Extracting the light quark mass ratio m_u/m_d from bottomonia transitions

TL;DR

This paper introduces a novel method to determine the light quark mass ratio m_u/m_d through bottomonia transitions, emphasizing the dominance of light quark mass differences in decay amplitudes for precise measurement.

Contribution

It presents a new approach using bottomonia transitions to extract m_u/m_d, with strategies to minimize theoretical uncertainties and suggestions for experimental searches.

Findings

Decay amplitudes mainly influenced by light quark mass differences.

Proposed decay channels offer a promising way to measure m_u/m_d.

Identification of the $9_b$ state via $9_b o h_b\u03b6$ transitions.

Abstract

We propose a new method to extract the light quark mass ratio $m_u/m_d$ using the $\Upsilon(4S)\to h_b\pi^0(\eta)$ bottomonia transitions. The decay amplitudes are dominated by the light quark mass differences, and the corrections from other effects are rather small, allowing for a precise extraction. We also discuss how to reduce the theoretical uncertainty with the help of future experiments. As a by-product, we show that the decay $\Upsilon(4S)\to h_b\eta$ is expected to be a nice channel for searching for the $h_b$ state.