Fermion flavors in quaternion basis and infrared QCD

TL;DR

This paper investigates the infrared behavior of QCD with multiple fermion flavors using quaternion basis lattice simulations, connecting instanton correlations to gauge field parameters and exploring phenomenological implications.

Contribution

It introduces a novel analysis of domain wall fermions in quaternion basis, linking Atiyah-Ward instanton solutions to lattice QCD data and infrared fixed points.

Findings

QCD effective coupling in the infrared is characterized.

Relation between fermion flavors and infrared fixed point is established.

Implications for baryon phenomenology are discussed.

Abstract

I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah-Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point is investigated. Consequence of this lepton flavor assignment to phenomenology of baryons is also discussed.