Home > Publications database > A status update on the determination of ${\Lambda}_{\overline{\rm MS}}^{N_{\rm f}=3}$ by the ALPHA collaboration |
Journal Article/Contribution to a conference proceedings/Internal Report | PUBDB-2015-05199 |
2015
SISSA
Trieste
Report No.: TCDMATH-15--11; DESY-15-218; CERN-PH-TH-2015-269; WUB-15-08; --HU-EP-15-54; IFT-UAM-CSIC-15-122; arXiv:1511.05831;
Abstract: The ALPHA collaboration aims to determine $\alpha_s(m_Z)$ with a total error below the percent level. A further step towards this goal can be taken by combining results from the recent simulations of 2+1-flavour QCD by the CLS initiative with a number of tools developed over the years: renormalized couplings in finite volume schemes, recursive finite size techniques, two-loop renormalized perturbation theory and the (improved) gradient flow on the lattice. We sketch the strategy, which involves both the standard SF coupling in the high energy regime and a gradient flow coupling at low energies. This implies the need for matching both schemes at an intermediate switching scale, $L_{\rm swi}$, which we choose roughly in the range 2-4 GeV. In this contribution we present a preliminary result for this matching procedure, and we then focus on our almost final results for the scale evolution of the SF coupling from $L_{\rm swi}$ towards the perturbative regime, where we extract the $N_{\rm f} = 3$ ${\Lambda}$-parameter, ${\Lambda}_{\overline{\rm MS}}^{N_{\rm f}=3}$, in units of $L_{\rm swi}$ . Connecting $L_{\rm swi}$ and thus the ${\Lambda}$-parameter to a hadronic scale such as $F_K$ requires 2 further ingredients: first, the connection of $L_{\rm swi}$ to $L_{\rm max}$ using a few steps with the step-scaling function of the gradient flow coupling, and, second, the continuum extrapolation of $L_{\rm max} F_K$.
Keyword(s): energy: high ; energy: low ; flow ; finite size ; ALPHA ; quantum chromodynamics ; perturbation theory ; lattice
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