Failure of the ladder approximation to QCD

TL;DR

This paper demonstrates that the ladder approximation in QCD fails in a gauge-invariant manner, showing it cannot account for quark masses or running couplings, thus questioning its validity across all energy scales.

Contribution

The paper provides a gauge-invariant proof of the failure of the ladder approximation to QCD, highlighting its limitations in describing quark masses and dynamics.

Findings

Ladder approximation requires zero quark masses.

It cannot produce running quark masses or couplings.

All previous results using this approximation should be reconsidered.

Abstract

The proof of the failure of the ladder approximation to QCD is given in manifestly gauge-invariant way. This proof is valid for the full gluon propagator and for all types of quarks. The summation of the ladder diagrams within the Schwinger-Dyson integral equation for the quark-gluon vertex, on account of the corresponding Slavnov-Taylor identity, provides an additional constraint on the quark Schwinger-Dyson equation itself in the ladder approximation. It requires that there is neither running nor current quark masses in the ladder approximation. Thus, all the results based on the nontrivial (analytical or numerical) solutions to the quark Schwinger-Dyson equation in the ladder approximation should be reconsidered, and its use in the whole energy/momentum range should be abandoned.