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Determination of Fπ from Individual Dirac Operator Eigenvalues

Presenter: Gernot Akemann — Brunel University West London

G. Akemann, P.H. Damgaard

In the є-regime of lattice QCD one can get an accurate measurement of the pion decay constant Fπ by monitoring how just one single Dirac operator eigenvalue splits into two when subjected to two different external vector sources. Based on the relevant Random Two-Matrix Theory we derive the analytical expression to leading order in the finite-volume є-expansion. As a simple byproduct we also show how the associated individual Dirac eigenvalue distributions and their correlations can be computed directly from the effective chiral Lagrangian.