Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation - Archive ouverte HAL Access content directly
Journal Articles Physical Review D Year : 2020

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

Jean-Loïc Kneur
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• PersonId : 1009131
Andre Neveu
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• PersonId : 1031428

#### Abstract

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.

### Dates and versions

hal-02464734 , version 1 (04-06-2021)

### Identifiers

• HAL Id : hal-02464734 , version 1
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### Cite

Jean-Loïc Kneur, Andre Neveu. Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation. Physical Review D, 2020, pp.074009. ⟨10.1103/PhysRevD.101.074009⟩. ⟨hal-02464734⟩

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