The chiral condensate from renormalization group optimized perturbation
Kneur, J. -L. · Neveu, A.
Original · EN
Our recently developed variant of variationnally optimized perturbation (OPT), in particular consistently incorporating renormalization group properties (RGOPT), is adapted to the calculation of the QCD spectral density of the Dirac operator and the related chiral quark condensate q q in the chiral limit, for nf=2 and nf=3 massless quarks. The results of successive sequences of approximations at two-, three-, and four-loop orders of this modified perturbation, exhibit a remarkable stability. We obtain q q¹/³ₙf₌₂(2 GeV) = -(0.833-0.845) Λ₂, and q q¹/³ₙf₌₃(2 GeV) = -(0.814-0.838) Λ₃ where the range spanned by the first and second numbers (respectively four- and three-loop order results) defines our theoretical error, and Λₙf is the basic QCD scale in the MS-scheme. We obtain a moderate suppression of the chiral condensate when going from nf=2 to nf=3. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).
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