arXiv 2001.116702020-01-31hep-phhep-lat

重整化群优化微扰的全五圈和部分六圈手征凝聚和谱密度

Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation

Jean-Loic Kneur, André Neveu

备注：: 28 pages, 4 figures
发表信息：: Phys. Rev. D 101, 074009 (2020)
DOI：: 10.1103/PhysRevD.101.074009

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摘要：

我们重新考虑我们以前的手征夸克凝聚$\langle \bar q q \rangle$确定从相关的QCD谱密度的欧几里德狄拉克运营商，使用我们的重整化群优化微扰（RGOPT）的方法。由于最近获得的{ \em complete}五圈QCD RG系数和其他一些相关的四圈结果，我们可以将我们的计算精确地扩展到$N^4LO$（五圈）RGOPT，并部分扩展到$N^5LO$（六圈），后者在一个定义良好的近似中考虑了所有六圈内容，可以从五圈RG性质精确地预测。RGOPT的结果总体上显示了很好的稳定性和收敛性，主要给出了RG不变凝聚，$\langle \bar q q\rangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) \barΛ_0 $，$\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) \barΛ_2 $，$\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) \barΛ_3 $，其中$\barΛ_{n_f}$是用于$n_f$夸克味的\overline{MS}方案中的基本QCD标度，所跨越的范围是我们相当保守的估计理论误差.这导致{ \it e.g.}至$ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(273^{+7}_{-4}\pm 13)$ MeV，使用给出第二不确定度的最新$\barΛ_3$值。我们比较了我们的结果与其他一些最近的测定。作为我们分析的副产品，我们还提供了完整的五圈和部分六圈的微扰QCD谱密度的表达式，这可能是有用的其他目的。

英文摘要：

We reconsider our former determination of the chiral quark condensate $\langle \bar q q \rangle$ from the related QCD spectral density of the Euclidean Dirac operator, using our Renormalization Group Optimized Perturbation (RGOPT) approach. Thanks to the recently available {\em complete} five-loop QCD RG coefficients, and some other related four-loop results, we can extend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to $N^5LO$ (six-loops), the latter within a well-defined approximation accounting for all six-loop contents exactly predictable from five-loops RG properties. The RGOPT results overall show a very good stability and convergence, giving primarily the RG invariant condensate, $\langle \bar q q\rangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) \barΛ_0 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) \barΛ_2 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) \barΛ_3 $, where $\barΛ_{n_f}$ is the basic QCD scale in the \overline{MS} scheme for $n_f$ quark flavors, and the range spanned is our rather conservative estimated theoretical error. This leads {\it e.g.} to $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(273^{+7}_{-4}\pm 13)$ MeV, using the latest $\barΛ_3$ values giving the second uncertainties. We compare our results with some other recent determinations. As a by-product of our analysis we also provide complete five-loop and partial six-loop expressions of the perturbative QCD spectral density, that may be useful for other purposes.

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