%0 Journal Article
%T Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
%+ Laboratoire Charles Coulomb (L2C)
%A Kneur, Jean-Loïc
%A Neveu, Andre
%< avec comité de lecture
%Z L2C:20-008
%@ 1550-7998
%J Physical Review D
%I American Physical Society
%P 074009
%8 2020-04-09
%D 2020
%Z 2001.11670
%R 10.1103/PhysRevD.101.074009
%Z Physics [physics]/High Energy Physics - Phenomenology [hep-ph]
%Z Physics [physics]/High Energy Physics - Lattice [hep-lat]Journal articles
%X 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}) \bar\Lambda_0 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) \bar\Lambda_2 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) \bar\Lambda_3 $, where $\bar\Lambda_{n_f}$ 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 $\bar\Lambda_3$ 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.
%G English
%2 https://hal.science/hal-02464734/document
%2 https://hal.science/hal-02464734/file/PhysRevD.101.074009.pdf
%L hal-02464734
%U https://hal.science/hal-02464734
%~ CNRS
%~ L2C
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021