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arXiv · 1110.6774

The k-th Smallest Dirac Operator Eigenvalue and the Pion Decay Constant

G. Akemann·A. C. Ipsen
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Abstract

We derive an analytical expression for the distribution of the k-th smallest Dirac eigenvalue in QCD with imaginary isospin chemical potential in the Dirac operator. Because of its dependence on the pion decay constant F through the chemical potential in the epsilon-regime of chiral perturbation theory this can be used for lattice determinations of that low-energy constant. On the technical side we use a chiral Random-Two Matrix Theory, where we express the k-th eigenvalue distribution through the joint probability of the ordered k smallest eigenvalues. The latter can be computed exactly for finite and infinite N, for which we derive generalisations of Dyson's integration Theorem and Sonine's identity.

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G. Akemann, A. C. Ipsen. 2012-03-05. The k-th Smallest Dirac Operator Eigenvalue and the Pion Decay Constant. https://doi.org/10.1088/1751-8113%2F45%2F11%2F115205

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