论文标题
在全五环和部分六环的重新归一化组优化扰动下，手性冷凝物和光谱密度优化
Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
论文作者
论文摘要
我们使用我们的重新分配组优化扰动（RGOPT）方法，重新考虑了我们以前对手性夸克冷凝物$ \ langle \ bar q q \ rangle $的确定。得益于最近可用的{\ em完整}五环QCD RG系数以及其他一些相关的四循环结果，我们可以将计算准确地扩展到$ n^4lo $（五环）RGOPT，部分地将$ n^5lo $（六环）扩展到了五个属性的五个属性中，可以完全定义所有六层属性。 RGOPT结果总体上显示出非常良好的稳定性和收敛性，主要给出RG不变的冷凝物，$ \ langle \ bar Q q q \ w {1/3} {1/3} _ {rgi}（n_f = 0）（n_f = 0） q \ rangle^{1/3} _ {rgi}（n_f = 2）= - （0.781 _ { - 0.009}^{+0.019}）\barλ_2$，美元 - （0.751 _ { - 。010}^{+0.019}）\barλ_3$，其中$ \barλ_{n_f} $是\ $ n_f $ quark风格的基本QCD量表{MS}方案中的基本量表，我们的范围是我们相当保守的估计估计的，这是我们相当保守的。这将{\ it e.g。}引导到$ \ langle \ bar q q \ rangle^{1/3} _ {n_f = 3}（2 \，{\ rm gev}）= - （273^{+7} _ {+7} _ { - { - 4} \ pm 13）$ mev，使用最新的$ \ $ \ $ \ $ \ $ \ $ \ coveling。我们将结果与其他一些最近的决定进行了比较。作为我们分析的副产品，我们还提供了扰动QCD光谱密度的完整的五环和部分六环表达式，这可能对其他目的有用。
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.
