2014/07/31 by J. J. M. Verbaarschot, Tilo Wettig, T. Wettig · 1 citation
Physics and Astronomy · #Bessel function #Black Holes and Theoretical Physics #Dirac operator #Mass spectrometry #Mass spectrum #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Quark #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.90.116004
published as Phys. Rev. D 90, 116004 (2014) · 12 pages, 6 figures
arxiv created 2014/07/31 · openalex publication_date 2014/12/17 · arxiv updated 2014/12/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We derive exact analytical expressions for the spectral density of the Dirac operator at fixed \ensuremathθ-angle in the microscopic domain of one-flavor QCD. These results are obtained by performing the sum over topological sectors using novel identities involving sums of products of Bessel functions. Because the fermion determinant is not positive definite for negative quark mass, the usual Banks-Casher relation is not valid and has to be replaced by a different mechanism first observed for QCD at nonzero chemical potential. Using the exact results for the spectral density we explain how this mechanism results in a chiral condensate that remains constant when the quark mass changes sign.