Radiative Leptonic Decay of Heavy Quarkonia

TL;DR

This paper analyzes the radiative leptonic decays of heavy quarkonia within the NRQCD framework, providing detailed distributions and establishing relations between decay widths, with implications for QED, QCD, and new physics searches.

Contribution

It offers a LO level analysis of heavy quarkonia decays, connecting decay widths across frames and highlighting discrepancies with existing literature, especially for tauonic channels.

Findings

Relative differences in decay width ratios are around 10% compared to literature.

Predicted decay width for $ au^+ au^-$ in $(2S)$ is four times larger than previous estimates.

Results have practical implications for QED, QCD, and new physics investigations.

Abstract

This study examines the properties of heavy quarkonia $X$ by treating them as bound states of $Q$ and $\bar{Q}$ at the LO level within the NRQCD framework, where $Q$ represents either a charm or a bottom quark. The branching ratios for the radiative leptonic decays $X\rightarrow \gamma l^{+} l^{-}$ are revisited and the angular and energy/momentum distributions of the final state particles are analyzed in the rest frame of $X$. Furthermore, we apply Lorentz transformations from the rest frame of $X$ to the center-of-mass frame of $l^+ l^-$ to establish the connection between the widths ${\Gamma_{X \rightarrow \gamma l^{+} l^{-}}}$ and ${\Gamma_{X \rightarrow l^{+} l^{-}}}$. When comparing the connection with those documented in the literature (divided by $2\pi$) for various $X$ states, such as $J/\Psi$, $\Psi(2S)$, $\Upsilon(1S)$, and $\Upsilon(2S)$, relative differences typically around or below 10\% can be found, which is comparable to the NLO corrections of $O(\alpha)$ and $O(v^4)$. However, we observe a significant disparity in the ratio between ${\Gamma_{\Psi(2S) \to \gamma \tau^+ \tau^-}}$ and ${\Gamma_{\Psi(2S) \to \tau^+ \tau^-}}$, with our prediction being four times larger than those in the literature. The outcomes derived from this study held practical implications in describing the QED radiative processes and contribute to the investigation of QCD processes associated with the decays of heavy quarkonia and the searches for new physics.