Year: 2012
Type: article
Abstract: 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 ${F}_{\ensuremath{\pi}}/{\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$, where ${F}_{\ensuremath{\pi}}$ is the pion decay constant and ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$ the basic QCD scale in the $\overline{\mathrm{MS}}$ scheme. Using experimental ${F}_{\ensuremath{\pi}}$ input value we obtain ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}^{{n}_{f}=2}\ensuremath{\simeq}{255}_{\ensuremath{-}15}^{+40}\text{ }\text{ }\mathrm{MeV}$, 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 ${\ensuremath{\alpha}}_{S}(\ensuremath{\mu})$ at perturbative $\ensuremath{\mu}$ values.
Authors: Jean-Loïc Kneur, André Neveu
Language: Latvian
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1550154158