Bremsstrahlung in Leptonic Onia Decays: Effects on Mass Spectra

TL;DR

The paper extends Jegerlehner's analytic treatment of radiative decays to heavy quarkonia (J/psi, psi(2S), Upsilon(1S)), deriving an analytic dilepton mass spectrum for decays with photon emission. It uses a Lohse-based Monte Carlo with realistic detector resolutions to quantify smearing effects on the radiative tail and to develop a simple, robust parameterisation describing smeared mass spectra across resolutions. The proposed parameterisation separates a Gaussian core from a mass-dependent tail and expresses parameters as smooth functions of the mass resolution, enabling inclusive fits of l+l− and l+l−γ contributions in data. These results provide practical tools for precise mass determinations in high-statistics quarkonium spectroscopy where internal bremsstrahlung is non-negligible.

Abstract

In this note we present a study of the radiative tails in the invariant mass spectra of muon or electron pairs from J/psi, psi(2S) and Upsilon(1S) decays which is due to an additional emission of a photon. An analytic formula for dilepton mass spectra in radiative decays is derived and a Monte Carlo simulation for realistic detector conditions is used to study effects on the spectra. A rather simple parameterisation is given, suitable for the treatment of real data.

Figures (14)

• Figure 1: Parameter $C_{hard}$ as a function of the minimal energy $E_{min}$ of the photon in the $J/\psi$ rest frame for radiative decays $J/\psi \rightarrow \mu^+\mu^-\gamma$ (solid line) and $J/\psi \rightarrow e^+e^-\gamma$ (dashed line). The point with errors was evaluated from the $E760$ result e760.
• Figure 2: The parameter $C_{hard}$ as a function of the minimal energy $E_{min}$ of the photon in the rest frame of $J/\psi$ (solid line), $\psi(2S)$ (dashed line), and $\Upsilon(1S)$ (dotted line) decaying into $\mu^+\mu^-\gamma$ (a) or $e^+e^-\gamma$ (b).
• Figure 3: The parameters $C_{hard}$ (solid line) and $C_{soft}$ (dashed line) for the radiative decay $J/\psi \rightarrow \mu^+\mu^-\gamma$ as functions of the minimal photon energy $E_{min}$ in the rest frame of the $J/\psi$.
• Figure 4: The dimuon mass spectrum defined by eq. \ref{['pmass']} (solid line) and results of Monte Carlo simulation (points) of the decay $J/\psi \rightarrow \mu^+\mu^-\gamma$ for an ideal detector (without smearing, $4\pi$ acceptance) for $E_{min}$ = 10 MeV.
• Figure 5: Dimuon mass spectra in the radiative decay $J/\psi \rightarrow \mu^+\mu^-\gamma$ for $E_{min} = 10$ MeV (solid line) smeared with mass resolution of about 42 MeV (points connected by dashed line).