The kth smallest Dirac operator eigenvalue and the pion decay constant
Abstract
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 ν. Because of its dependence on the pion decay constant F_{π} through the chemical potential in the epsilon regime of chiral perturbation theory, this can be used for lattice determinations of that lowenergy constant. On the technical side, we use a chiral randomtwo 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 March 2012
 DOI:
 10.1088/17518113/45/11/115205
 arXiv:
 arXiv:1110.6774
 Bibcode:
 2012JPhA...45k5205A
 Keywords:

 High Energy Physics  Lattice
 EPrint:
 27 pages, 5 figures