RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function

Abstract

The three renormalization-group-accessible three-loop coefficients of powers of logarithms within the \bar{MS} series momentum-space for the QCD static potential are calculated and compared to values obtained via asymptotic Padé-approximant methods. The leading and next-to-leading logarithmic coefficients are both found to be in exact agreement with their asymptotic Padé-predictions. The predicted value for the third RG-accessible coefficient is found to be within 7% relative |error| of its true value for n_f leq 6, and is shown to be in exact agreement with its true value in the n_f \to \infty limit. Asymptotic Padé estimates are also obtained for the remaining (RG-inaccessible) three-loop coefficient. Comparison is also made with recent estimates of the three-loop contribution to the configuration-space static-potential function.

13 pages, LaTeX, additional discussion on the results

References in corpus (1)

• Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Cited by in corpus (33)

• Effective field theories for heavy quarkonium
• The QCD Running Coupling
• Three-loop static potential
• Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order
• Fermionic contributions to the three-loop static potential
• Heavy Quarkonium Spectrum at $\mathcal{O}({\alpha }_s^5{m}_q)$ and Bottom/Top Quark Mass Determination
• Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin
• The static potential: lattice versus perturbation theory in a renormalon-based approach
• The QCD static energy at NNNLL
• The logarithmic contribution to the QCD static energy at NNNNLO
• Heavy Quarkonium Spectrum and Production/Annihilation Rates to order ${\beta }_0^3{\alpha }_s^3$
• Determination of the Static Potential with Dynamical Fermions
• Precision determination of r_0Lambda_MS from the QCD static energy
• Power corrections in the quark-antiquark potential at finite temperature
• Closed-Form Summation of RG-Accessible Logarithmic Contributions to Semileptonic B-Decays and Other Perturbative Processes
• Lambda_msbar from the static potential for QCD with n_f=2 dynamical quark flavors
• Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• QED Effective Action Revisited
• Determination of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ and analytic parameterization of the static quark-antiquark potential
• ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential
• Top mass determination and O (alpha_S^5 m) correction to toponium 1S energy level
• The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods
• Resummations of free energy at high temperature
• Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation
• Extraction of alpha_s from the Gross--Llewellyn Smith sum rule using Borel resummation
• Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation
• Heavy quark mass determination from the quarkonium ground state energy: a pole mass approach
• NNNLO correction to the toponium and bottomonium wave-functions at the origin
• Three Loop Estimate of the Inclusive Semileptonic $b\to c$ Decay Rate
• Quark-antiquark static energy from a restricted Fourier transform
• $\sigma (e^{+}{e}^{-}\to hadrons)$ and the Heavy Quark Masses
• Potential Nonrelativistic QCD and Heavy Quarkonium Spectrum in Next-to-Next-to-Next-to-Leading Order