October 12, 1998
We compute the flavorless running coupling constant of QCD from the three gluon vertex in the (regularisation independent) momentum subtraction renormalisation scheme. This is performed on the lattice with high statistics. The expected color dependence of the Green functions is verified. There are significant $O(a^2\mu^2)$ effects which can be consistently controlled. Scaling is demonstrated when the renormalisation scale is varied between 2.1 GeV and 3.85 GeV. Scaling when the lattice spacing is varied is very well satisfied. The resulting flavorless conventional two loop $\Lambda^{(c)}_{\bar{MS}}$ is estimated to be, respectively for the MOM and $\widetilde{MOM}$ scheme, 361(6) MeV and 345(6) MeV, while the three loop results are, depending on $\beta_2: \Lambda^{(3)}_{\bar{MS}} = (412 - 59 \frac{\beta_2} {\beta_{2, \bar{MS}}} \pm 6 MeV) $ and $\Lambda^{(3)}_{\bar{MS}} = (382- 46\frac{\beta_2} {\beta_{2, \bar{MS}}}\pm 5 MeV) $. A preliminary computation of $\beta_2$ in the $\widetilde{MOM}$ scheme leads to $\Lambda^{(3)}_{\bar{MS}} = 303(5)\frac {a^{-1}(\beta=6.0)} {1.97 GeV}$ MeV.
Similar papers 1
May 26, 1996
We compute the running QCD coupling on the lattice by evaluating two-point and three-point off-shell gluon Green's functions in a fixed gauge and imposing non-perturbative renormalisation conditions on them. Our exploratory study is performed in the quenched approximation at beta=6.0 on 16^4 and 24^4 lattices. We show that, for momenta in the range 1.8-2.3 Gev, our coupling runs according to the two-loop asymptotic formula, allowing a precise determination of the correspondin...
March 3, 2000
We report on very strong evidence of the occurrence of power terms in $\as(p)$, the QCD running coupling constant in the $\widetilde{MOM}$ scheme, by analyzing non-perturbative measurements from the lattice three-gluon vertex between 2.0 and 10.0 GeV at zero flavor. While putting forward the caveat that this definition of the coupling is a gauge dependent one, the general relevance of such an occurrence is discussed. We fit $\Lambda_{\bar{\rm MS}}^{(n_f=0)}= 237 \pm 3 ^{+ 0}_...
October 24, 1995
We compute the QCD running coupling on the lattice as defined from the 3-gluon vertex. We present the results of an exploratory study at $\beta=6.0$ on a $16^4$ lattice, which show that for momenta larger than 2 \Gev, the coupling runs according to the 2-loop asymptotic formula, allowing a precise determination of the $\Lambda$ parameter. Our renormalization procedure corresponds to a momentum subtraction scheme in the continuum and, most remarkably, one does not need lattice...
October 21, 1998
We determine the three-loop coefficient of the beta function in the asymmetric momentum subtraction scheme in Landau gauge. This scheme is convenient for lattice studies of \alpha_s, the running coupling constant of QCD. We present high statistics lattice results for \alpha_s in the SU(3) Yang-Mills theory without quark, compare with the three-loop running and extract the value of the corresponding \Lambda_\msbar parameter. We estimate the systematic error coming from four-lo...
July 26, 2001
We present preliminary results on the computation of the QCD running coupling constant in the $\widetilde{MOM}$ scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV ($\beta =$ 5.6, 5.8 and 6.0) with a constant dynamical-quark mass. This range already allows to exhibit some evidence for a sizable $1/\mu^2$ correction to the asymptotic behaviour, as in the quenched approximation, although a fit without power corrections is ...
October 12, 2001
We present preliminary results on the computation of the QCD running coupling constant in the MOM_tilde scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV (beta=5.6, 5.8 and 6.0) with a constant dynamical quark mass. This range already allows to exhibit some evidence for a sizeable 1/mu^2 correction to the asymptotic behaviour, as in the quenched approximation. We find Lambda_MS^(N_f=2) = 264(27) MeV x [a^{-1}(5.6,0.156...
March 12, 2020
In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), $\alpha^{\overline{\mathrm{MS}}}_s(\mu)$, for $\overline{\mathrm{MS}}$ renormalization scales $\mu \in (1,\,2)$ GeV. The computation uses gauge field configuration ensembles with $\mathcal{O}(a)$-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has ...
March 27, 2018
Using continuum extrapolated lattice data we trace a family of running couplings in three-flavour QCD over a large range of scales from about 4 to 128 GeV. The scale is set by the finite space time volume so that recursive finite size techniques can be applied, and Schr\"odinger functional (SF) boundary conditions enable direct simulations in the chiral limit. Compared to earlier studies we have improved on both statistical and systematic errors. Using the SF coupling to impl...
November 19, 2004
We present a non-perturbative computation of the running of the coupling alpha_s in QCD with two flavours of dynamical fermions in the Schroedinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Lambda-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Lambda*r_0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 f...
April 21, 2016
We discuss the determination of the strong coupling $\alpha_\mathrm{\overline{MS}}^{}(m_\mathrm{Z})$ or equivalently the QCD $\Lambda$-parameter. Its determination requires the use of perturbation theory in $\alpha_s(\mu)$ in some scheme, $s$, and at some energy scale $\mu$. The higher the scale $\mu$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\Lambda$-parameter in three-flavor QCD, we perform lattice com...