Model-independent mass determination of near-threshold states from short-range production

TL;DR

The paper introduces a new, model-independent method to precisely determine the masses of near-threshold dimer states using short-range production rates and characteristic line shapes within effective field theory.

Contribution

It proposes a novel observable based on short-range production rates that allows for accurate mass extraction of near-threshold states, independent of specific models.

Findings

The method enables precise mass determination from experimental line shapes.

Characteristic line shapes exhibit a model-independent minimum for specific partial waves.

Application to $T_{bar{b}1}(10610)$ and $T_{bar{b}1}(10650)$ systems yields accurate binding energies.

Abstract

We propose a novel observable for the precision measurements of a wide class of near-threshold dimer states: the short-range production rate of a dimer--spectator two-body system, composed of the given near-threshold state and one of its constituents. Within the framework of nonrelativistic effective field theory, these production rates exhibit characteristic line shapes for the specific partial wave and reach a model-independent minimum. This feature enables a precise extraction of their masses from experimental data, provided that the line shape can be resolved with sufficient accuracy. Applying this novel method to both the $T_{b\bar{b}1}(10610)B$ and $T_{b\bar{b}1}(10650)B^*$ systems allows for a precise determination of the binding energy $\delta$ of the $T_{b\bar{b}1}(10610)$ and $T_{b\bar{b}1}(10650)$ via the relation of $\delta=-{E_{\text{dip}}^{\text{exp}}}/{0.1983}$ once the respective dip position $E_{\text{dip}}^{\text{exp}}$ is experimentally identified.