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Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate

Reinhard Alkofer
Sep 2023
Dynamical Chiral Symmetry Breaking (DCSB) in Quantum Chromo Dynamics (QCD) for the light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In Functional Approaches to QCD the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in QCD's terms. It not only highlights one of the most important aspects of DCSB, the dynamical generation of constituent quark masses, but also makes plausible that DCSB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher $n$-point functions are taken into account. In particular, the quark-gluon vertex, i.e., the most elementary $n$-point function describing the full, non-perturbative quark-gluon interaction, plays a dichotomous role: It is subject to DCSB as signalled by its scalar and tensor components but it is also a driver of DCSB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, DCSB in QCD is located close to the critical point and is thus a delicate effect. And, requiring a precise determination of QCD's three-point functions, DCSB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon-gluon and the quark-gluon interactions.
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