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• W3082418859 abstract "A bstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mn>3</mml:mn> <mml:mi>F</mml:mi> </mml:msubsup> </mml:math> ( n f = 3) = $$ 2{Z}_3^V $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mn>2</mml:mn> <mml:msubsup> <mml:mi>Z</mml:mi> <mml:mn>3</mml:mn> <mml:mi>V</mml:mi> </mml:msubsup> </mml:math> ( n f = 3) = 0 . 37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {Lambda}_{overline{mathrm{MS}}} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:msub> </mml:math> when fitting to short-distance lattice data of the static energy. We obtain $$ {Lambda}_{overline{mathrm{MS}}}^{left({n}_f=3right)} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>Λ</mml:mi> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfenced> </mml:msubsup> </mml:math> = 338(12) MeV and α ( M z ) = 0 . 1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied." @default.
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• W3082418859 date "2020-09-01" @default.
• W3082418859 modified "2023-10-17" @default.
• W3082418859 title "Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair" @default.
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• W3082418859 doi "https://doi.org/10.1007/jhep09(2020)016" @default.
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