Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case

Abstract

We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to $\mathcal{O}(1/m^2)$, and the corresponding contribution to the spectrum. This includes the static energy at next-to-next-to-next-to-leading logarithmic (NNNLL) order. As a byproduct of these results one could obtain the heavy quarkonium spectrum with N${}^3$LL accuracy for $l\ne 0$ (angular momentum) and $s=0$ (spin) states, setting the stage for the full analytic and numerical N${}^3$LL analysis of such quantity. We also compute the next-to-next-to-next-to-next-to-leading order (N${}^4$LO) ultrasoft spin-independent contribution to the heavy quarkonium mass and static energy.

23 pages. Some minor typos and mistakes throughout the text corrected. Physical results unchanged

References in corpus (9)

• Three-loop static potential
• Static QCD potential at three-loop order
• Nonperturbative determination of the QCD potential at O(1/m)
• Spin-dependent potentials from lattice QCD
• Heavy Quark Pair Production near Threshold with Potential Non-Relativistic QCD
• The QCD static energy at NNNLL
• The static potential in {\cal N}=4 supersymmetric Yang-Mills at weak coupling
• Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials
• The QCD static potential in D<4 dimensions at weak coupling

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• P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential
• Matching coefficients in NRQCD to two-loop accuracy
• Top quark precision physics at the International Linear Collider
• NNLL top-antitop production at threshold
• S-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Manifestly Soft Gauge Invariant Formulation of vNRQCD
• On renormalons of static QCD potential at $u=1/2$ and $3/2$
• Relativistic corrections to the static energy in terms of Wilson loops at weak coupling
• Renormalon free part of an ultrasoft correction to the static QCD potential