AI 中文总结
该研究从1PI有效作用量视角出发，通过施加Ward恒等式约束，证明QCD中同时解决U(1)问题与强CP问题存在张力，指出拓扑磁化率是该张力与领头阶修正的关键决定因素。
AI 中文摘要
我们讨论了在QCD内部、存在轻夸克且$\barθ$角很小的情况下，试图同时解决QCD中的$U(1)$问题和强$CP$问题时所遇到的张力。我们通过考虑1PI有效作用量$\boldsymbolΓ$的低能展开来开展研究，$\boldsymbolΓ$是一组恰当选取的规范不变（复合）算符的泛函。在对$\boldsymbolΓ$施加Ward恒等式约束后，我们在较弱的假设下证明：只有当反常对赝标量质量矩阵的贡献与其非反常对应项相比完全可忽略时——也就是说，只有当$U(1)$问题未被解决时，非零小$\barθ$下的$CP$破坏才能被避免。QCD中的拓扑磁化率以及纯Yang-Mills理论中拓扑磁化率的精确推广，是确立上述张力、确定$\barθ$领头阶下各类已知结果修正项的最关键因素。
英文摘要
We discuss the tension one encounters in trying to solve, simultaneously, the $U(1)$ and strong-$CP$ problems in QCD with light quarks and a small $\barθ$ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action $Γ$, a functional of a properly chosen set of gauge-invariant (composite) operators. After enforcing Ward-identity constraints on $Γ$, we prove, under minor assumptions, that $CP$ violation at small non-vanishing $\barθ$ can be avoided only if the anomaly-induced contribution to the pseudoscalar mass matrix is completely negligible when compared to its non-anomalous counterpart - that is, only if the $U(1)$ problem is not solved. The topological susceptibility in QCD and a precise generalization of the one in pure Yang-Mills theory emerge as the most important players in establishing the above tension and in determining the corrections to various known results at leading order in $\barθ$.
Comments27 pages, LaTeX
