格点量子色动力学中的多π态与带电π凝聚
Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
摘要：
在动力学混合作用格点量子色动力学中，计算了在空间体积V ~（2.5 fm）^[3]中含有多达12个$π^+$的系统的基态能量，晶格间距为~ 0.125 fm，轻夸克质量为4个不同的值。对于每个基态都可以看到清晰的信号，从而可以从包含不同数量的$π^+$的系统的相关分析中精确提取$π^+π^+$散射长度和$π^+π^+π^+$相互作用。这种$π^+π^+$散射长度的提取与单独的$π^+π^+$ -系统的提取一致。这里研究的大量系统大大加强了我们早期工作中提出的论点，并明确地证明了低能量$π^+π^+π^+$相互作用的存在。利用数值计算结果研究了$π^+$气体的物态方程，得到了与手征微扰理论相一致的同位旋化学势的密度依赖关系.发现化学势在较轻的π介子质量下从$π^+π^+π^+$相互作用中得到了很大的贡献。这项工作的一个重要的技术方面是演示的必要性，执行传播收缩大于两倍的精度，以提取正确的结果。
英文摘要：
The ground-state energies of systems containing up to twelve $π^+$'s in a spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice QCD at a lattice spacing of ~ 0.125 fm for four different values of the light quark masses. Clean signals are seen for each ground state, allowing for a precise extraction of both the $π^+π^+$ scattering length and $π^+π^+π^+$-interaction from a correlated analysis of systems containing different numbers of $π^+$'s. This extraction of the $π^+π^+$ scattering length is consistent with than that from the $π^+π^+$-system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy $π^+π^+π^+$-interaction. The equation of state of a $π^+$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretical expectations of leading order chiral perturbation theory. The chemical potential is found to receive a substantial contribution from the $π^+π^+π^+$-interaction at the lighter pion masses. An important technical aspect of this work is the demonstration of the necessity of performing propagator contractions in greater than double precision to extract the correct results.
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