Exotic to standard bottomonium transitions

TL;DR

This paper investigates the transition widths of certain bottomonium states, proposing that some are hybrid states, and employs effective field theory to compute decay widths, comparing results with experimental data.

Contribution

It introduces a novel analysis of bottomonium transitions using weakly coupled potential NRQCD, supporting the hybrid nature of $
10020$.

Findings

$
10020$ likely a hybrid bottomonium state

Computed transition widths agree with experimental data

Provided detailed decay mechanisms involving gluonic operators

Abstract

We study the transition widths of $\Upsilon(10753)$ and $\Upsilon(11020)$ into standard bottomonium under the hypothesis that they correspond to the two lowest laying $1^{--}$ hybrid bottomonium states. We employ weakly coupled potential NRQCD an effective filed theory incorporating the heavy quark and multipole expansions. We consider the transitions generated by the leading order and next-to-leading order singlet-octet operators. In the multipole expansion the heavy quark matrix elements factorize from the production of light-quark mesons by gluonic operators. For the leading order operator we compute the widths with a single $\pi^0$, $\eta$ or $\eta'$ in the final state and for the next-to-leading operator for $\pi^+\pi^-$ or $K^+K^-$. The hadronization of the gluonic operators is obtained, in the first case, from the axial anomaly and a standard $\pi^0-\eta-\eta'$ mixing scheme and, in the second case, we employ a coupled-channel dispersive representation matched to chiral perturbation theory for both the $S$ and $D$ wave pieces of the gluonic operator. We compare with experimental values and semi-inclusive widths. Our results strongly suggest that $\Upsilon(11020)$ is indeed a hybrid bottomonium state.