The k-th smallest Dirac operator eigenvalue and the pion decay constant

Akemann G, Ipsen AC (2012)
Journal of Physics A Mathematical and Theoretical 45(11): 115205.

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We derive an analytical expression for the distribution of the kth smallest Dirac eigenvalue in QCD with an imaginary isospin chemical potential in the Dirac operator for arbitrary gauge field topology.. Because of its dependence on the pion decay constant F-pi 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 kth 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 generalizations of Dyson's integration theorem and Sonine's identity.
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Akemann G, Ipsen AC. The k-th smallest Dirac operator eigenvalue and the pion decay constant. Journal of Physics A Mathematical and Theoretical. 2012;45(11):115205.
Akemann, G., & Ipsen, A. C. (2012). The k-th smallest Dirac operator eigenvalue and the pion decay constant. Journal of Physics A Mathematical and Theoretical, 45(11), 115205. doi:10.1088/1751-8113/45/11/115205
Akemann, G., and Ipsen, A. C. (2012). The k-th smallest Dirac operator eigenvalue and the pion decay constant. Journal of Physics A Mathematical and Theoretical 45, 115205.
Akemann, G., & Ipsen, A.C., 2012. The k-th smallest Dirac operator eigenvalue and the pion decay constant. Journal of Physics A Mathematical and Theoretical, 45(11), p 115205.
G. Akemann and A.C. Ipsen, “The k-th smallest Dirac operator eigenvalue and the pion decay constant”, Journal of Physics A Mathematical and Theoretical, vol. 45, 2012, pp. 115205.
Akemann, G., Ipsen, A.C.: The k-th smallest Dirac operator eigenvalue and the pion decay constant. Journal of Physics A Mathematical and Theoretical. 45, 115205 (2012).
Akemann, Gernot, and Ipsen, A. C. “The k-th smallest Dirac operator eigenvalue and the pion decay constant”. Journal of Physics A Mathematical and Theoretical 45.11 (2012): 115205.
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