Ref HAL: hal-03252526_v1
DOI: 10.1063/5.0039868
WoS: 000630507900001
Exporter : BibTex | endNote
Résumé:

We exhibit a set of six explicit higher nonlocal integral invariants of free-surface deep-water gravity waves conservedin lowest nontrivial orders of perturbation in the amplitude of the surface displacement.

Ref HAL: hal-02464734_v1
Ref Arxiv: 2001.11670
DOI: 10.1103/PhysRevD.101.074009
WoS: 000525109000003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

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.

Ref HAL: hal-01938198_v1
Exporter : BibTex | endNote
Résumé:

How the Neveu-Schwarz string was discovered is the result of a most unlikely sequence of four coincidences.

Ref HAL: hal-01924596_v1
DOI: 10.1142/S0129055X18400123
WoS: WOS:000439964100006
Exporter : BibTex | endNote
Résumé:

We apply an integral transformation to solutions of a partial differential equa-tion for the five-point correlation functions in Liouville theory on a sphere withone degenerate field $V_{ − 1/(2b)}$ . By repeating this transformation, we can reach a whole lattice of values for the conformal dimensions of the four other operators. Factorizing out the degenerate field leads to integral representations of the corresponding four-point conformal blocks. We illustrate this procedure on the elliptic conformal blocks discovered in a previous publication.

Ref HAL: hal-01757993_v1
Ref Arxiv: 1803.03564
Ref INSPIRE: 1659300
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We apply an integral transformation to solutions of a partial differential equation for five-point correlation functions in Liouville theory on a sphere with one degenerate field $V_{-\frac{1}{2b}}$. By repeating this transformation, we can reach a whole lattice of values for the conformal dimensions of the four other operators. Factorizing out the degenerate field leads to integral representations of the corresponding four-point conformal blocks. We illustrate this procedure on the elliptic conformal blocks discovered in a previous publication.

Ref HAL: hal-01405689_v1
DOI: 10.1016/j.nuclphysbps.2015.01.014
WoS: WOS:000381173300014
Exporter : BibTex | endNote
Résumé:

A new version of the optimized perturbation (OPT), implementing renormalization group properties consistently, allows to calculate the nonperturbative ratio of the pion decay constant and the basic QCD scale in the MSbar scheme. From the experimental Fπ input value it gives a new determination of $\Lambda_{MSbar}$ for nf=2 and nf=3, and thus of the QCD coupling constant $\alpha_S$ at various scales once combined with a standard perturbative evolution. The empirical convergence properties of the RGOPT modified series is exhibited up to the third order. We examine the various sources of theoretical uncertainties and obtain $\alpha_S(mZ)= 0.1174 ^{+.001}_{-.0005} \pm .001\pm .0005_{evol}$, where the first errors are estimates of the intrinsic theoretical uncertainties of our method, and the second errors come from present uncertainties in Fπ/F0, where F0 is Fπ in the exact chiral SU(3) limit.

Ref HAL: hal-01264155_v1
Ref Arxiv: 1512.03406
DOI: 10.1016/j.nuclphysbps.2016.02.021
WoS: WOS:000375626800021
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

Our renormalization group consistent variant of optimized perturbation, RGOPT, is used to calculate the nonperturbative QCD spectral density of the Dirac operator and the related chiral quark condensate $\langle \bar q q \rangle$, for $n_f=2$ and $n_f=3$ massless quarks. Sequences of approximations at two-, three-, and four-loop orders are very stable and give $\langle \bar q q \rangle^{1/3}_{n_f=2}(2\, {\rm GeV}) = -(0.833-0.845) \bar\Lambda_2 $, and $ \langle \bar q q \rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(0.814-0.838) \bar\Lambda_3 $ where the range is our estimated theoretical error and $\bar\Lambda_{n_f}$ the basic QCD scale in the $\rm \bar{MS}$-scheme. We compare those results with other recent determinations (from lattice calculations and spectral sum rules).

Commentaires: 5 pages, talk given at 18th International Conference in Quantum Chromodynamics (QCD 15) Montpellier, published in the proceedings