has been identified to roughly G ∝ 1/M 2 G .…”