English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We give the hyperasymptotic expansion of the energy of a staticquark-antiquark pair with a precision that includes the effects of thesubleading renormalon. The terminants associated to the first and secondrenormalon are incorporated in the analysis when necessary. In particular, wedetermine the normalization of the leading renormalon of the force and,consequently, of the subleading renormalon of the static potential. We obtain$Z_3^F(n_f=3)=2Z_3^V(n_f=3)=0.37(17)$. The precision we reach in strictperturbation theory is next-to-next-to-next-to-leading logarithmic resummedorder both for the static potential and for the force. We find that theresummation of large logarithms and the inclusion of the leading terminantsassociated to the renormalons are compulsory to get accurate determinations of$\Lambda_{\overline{\rm MS}}$ when fitting to short-distance lattice data ofthe static energy. We obtain $\Lambda_{\overline{\rm MS}}^{(n_f=3)}=338(12)$MeV and $\alpha(M_z)=0.1181(9)$. We have also found strong consistency checksthat the ultrasoft correction to the static energy can be computed at weakcoupling in the energy range we have studied.

Determination of $\alpha(M_z)$ from an hyperasymptotic approximation to the energy of a static quark-antiquark pair