The origin of quark–hadron duality violations (DVs) can be related to the singularities of the Laplace transform of the spectral function. With the help of rather generic properties of the large-\(N_c\) approximation and a generalized form for the radial trajectories found in Regge Theory, we may locate these singularities in the complex plane and obtain an expression for the DVs which turns out to agree with general expectations. Using the two-point vector correlator as a test laboratory, we show how the usual dispersion relation may give rise to perturbation theory, the power corrections from the condensate expansion and DVs.

中文翻译：

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违反夸克-强子二象性

夸克-强子对偶性违反 (DV) 的起源可能与谱函数的拉普拉斯变换的奇点有关。借助大\(N_c\)近似的相当通用的性质和雷格理论中径向轨迹的广义形式，我们可以在复平面中定位这些奇点并获得 DV 的表达式，结果为同意普遍预期。使用两点矢量相关器作为测试实验室，我们展示了通常的色散关系如何产生扰动理论、来自冷凝膨胀和 DV 的功率校正。