Renormalons in Electromagnetic Annihilation Decays of Quarkonium

TL;DR

This work analyzes the large-order behavior of perturbative series in NRQCD factorization for electromagnetic quarkonium decays (notably $J/\psi \to e^+e^-$ and $\eta_c \to \gamma\gamma$) using the large-$N_f$ limit and Borel resummation. It uncovers a universal, Borel-resummable renormalon at $u=-\tfrac{1}{2}$ arising from Coulomb-singularity cancellation, and shows that infrared renormalon ambiguities at $u=+\tfrac{1}{2}$ cancel with NRQCD matrix-element ambiguities at relative order $v^2$. The residues of the leading renormalons are computed for multiple decays, enabling estimates of higher-order radiative corrections and providing insight into the convergence properties of NRQCD perturbation theory for quarkonium EM decays. Overall, the paper links renormalon structure to NRQCD factorization and offers a framework to anticipate and absorb nonperturbative ambiguities into matrix elements, guiding future refinements of decay-rate predictions.

Abstract

We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/psi --> e^+e^- and eta_c --> gamma gamma. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-N_f limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the Coulomb singularity in the short-distance coefficients. We verify that the ambiguities in the short-distance coefficients from the first infrared renormalon are canceled by ambiguities in the nonperturbative NRQCD matrix elements that contribute through relative order v^2. Our results are used to estimate the coefficients of higher order radiative corrections in the decay rates for J/psi --> e^+ e^-, eta_c --> gamma gamma, and J/ψ--> gamma gamma gamma.