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In the epsilon-regime of lattice QCD one can get an accurate measurement ofthe pion decay constant F_pi by monitoring how just one single Dirac operatoreigenvalue splits into two when subjected to two different external vectorsources. Because we choose imaginary chemical potentials our Dirac eigenvaluesremain real. Based on the relevant chiral Random Two-Matrix Theory we deriveindividual eigenvalue distributions in terms of density correlations functionsto leading order in the finite-volume epsilon-expansion. As a simple byproductwe also show how the associated individual Dirac eigenvalue distributions andtheir correlations can be computed directly from the effective chiralLagrangian.

Determination of F_pi from Distributions of Dirac Operator Eigenvalues with Imaginary Density