arXiv 2407.062522024-07hep-phhep-th

QCD类理论中的自发CP破缺

Spontaneous CP Breaking in a QCD-like Theory

Csaba Csáki, Maximilian Ruhdorfer, Taewook Youn

备注：: 36 pages, 7 figures; v2: Minor changes. Matches published version

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AI总结：

研究QCD类理论在超对称破缺下的自发CP破缺，通过解析和数值方法确定相结构、临界质量及相边界，结果与广义对称性异常匹配和有效手征拉格朗日预言一致。

摘要：

我们研究了在$\barθ=π$下一类QCD类理论的相结构，该理论源自超对称$SU(N)$QCD，通过反常中介效应（AMSB QCD）引入少量超对称破缺微扰。尽管超对称伴子并未退耦，但该理论的无质量能谱与QCD的能谱一致。在该理论中，我们可以明确$\barθ=π$下的相结构作为夸克质量和味数$F$的函数。对于单味情形，我们发现存在一个临界夸克质量：低于该质量时CP未破缺，高于临界质量时CP发生自发破缺。在临界质量处存在二级相变，同时伴随一个无质量的$η'$。我们能够解析求解$N=2,3$以及大$N$极限下的极小值和临界质量，而对于其他$N$情形可得到数值结果。对于两味情形，我们发现只要夸克质量相等且非零，CP总是破缺的；但当夸克质量不等时，存在非平凡的相边界，我们通过数值方法得到了该边界。对于$F\geq 3$，我们得到了复杂的相边界，其重现了不同夸克质量极限下的行为。我们的所有结果均与基于广义对称性反常匹配论证和有效手征拉格朗日的普通QCD预言一致。我们还简要评述了Draper首次讨论的畴壁解，并给出了单味$SU(2)$最简单情形的解析结果。

英文摘要：

We examine the phase structure of a QCD-like theory at $\barθ=π$ obtained from supersymmetric $SU(N)$ QCD perturbed by a small amount of supersymmetry breaking via anomaly mediation (AMSB QCD). The spectrum of this theory matches that of QCD at the massless level, though the superpartners are not decoupled. In this theory it is possible to nail down the phase structure at $\barθ=π$ as a function of the quark masses and the number of flavors $F$. For one flavor we find that there is a critical quark mass, below which CP is unbroken, while above the critical mass CP is spontaneously broken. At the critical mass there is a second-order phase transition along with a massless $η'$. We are able to analytically solve for the minima and the critical mass for $N=2,3$ as well as for the large $N$ limit, while for other $N$ one can find numerical results. For two flavors, we find that CP is always broken as long as the quark masses are equal and non-zero, however there is a non-trivial phase boundary for unequal quark masses, which we find numerically. For $F\geq 3$ we obtain an intricate phase boundary which reproduces the various quark mass limits. All our results are in agreement with the predictions for ordinary QCD that were based on anomaly matching arguments for generalized symmetries and the effective chiral Lagrangian. We also briefly comment on the domain wall solutions first discussed by Draper, and are able to present analytic results for the simplest case of $SU(2)$ with one flavor.

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