The kth smallest Dirac operator eigenvalue and the pion decay constant

TY - JOUR

T1 - The kth smallest Dirac operator eigenvalue and the pion decay constant

AU - Akemann, G.

AU - Ipsen, Asger Cronberg

PY - 2012/3/23

Y1 - 2012/3/23

N2 - 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 v. 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 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 Dysons integration theorem and Sonines identity.

AB - 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 v. 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 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 Dysons integration theorem and Sonines identity.

U2 - 10.1088/1751-8113/45/11/115205

DO - 10.1088/1751-8113/45/11/115205

M3 - Journal article

SN - 1751-8113

VL - 45

SP - 115205

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 11

ER -