Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi

Abstract

Dirac operator eigenvalues split into two when subjected to two different external vector sources. In a specific finite-volume scaling regime of gauge theories with fermions, this problem can be mapped to a chiral Random Two-Matrix Theory. We derive analytical expressions to leading order in the associated finite-volume expansion, showing how individual Dirac eigenvalue distributions and their correlations equivalently can be computed directly from the effective chiral Lagrangian in the epsilon-regime. Because of its equivalence to chiral Random Two-Matrix Theory, we use the latter for all explicit computations. On the mathematical side, we define and determine gap probabilities and individual eigenvalue distributions in that theory at finite N, and also derive the relevant scaling limit as N is taken to infinity. In particular, the gap probability for one Dirac eigenvalue is given in terms of a new kernel that depends on the external vector source. This expression may give a new and simple way of determining the pion decay constant F_pi from lattice gauge theory simulations.

24 pages, 6 figures

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• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
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• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Quark condensate in one-flavor QCD
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• Determining F_pi from spectral sum rules

Cited by in corpus (9)

• Probing the chiral regime of Nf=2 QCD with mixed actions
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Finite size scaling of meson propagators with isospin chemical potential
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• The gradient flow of the Dirac spectrum
• Janossy densities for chiral random matrix ensembles and their applications to two-color QCD