Chiral condensate and Dirac spectrum of one-and two-flavor QCD at nonzero θ-angle
Department of Physics, University of Bielefeld, 33501 Bielefeld, Germany
2 Department of Physics and Astronomy, Stony Brook University, New York 11794, USA
3 Department of Physics, University of Regensburg, 93040 Regensburg, Germany
* Speaker, e-mail: email@example.com
Published online: 26 March 2018
In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a similar Silver Blaze phenomenon takes places for QCD with one flavor and arbitrary θ- angle, and for QCD with two flavors with different quark masses m1 and m2. In the latter case the chiral condensate remains constant when m1 crosses zero at fixed m2 > 0 until the Dashen point m1 = –m2 is reached, where the chiral condensate has a discontinuity. In terms of contributions from the Dirac spectrum the shift of the discontinuity from m1 = 0 to m1 = -m2 also arises from exponentially large cancellations between the zero and nonzero modes when m1m2 < 0. All calculations are performed in the microscopic or ε-domain of QCD. Results for arbitrary θ-angle are discussed as well.
© The Authors, published by EDP Sciences, 2018
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