Order alpha_s^3 ln^2(1/alpha_s) Corrections to Heavy-Quarkonium Creation and Annihilation

TL;DR

The paper computes the leading non-RG double logarithms at N$^3$LO in NRQCD for heavy-quarkonium, specifically the corrections of order $\\alpha_s^3 \\ln^2(1/\\alpha_s)$ to the wave function at the origin, which controls production and annihilation rates. Two independent methods—the effective-theory (pNRQCD) framework and a direct phase-space analysis—yield the same non-RG LL corrections, validating the results. Numerical applications to top threshold production show roughly 7% normalization reduction near the 1S peak and a ~10% shrinkage of the 1S–threshold gap, while bottom-quark sum rules imply shifts of order tens of MeV in $m_b$. Overall, the work highlights the significance of non-RG LL terms at $N^3$LO and their interplay with RG logs, informing scale choices and the potential need for resummation in NRQCD threshold phenomenology.

Abstract

In the framework of nonrelativistic QCD, we compute the leading double-logarithmic corrections of order alpha_s^3 ln^2(1/alpha_s) to the heavy-quark-antiquark bound-state wave function at the origin, which determines the production and annihilation rates of heavy quarkonia. The phenomenological implications for the top-antitop and Upsilon systems are discussed.