Computation of the strong coupling in QCD with two dynamical flavors

Abstract

We present a non-perturbative computation of the running of the coupling α s in QCD with two flavours of dynamical fermions in the Schrödinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Λ-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Λr 0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 fm. It translates into Λ (2) MS = 245(16)(16) MeV [assuming r 0 = 0.5 fm]. The last step still has to be improved to reduce the uncertainty.

A non-perturbative exploration of the high energy regime in $$N_{\mathrm{f}}=3$$ N f = 3 QCD

“…Inserting the field tensor into the gauge action, S g , one obtains 19) which, for given η (and independently of ν) constitutes the absolute minimum of the action [23]. One may thus define the effective action as a function of this background field, 20) and its perturbative expansion,…”

“…In particularv gives rise to 2 lattice observables 18) which differ by the chiral limit definition. The appearance of 2 lattice versions for ω(u) is a consequence of the definition of the lattice step-scaling functions through 19) which requires simulations on lattices with resolutions L/a and 2L/a, at the same bare parameters. In particular, the simulations on the 2L/a-lattices are performed at the bare mass parameters for which the PCAC mass vanishes on the L/a lattice.…”

“…The technique, used earlier for between N f = 0 and N f = 4 quark flavours [18][19][20][21], allows one to non-perturbatively verify the close-to perturbative running of the coupling and observe the small effects of dynamical quarks, as illustrated in Fig. 1.…”

“…Section 3 then presents the lattice set-up, the numerical simulations and statistics produced, and discusses the perturba- Table 5). Data points for N f = 0, 2, 3, 4 are taken from the literature [18][19][20][21] tive improvement of the data. The impatient reader might skip this section and directly pass to Sect.…”

Instantons in lepton pair production

“…7, our results for the coefficient functions are not largely affected if we choose instead the nominal value n f = 1 and a corresponding value for the Λ parameter, Λ (1) MS = 0.241 GeV. This value was obtained by a linear interpolation between the central values found in recent lattice investigations for n f = 0, Λ (0) MS = 0.237 GeV [40], and n f = 2, Λ (2) MS = 0.245 GeV [41]. Again, such details cancel to a great extend in the ratios of structure functions.…”