Double Logarithms in $e^+ e^- \to J/\psi + \eta_c$

TL;DR

This paper investigates the origin of double logarithms in the NLO cross section of $e^+ e^- o J/ au + au_c$, identifying their sources and implications for factorization and resummation in helicity-flip processes.

Contribution

It provides a detailed analysis of the double logarithms in NLO corrections, distinguishing between Sudakov and end-point contributions, and discusses their impact on factorization theorems.

Findings

Double logarithms cancel in Sudakov regions after summing diagrams.

End-point regions correspond to soft or collinear spectator fermions.

Interpretation of end-point regions aids in establishing factorization and resummation methods.

Abstract

Double logarithms of $Q^2/m_c^2$ that appear in the cross section for $e^+e^-\to J/\psi + \eta_c$ at next-to-leading order (NLO) in the strong coupling $\alpha_s$ account for the bulk of the NLO correction at $B$-factory energies. (Here, $Q^2$ is the square of the center-of-momentum energy, and $m_c$ is the charm-quark mass.) We analyze the double logarithms that appear in the contribution of each NLO Feynman diagram, and we find that the double logarithms arise from both the Sudakov and the end-point regions of the loop integration. The Sudakov double logarithms cancel in the sum over all diagrams. We show that the end-point region of integration can be interpreted as a pinch-singular region in which a spectator fermion line becomes soft or soft and collinear to a produced meson. This interpretation may be important in establishing factorization theorems for helicity-flip processes, such as $e^+e^-\to J/\psi + \eta_c$, and in resumming logarithms of $Q^2/m_c^2$ to all orders in $\alpha_s$.