Line shape and the experimental determination of the $J/\psi \to \gamma\eta_c$ branching fraction

TL;DR

This paper models the photon spectrum in the decay of J/psi to eta_c using effective field theory, addressing divergences and proposing a subtraction method that aligns well with experimental data.

Contribution

It introduces a divergence subtraction method at the line-shape level within EFT, improving the theoretical-experimental agreement for the J/psi to eta_c gamma decay.

Findings

The proposed subtraction method effectively handles divergences in the photon spectrum.

Theoretical predictions show good agreement with CLEO experimental data.

Finite width and relativistic corrections are incorporated into the EFT framework.

Abstract

We study the photon spectrum line-shape of the $J/\psi \to \gamma\eta_c\to \gamma X$ decay process in a nonrelativistic effective field theory (EFT) framework of quantum chromodynamics (QCD). We take into account the finite width of the $\eta_c$ and include $\mathcal{O}(v^2)$ corrections. We observe that the photon spectrum line-shape is divergent at large energies due to polynomially and logarithmically divergent terms, that upon integration over the photon energies in Dimensional Regularization (DR) produce no contribution or can be renormalized. We propose to subtract these divergences at the line-shape level in a manner consistent with the calculation of the width in DR and $\overline{\hbox{MS}}$ scheme. We analyze CLEO's data with the proposed subtracted line-shape and find good agreement between the theoretical prediction and the experimental result.