广义Witten-Veneziano关系支持的$U_A(1)$对称性恢复方案及其解析解
A $U_A(1)$ symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution
摘要：
Witten-Veneziano关系，或者说Shore提出的它的推广，有助于理解和描述η介子和η '介子的复合体。我们提出了一个解析的，封闭形式的解决方案，肖氏方程，给出了结果的η-η '复杂的完全符合先前获得的数值结果。虽然Witten-Veneziano关系和Shore方程是相关的，但它们以前在动力学模型中用于计算eta和eta '属性的方法是相当不同的。然而，通过解析解，计算可以类似于通过Witten-Veneziano关系的方法进行公式化，并且具有一些概念上的改进。在这个过程中，我们加强了支持U_A（1）和SU_A（3）手征对称性破缺和恢复之间可能存在联系的论点。为了验证这种情况，RHIC、NICA和FAIR等实验将RHIC（和LHC）的高温扫描扩展到QCD相图的有限密度部分，应该特别注意来自eta '-eta复合体的信号，表明对称性恢复。
英文摘要：
The Witten-Veneziano relation, or, alternatively, its generalization proposed by Shore, facilitates understanding and describing the complex of eta and eta' mesons. We present an analytic, closed-form solution to Shore's equations which gives results on the eta-eta' complex in full agreement with results previously obtained numerically. Although the Witten-Veneziano relation and Shore's equations are related, the ways they were previously used in the context of dynamical models to calculate eta and eta' properties, were rather different. However, with the analytic solution, the calculation can be formulated similarly to the approach through the Witten-Veneziano relation, and with some conceptual improvements. In the process, one strengthens the arguments in favor of a possible relation between the U_A(1) and SU_A(3) chiral symmetry breaking and restoration. To test this scenario, the experiments such as those at RHIC, NICA and FAIR, which extend the RHIC (and LHC) high-temperature scans also to the finite-density parts of the QCD phase diagram, should pay particular attention to the signatures from the eta'-eta complex indicating the symmetry restoration.
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