拓扑荷的非平衡性及其效应
Non-equilibration of topological charge and its effects
摘要：
在小晶格间距的QCD模拟中，拓扑荷Q的演化非常缓慢，如果这个量没有得到适当的平衡，我们可能会得到错误的物理量结果，或者错误的估计它们的误差。我们利用已知的质量和衰变常数对QCD真空角θ和平方拓扑荷Q^2的依赖关系，以及手征微扰理论关于质量和衰变常数对θ的依赖关系的结果，来估计这些效应的大小，并提出处理它们的策略。对于部分淬灭的情况下，我们勾勒出一个替代的推导已知的$χ$ PT青木和谷的结果，使用非微扰正确的手征理论由Golterman，夏普和Singleton，夏普和Shoresh。利用MILC合作组的四种HISQ动力学夸克的晶格系综，我们测量了质量和衰变常数对$Q^2$的依赖性，并与$χ$ PT形式进行了比较。观察到的一致性使我们相信，我们可以可靠地估计缓慢的拓扑变化的错误，甚至纠正其领先的影响。
英文摘要：
In QCD simulations at small lattice spacings, the topological charge Q evolves very slowly and, if this quantity is not properly equilibrated, we could get incorrect results for physical quantities, or incorrect estimates of their errors. We use the known relation between the dependence of masses and decay constants on the QCD vacuum angle theta and the squared topological charge Q^2 together with chiral perturbation theory results for the dependence of masses and decay constants on theta to estimate the size of these effects and suggest strategies for dealing with them. For the partially quenched case, we sketch an alternative derivation of the known $χ$PT results of Aoki and Fukaya, using the nonperturbatively correct chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. With the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks, we measure the $Q^2$ dependence of masses and decay constants and compare to the $χ$PT forms. The observed agreement gives us confidence that we can reliably estimate the errors from slow topology change, and even correct for its leading effects.
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