Study on the radiative decays of $\Upsilon(nS)\to \eta_b+\gamma$

TL;DR

This paper investigates the radiative decay of bottomonium states, especially $Upsilon(nS) o eta_b+gamma$, using the light-front quark model, and compares theoretical predictions with recent experimental data to explore potential exotic components of $Upsilon(5S)$.

Contribution

It provides a theoretical estimation of decay widths for $Upsilon(nS) o eta_b+gamma$ within the light-front quark model, analyzing the $Upsilon(5S)$ decay to test for exotic state components.

Findings

The direct decay rate of $Upsilon(5S) o eta_b+gamma$ is consistent with lower $Upsilon(nS)$ states.

If inelastic final state interactions are significant, the decay rate for $Upsilon(5S)$ should be notably larger.

The study supports the potential for using radiative decays to probe exotic components in $Upsilon(5S)$.

Abstract

In this work, we investigate the characteristics of the spin-singlet state $\eta_b$ of the bottomonia family via the radiative decays of $\Upsilon(nS)\to \eta_b+\gamma$. The theoretical estimation of the decay widths is carried out in terms of the light-front quark model (LFQM). Recently CLEO and BaBar collaborations have measured $\mathcal{B}(\Upsilon(3S)\to\gamma\eta_b)$ and the mass of ${\eta_b}$. In terms of the data we fix the concerned input parameters in our calculations of $\Upsilon(nS)\to \eta_b+\gamma$. A special attention is paid on the transition of $\Upsilon(5S)\to \eta_b+\gamma$. The BELLE data showed that the width of $\Upsilon(5S)\to \Upsilon(2S,1S)+\pi\pi$ is two orders larger than that of $\Upsilon(4S)\to \Upsilon(2S,1S)+\pi\pi$, thus some theoretical explanations have been proposed. Among them, it is suggested the inelastic final state interaction (IFSI) $\Upsilon(5S)\to B\bar B\to \Upsilon(1S)+\pi\pi$ may be a natural one. If so, a similar mechanism also applies to $\Upsilon(5S)\to B^{(*)}\bar B^{(*)}\to \eta_b+\gamma$, the precise measurement would serve as a good test whether $\Upsilon(5S)$ possess exotic components. Our calculation in the LFQM indicates that the rate of the direct process $\Upsilon(5S)\to\eta_b+\gamma$ is not anomalous compared to $\Upsilon(mS)\to\eta_b+\gamma (m=1,2,3,4)$, thus if the IFSI does apply, the rate of $\Upsilon(5S)\to\eta_b+\gamma$ should be larger than the others by orders.