Derivation of the effective chiral Lagrangian for pseudoscalar mesons from QCD

Abstract

We formally derive the chiral Lagrangian for low lying pseudoscalar mesons from the first principles of QCD considering the contributions from the normal part of the theory without taking approximation.The derivation is based on the standard generating functional of QCD in the path integral formalism.The gluon-field integration is formally carried out by expressing the result in terms of physical Green's functions of the gluon. To integrate over the quark-field, we introduce a bilocal auxiliary field Φ(x, y) representing the mesons. We then develop a consistent way of extracting the local pseudoscalar degree of freedom U (x) in Φ(x, y) and integrating out the rest degrees of freedom such that the complete pseudoscalar degree of freedom resides in U (x). With certain techniques, we work out the explicit

Calculation of the chiral Lagrangian coefficients from the underlying theory of QCD: A simple approach

“…As has been pointed out in Ref. [3] this term is exactly cancelled by a corresponding term in the normal part contribution [cf. Eq.…”

“…In Ref. [3], all the chiral Lagrangian coefficients contributed from the normal part of the theory are expressed in terms of certain Green's functions in QCD, which can be regarded as exact QCD definitions of the chiral Lagrangian coefficients. After expanding the effective action in powers of the rotated sources (momentum expansion), the effective action , up to O(p 4 ), contributed from the normal part is of the form [3] S (norm) eff …”

“…It has been shown in Ref. [3] that in the approximations of large-N c limit, leading order in dynamical perturbation, and improved ladder approximation, the formula for F 2 0 in Eqs. (2) reduces to the well-known Pagels-Stokar formula [6] in which all dynamical effects from QCD are represented by the quark self-energy Σ(p 2 ) in the formula.…”

Low-energy chiral Lagrangian from the spectral quark model

“…In the quest to understand the microscopic dynamics underlying the LEC's, their calculation in chiral quark models has been undertaken many times [17,18,19,20,21,22,23,24,25,26,27,28,29,30]. The effort has been made to compute L 1 , .…”

Derivation of the gap and Bethe-Salpeter equations at large Nc limit and symmetry preserving truncations

“…In the present paper, we shall employ a bilocal action which was first introduced in Ref. [3] and was used to study chiral perturbation theory therein. With this action, various problems can be addressed.…”