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arXiv 1203.4469hep-lathep-phnucl-th
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格点量子色动力学中的高精度标度设置

High-precision scale setting in lattice QCD

S. Borsanyi, S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, C. McNeile, K. K. Szabo

摘要:

标度设置是格点量子色动力学的核心问题。需要预测物理单位中的尺寸量。此外,它确定了在不同裸耦合值下进行计算的相对晶格间距,这是将结果外推到连续体中所需要的。因此,我们计算了一个新的量$w_0$,用于设置格点量子色动力学的标度,它是基于Wilson流的,类似于标度$t_0$(M. Luscher,JHEP 1008(2010)071)。它是廉价和简单的实现和计算。特别是,它不涉及在渐近时间的关联函数的精细拟合。它通常可以在每千分之几的水平上确定。我们计算了它的连续外推值在2+1味QCD的物理和非物理的π介子和K介子的质量,允许质量无关的标度设置,甚至远离物理质点。我们证明了它的鲁棒性计算它与两个非常不同的行动(其中之一与交错,另一个与威尔逊费米子),并通过显示的结果同意物理夸克质量在连续极限。

英文摘要:

Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and this is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit.

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