TY - JOUR

T1 - The analysis of space-time structure in QCD vacuum II

T2 - Dynamics of polarization and absolute X-distribution

AU - Alexandru, Andrei

AU - Draper, Terrence

AU - Horváth, Ivan

AU - Streuer, Thomas

PY - 2011/8

Y1 - 2011/8

N2 - 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.

AB - 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.

KW - High energy physics

KW - Lattice gauge theory

KW - QCD vacuum structure

KW - Quantum chromodynamics

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UR - http://www.scopus.com/inward/citedby.url?scp=79957975487&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2011.04.007

DO - 10.1016/j.aop.2011.04.007

M3 - Article

AN - SCOPUS:79957975487

SN - 0003-4916

VL - 326

SP - 1941

EP - 1971

JO - Annals of Physics

JF - Annals of Physics

IS - 8

ER -