Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2010-09-22
Annals Phys.326:1941-1971,2011
Physics
High Energy Physics
High Energy Physics - Lattice
v2: 38 pages, 12 figures, author-preferred version; v3: journal-preferred version
Scientific paper
10.1016/j.aop.2011.04.007
We propose a framework for quantitative evaluation of dynamical tendency for polarization in 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 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.
Alexandru Andrei
Draper Terrence
Horváth Ivan
Streuer Thomas
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