arXiv 2005.123012020-05hep-phhep-lathep-th

从静态夸克-反夸克对能量的超渐近近似确定$α(M_z)$

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

Cesar Ayala, Xabier Lobregat, Antonio Pineda

备注：: 37 pages, 14 figures. References added. Minor modification. To meet journal version

摘要：

我们给出了静态夸克-反夸克对能量的超渐近展开式，其精确度包括次领导重正子的影响。必要时，将与第一和第二renormalon相关的终止子纳入分析中。特别是，我们确定的正规化的领导renormalon的力量，因此，subleading renormalon的静态电位。我们得到了$Z_3^F(n_f=3)=2Z_3^V(n_f=3)=0.37(17)$。在严格微扰理论中，我们对静势和力的计算精度都达到了次领先的对数级。我们发现，重新确认的大尺寸和包含的领先终止相关的重正丙二烯是强制性的，以获得准确的测定时，$Λ_{\overline{\rm MS}}$拟合到短距离晶格数据的静态能量。我们得到了$Λ_{\overline{\rm MS}}^{(n_f=3)}=338(12)$ MeV和$α(M_z)=0.1181(9)$ .我们还发现了强的一致性检查，超软修正的静态能量可以计算在弱耦合的能量范围内，我们已经研究。

英文摘要：

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 $Z_3^F(n_f=3)=2Z_3^V(n_f=3)=0.37(17)$. 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 $Λ_{\overline{\rm MS}}$ when fitting to short-distance lattice data of the static energy. We obtain $Λ_{\overline{\rm MS}}^{(n_f=3)}=338(12)$ MeV and $α(M_z)=0.1181(9)$. We have also 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.

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摘要：

英文摘要：

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