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تسجيل مستخدم جديدChiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
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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 qrangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) barLambda_0 $, $langlebar q qrangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) barLambda_2 $, $langlebar q qrangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) barLambda_3 $, where $barLambda_{n_f}$ 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 $ langlebar q qrangle^{1/3}_{n_f=3}(2, {rm GeV}) = -(273^{+7}_{-4}pm 13)$ MeV, using the latest $barLambda_3$ 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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