Line shape and the experimental determination of the J/ψ→γηc branching fraction

Jorge Segovia,Jaume Tarrús Castellà

doi:10.1103/physrevd.104.074032

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.

Highlights

Heavy quarkonium systems are nonrelativistic bound states characterized by three well-separated scales m ≫ p ∼ 1=r ∼ mv ≫ E ∼ mv2; ð1Þ with m the heavy quark mass, p the relative momentum of the heavy quarks, and E the bound state energy
We study this line shape in a nonrelativistic effective field theory framework of quantum chromodynamics including the finite width of the ηc and include Oðv2Þ corrections
We propose a modified version of the potential NRQCD (pNRQCD) photon spectrum line shape for the J=ψ → γηc → γX decay in which the terms that originate the UV divergences in the width are subtracted in a manner consistent with the calculation of the decay width in dimensional regularization (DR) and the MS scheme, which we detail in Sec

Summary

INTRODUCTION

Heavy quarkonium systems are nonrelativistic bound states characterized by three well-separated scales m ≫ p ∼ 1=r ∼ mv ≫ E ∼ mv; ð1Þ with m the heavy quark mass, p the relative momentum of the heavy quarks, and E the bound state energy. A line shape for the photon spectrum of the J=ψ → γηc → γX decay process obtained from weakly coupled pNRQCD, incorporating a finite width for the ηc, was presented in Ref.

SUBTRACTED LINE SHAPE AND DECAY WIDTH FROM EFT

ANALYSIS OF CLEO’S DATA

CONCLUSIONS