发表机构
Brookhaven National Laboratory（布鲁海文国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建超越朗道的融合模型，提出在T_χ以下反常行列式出现分数次幂，推广Witten-Veneziano项，预测手征相变通常为二级，并给出格点QCD检验方案及对称相重子数算符。
AI 中文摘要
在高温下，瞬子形成稀薄气体，因此在类QCD理论中，反常U(1)_A对称性的破缺由反常行列式的整数次幂给出，即~ (det Φ)^Q，其中Φ~ \\(\overline{q}_L q_R\\) 是夸克场的双线性形式，且在无扭曲边界条件下，拓扑荷Q为整数。我们构建了一个“超越朗道”的融合模型。在手征极限下，当温度高于手征相变温度T_χ时，仅出现反常行列式的整数次幂。在T_χ以下，遵循特胡夫特等人的假设，我假定拓扑荷Q是分数化的，即整数乘以1/N_c，其中N_c是颜色数。我提出，因此手征有效拉格朗日量中会出现反常行列式的分数次幂。对于N_f个简并味，这将Witten-Veneziano项（适用于小N_f/N_c）推广到任意N_f/N_c。在该模型中，手征相变通常为二级相变。两个例外是：单味情形，可能为交叉过渡；三味情形，可能为弱一级相变。这可以通过格点QCD中的2+1味模拟来检验，即比较π^a和a_0^a传播子之差（已知的温度依赖性）与奇异夸克手征凝聚在T_χ至约2 T_χ之间的行为。对于一至四味简并夸克，在T_χ附近也可进行类似测量。最后，我提出了对称相中重子数的一个算符。
英文摘要
At high temperature instantons form a dilute gas, so in QCD-like theories the breaking of the anomalous $U(1)_A$ symmetry is given by integral powers of the anomalous determinant, $\sim (\det Φ)^{Q}$, where $Φ\sim \overline{q}_L q_R$ is bilinear in the quark fields, and with untwisted boundary conditions, the topological charge, $Q$, is an integer. A syncretic model is constructed, which is manifestly "beyond Landau". In the chiral limit, at temperatures above the chiral phase transition, $T > T_χ$, only integral powers of the anomalous determinant appear. Below $T_χ$, following 't Hooft et al. I assume that the topological charge $Q$ is fractional, as an integer times $1/N_c$, where $N_c$ is the number of colors. I suggest that consequently, fractional powers of the anomalous determinant appear in the chiral effective Lagrangian. For $N_f$ degenerate flavors, this generalizes the Witten-Veneziano term, valid for small $N_f/N_c$, to arbitrary $N_f/N_c$. In this model the chiral phase transition is generically of second order. The two exceptions are for one flavor, where it is probably crossover, and three flavors, where it could well be weakly first order. This can be tested in lattice QCD with $2+1$ flavors by comparing the (known) temperature dependence of the difference of the $π^a$ and $a_0^a$ propagators, to the chiral condensate of the strange quark, between $T_χ$ and $\sim 2 \, T_χ$. Analogous measurements are possible for one to four degenerate flavors about $T_χ$. Lastly, I propose an operator for baryon number in the symmetric phase.
