Ref HAL: hal-01177136_v1
Ref Arxiv: 1506.07506
DOI: 10.1103/PhysRevD.92.074027
WoS: WOS:000363237400004
Ref. & Cit.: NASA ADS
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18 Citations
Résumé:

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 $\langle \bar q q \rangle$ in the chiral limit, for $n_f=2$ and $n_f=3$ 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 $\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 spanned by the first and second numbers (respectively four- and three-loop order results) defines our theoretical error, and $\bar\Lambda_{n_f}$ is the basic QCD scale in the $\overline{MS}$-scheme. We obtain a moderate suppression of the chiral condensate when going from $n_f=2$ to $n_f=3$. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).

Commentaires: 20 pages, 1 figure

Ref HAL: hal-01936979_v1
Ref Arxiv: 1310.6724
Ref. & Cit.: NASA ADS
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Résumé:

A new version of the so-called optimized perturbation (OPT), implementing consistently renormalization group properties, is used to calculate the nonperturbative ratio $F_\pi/\overline\Lambda$ of the pion decay constant and the basic QCD scale in the $\overline{MS}$ scheme. Using the experimental $F_\pi$ input value it provides a new determination of $\overline\Lambda$ for $n_f=2$ and $n_f=3$, and of the QCD coupling constant $\overline\alpha_S $ at various scales once combined with a standard perturbative evolution. The stability and empirical convergence properties of the RGOPT modified series is demonstrated up to the third order. We examine the difference sources of theoretical uncertainties and obtain $\overline\alpha_S (m_Z) =0.1174 ^{+.0010}_{-.0005} \pm .001 \pm .0005_{evol}$, where the first errors are estimates of the intrinsic theoretical uncertainties of our method, and the second errors come from present uncertainties in $F_\pi/F_0$, where $F_0$ is $F_\pi$ in the exact chiral $SU(3)$ limit.

Commentaires: 5 pages, talk given at EPS-HEP, Stockholm, Sweden 18-24 July, 2013

Ref HAL: hal-00828057_v1
Ref Arxiv: 1305.6910
DOI: 10.1103/PhysRevD.88.074025
WoS: WOS:000326106600004
Ref. & Cit.: NASA ADS
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34 Citations
Résumé:

A variant of variationally optimized perturbation, incorporating renormalization group properties in a straightforward way, uniquely fixes the variational mass interpolation in terms of the anomalous mass dimension. It is used at three successive orders to calculate the nonperturbative ratio $F_\pi/\Lambda$ of the pion decay constant and the basic QCD scale in the MSbar scheme. We demonstrate the good stability and (empirical) convergence properties of this modified perturbative series for this quantity, and provide simple and generic cures to previous problems of the method, principally the generally non-unique and non-real optimal solutions beyond lowest order. Using the experimental $F_\pi$ input value we determine \Lambda^{n_f=2}\simeq 359^{+38}_{-25} \pm 5 MeV and \Lambda^{n_f=3}=317^{+14}_{-7} \pm 13 MeV, where the first quoted errors are our estimate of theoretical uncertainties of the method, which we consider conservative. The second uncertainties come from the present uncertainties in F_\pi/F and F_\pi/F_0, where F (F_0) is $F_\pi$ in the exact chiral SU(2) (SU(3)) limits. Combining the \Lambda^{n_f=3} results with a standard perturbative evolution provides a new independent determination of the strong coupling constant at various relevant scales, in particular \alpha_S (m_Z) =0.1174 ^{+.0010}_{-.0005} \pm .001 \pm .0005_{evol} and \alpha_S^{n_f=3}(m_\tau)= 0.308 ^{+.007}_{-.004} \pm .007 \pm .002_{evol}. A less conservative interpretation of our prescriptions favors central values closer to the upper limits of the first uncertainties. The theoretical accuracy is well comparable to the most precise recent {\em single} determinations of \alpha_S, including some very recent lattice simulation determinations with fully dynamical quarks.

Commentaires: 28 pages, 5 figures

Ref HAL: hal-00653509_v1
Ref Arxiv: 1108.3501
DOI: 10.1103/PhysRevD.85.014005
WoS: WOS:000298925900001
Ref. & Cit.: NASA ADS
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24 Citations
Résumé:

A recent extension of a variationally optimized perturbation, combined with renormalization group properties in a straightforward way, can provide approximations to nonperturbative quantities such as the chiral symmetry breaking order parameters typically. We apply this to evaluate, up to third order in this modified perturbation, the ratio Fpi/Lambda, where Fpi is the pion decay constant and Lambda the basic QCD scale in the modified MS scheme. Using experimental Fpi input value we obtain Lambda(nf=2) ~ 255_{-15}^{+40} MeV, where quoted errors are estimates of theoretical uncertainties of the method. This compares reasonably well with some recent lattice simulation results. We briefly discuss prospects (and obstacles) for extrapolation to alpha_S(mu) at perturbative mu values.

Commentaires: 5 pages

Ref HAL: hal-00494268_v1
Ref Arxiv: 1004.4834
DOI: 10.1103/PhysRevD.81.125012
WoS: 000278882200001
Ref. & Cit.: NASA ADS
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26 Citations
Résumé:

We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a clear improvement of the non-perturbative results with respect to previous similar variational approaches. This is illustrated here by deriving optimized results for the mass gap of the O(2N) Gross-Neveu model, compared with the exactly know results for arbitrary N. At large N, the exact result is reproduced already at the very first order of the modified perturbation using this procedure. For arbitrary values of N, using the original perturbative information only known at two-loop order, we obtain a controllable percent accuracy or less, for any N value, as compared with the exactly known result for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very general and can be extended straightforwardly to any renormalizable Lagrangian model, being systematically improvable provided that a knowledge of enough perturbative orders of the relevant quantities is available.

Commentaires: 18 pages, 1 figure

Ref HAL: hal-00379184_v1
Ref Arxiv: 0902.1331
DOI: 10.1088/1751-8113/42/30/304011
WoS: 000267943000012
Ref. & Cit.: NASA ADS
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41 Citations
Résumé:

Liouville field theory on a sphere is considered. We explicitly derive adifferential equation for four-point correlation functions with one degeneratefield $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-pointconformal blocks which can be calculated exactly and represented by finitedimensional integrals of elliptic theta-functions for arbitrary intermediatedimension. We study also the bootstrap equations for these conformal blocks andderive integral representations for corresponding four-point correlationfunctions. A relation between the one-point correlation function of a primaryfield on a torus and a special four-point correlation function on a sphere isproposed.

Commentaires: 29 pp.

Ref HAL: hal-00288520_v1
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Résumé:

In this talk, I reveal many of the rather remarkable coincidences which led to my involvement in string theory almost forty years ago, first with Joel Scherk, later with David Gross, and of course John Schwarz, Pierre Ramond and Charles Thorn, and how these coincidences played a crucial role in our discoveries.