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Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation

Antonio Pineda

TL;DR

The paper develops a next-to-leading-log renormalization-group framework for heavy-quarkonium production and annihilation near threshold within pNRQCD, enabling NLL accuracy for S-wave observables. It bridges QCD to NRQCD and then to pNRQCD, deriving RG equations for potentials and production currents to resum logs across hard, soft, and ultrasoft scales, and provides explicit expressions for vector and pseudoscalar current matching coefficients. A key finding is a disagreement with vNRQCD-based results in the spin-independent sector, while the spin-dependent terms agree; the work also yields the O(m α^8 ln^3 α) hydrogen-energy correction in the Appendix, extending the reach of precision predictions to near-threshold processes and sum-rule applications.

Abstract

In the framework of potential NRQCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy quarkonium production currents near threshold. This allows to obtain S-wave heavy-quarkonium production/annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to e^+e^- and to two photons. We also compute the O(mα^8\ln^3α) corrections to the Hydrogen spectrum.

Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation

TL;DR

The paper develops a next-to-leading-log renormalization-group framework for heavy-quarkonium production and annihilation near threshold within pNRQCD, enabling NLL accuracy for S-wave observables. It bridges QCD to NRQCD and then to pNRQCD, deriving RG equations for potentials and production currents to resum logs across hard, soft, and ultrasoft scales, and provides explicit expressions for vector and pseudoscalar current matching coefficients. A key finding is a disagreement with vNRQCD-based results in the spin-independent sector, while the spin-dependent terms agree; the work also yields the O(m α^8 ln^3 α) hydrogen-energy correction in the Appendix, extending the reach of precision predictions to near-threshold processes and sum-rule applications.

Abstract

In the framework of potential NRQCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy quarkonium production currents near threshold. This allows to obtain S-wave heavy-quarkonium production/annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to e^+e^- and to two photons. We also compute the O(mα^8\ln^3α) corrections to the Hydrogen spectrum.

Paper Structure

This paper contains 1 section, 24 equations, 4 figures.

Table of Contents

  1. Appendix: $O(m\alpha^8\ln^3\alpha)$ contributions to the Hydrogen energy

Figures (4)

  • Figure 1: One possible contribution to the running of $D_{d,s}^{(2)}$ at NLL. The first picture represents the calculation in terms of the free quark-antiquark propagator $G_c^{(0)}$ and the small rectangles the potentials. The picture below is the representation within a more standard diagrammatic interpretation in terms of quarks and antiquarks. The delta potentials are displayed as local interactions and the Coulomb potential as an extended in space (but not in time) object.
  • Figure 2: Diagrams, up to permutations, that contribute to the running of $B_s$.
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