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arXiv · 1407.7503

$\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential

Felix Karbstein·Antje Peters·Marc Wagner
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Abstract

We determine $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ by fitting perturbative expressions for the quark-antiquark static potential to lattice results for QCD with $n_f=2$ dynamical quark flavors. To this end we use the perturbative static potential at the presently best known accuracy, i.e. up to ${\cal O}(\alpha_s^4)$, in momentum space. The lattice potential is computed on a fine lattice with $a \approx 0.042 \, \textrm{fm}$ in position space. To allow for a comparison and matching of both results, the lattice potential is transformed into momentum space by means of a discrete Fourier transform. The value of $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data.

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Felix Karbstein, Antje Peters, Marc Wagner. 2014-07-28. $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential. https://doi.org/10.1007/jhep09(2014)114

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