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Chiral condensate and Dirac spectrum of one-and two-flavor QCD at nonzero θ-angle

机译:非零θ角的一味和两味QCD的手性缩合物和狄拉克谱

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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 m _(1)and m _(2). In the latter case the chiral condensate remains constant when m1 crosses zero at fixed m _(2)> 0 until the Dashen point m _(1)= – m _(2)is reached, where the chiral condensate has a discontinuity. In terms of contributions from the Dirac spectrum the shift of the discontinuity from m _(1)= 0 to m _(1)= - m _(2)also arises from exponentially large cancellations between the zero and nonzero modes when m _(1) m _(2)< 0. All calculations are performed in the microscopic or ε-domain of QCD. Results for arbitrary θ-angle are discussed as well.
机译:在先前的工作中,我们表明当夸克质量超过m = 0时,单味QCD的手性冷凝物表现出Silver Blaze现象:手性冷凝物保持恒定,而夸克质量超过Dirac算子的光谱,在Dirac算子上密度很高。虚轴。当夸克质量为负时,可以用零模和非零模的贡献之间的指数大抵消来解释此行为。在这些过程中,我们表明,对于具有一种风味和任意θ-角的QCD,以及对于具有两种夸克质量m _(1)和m _(2)的两种风味的QCD,也会发生类似的Silver Blaze现象。在后一种情况下,当m1在固定m _(2)> 0处越过零时,手性冷凝物保持恒定,直到达到大神点m _(1)= – m _(2)为止,其中手性冷凝物不连续。根据狄拉克谱的贡献,不连续性从m _(1)= 0到m _(1)=-m _(2)的移动也源自于零模式和非零模式之间在m _( 1)m _(2)<0。所有计算都在QCD的微观或ε域内进行。还讨论了任意θ角的结果。

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