Coupled fermion gap and vertex equations for chiral-symmetry breakdown in QCD

The QCD Adler Function and the Muon g − 2 Anomaly from Renormalons

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon’s anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon’s anomalous magnetic moment and the experimental value obtained by the most recent muon g−2 collaboration. The latter shows that the Adler function’s new representation can also be consistent with recent lattice determinations.

Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the beta function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.