The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods

Abstract

The perturbative QCD static potential and ultrasoft contributions, which together give the static energy, have been calculated to three- and four-loop order respectively, by several authors. Using the renormalization group, and Padé approximants, we estimate the four-loop corrections to the static energy. We also employ the optimal renormalization method and resum the logarithms of the perturbative series in order to reduce sensitivity to the renormalization scale in momentum space. This is the first application of the method to results at these orders. The convergence behaviour of the perturbative series is also improved in position space using the Restricted Fourier Transform scheme. Using optimal renormalization, we have extracted the value of ${\Lambda }_{\text{QCD}}^{\overline{\text{MS}}}$ at different scales for two active flavours by matching to the static energy from lattice QCD simulations.

16 pages, 3 figures, 3 tables. Version published in Phys.Rev.D

References in corpus (10)

• The five-loop beta function of Yang-Mills theory with fermions
• The QCD static energy at NNNLL
• The bottom-quark mass from non-relativistic sum rules at NNNLO
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Analytic three-loop static potential
• Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$ bound states at N${}^3$LO
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential
• Optimal renormalization and the extraction of the strange quark mass from moments of the $\tau$-decay spectral function
• Non-relativistic high-energy physics: top production and dark matter annihilation

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