The analysis of space-time structure in QCD vacuum II: Dynamics of polarization and absolute X-distribution

Andrei Alexandru, Terrence Draper, Ivan Horváth, Thomas Streuer

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We propose a framework for quantitative evaluation of dynamical tendency for polarization in an arbitrary random variable that can be decomposed into a pair of orthogonal subspaces. The method uses measures based on comparisons of given dynamics to its counterpart with statistically independent components. The formalism of previously considered X-distributions is used to express the aforementioned comparisons, in effect putting the former approach on solid footing. Our analysis leads to the definition of a suitable correlation coefficient with clear statistical meaning. We apply the method to the dynamics induced by pure-glue lattice QCD in local left-right components of overlap Dirac eigenmodes. It is found that, in finite physical volume, there exists a non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at smaller (fixed) eigenvalues exhibit convex X-distribution (positive correlation), while at larger eigenvalues the distribution is concave (negative correlation). This chiral polarization scale thus separates a regime where dynamics enhances chirality relative to statistical independence from a regime where it suppresses it, and gives an objective definition to the notion of " low" and " high" Dirac eigenmode. We propose to investigate whether the polarization scale remains non-zero in the infinite volume limit, in which case it would represent a new kind of low energy scale in QCD.

Original languageEnglish
Pages (from-to)1941-1971
Number of pages31
JournalAnnals of Physics
Issue number8
StatePublished - Aug 2011


  • High energy physics
  • Lattice gauge theory
  • QCD vacuum structure
  • Quantum chromodynamics

ASJC Scopus subject areas

  • General Physics and Astronomy


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