Quantifying zigzag motion of quarks

TL;DR

This paper models quark motion as zigzag trajectories influenced by string tension, linking geometric properties to phase transition behavior in SU(3) Yang-Mills theory.

Contribution

It introduces a novel gluon-chain model based on branched polymer-like quark trajectories with decreasing string tension over proper time.

Findings

Constituent quark mass bounded below at 460 MeV

Trajectories exhibit Hausdorff dimension of 4

Model suggests a weak first-order deconfinement transition

Abstract

The quark condensate is calculated in terms of the effective string tension and the constituent quark mass. For 3 colors and 2 light flavors, the constituent mass is bounded from below by the value of 460 MeV. This value is only accessible when the string tension decreases linearly with the Schwinger proper time. For this reason, the Hausdorff dimension of a light-quark trajectory is equal to 4, indicating that these trajectories are similar to branched polymers, which can describe a weak first-order deconfinement phase transition in SU(3) Yang-Mills theory. Using this indication, we develop a gluon-chain model based on such trajectories.