# Update on Quarkonium Spectroscopy and $\alpha_{strong}$ from NRQCD

## TL;DR

This paper updates quarkonium spectroscopy results using NRQCD, combining dynamical and quenched configurations to accurately determine the strong coupling constant and resolve discrepancies between different quarkonium systems.

## Contribution

It provides new NRQCD calculations for Upsilon and Charmonium, including dynamical quark effects, and refines the determination of the strong coupling constant at physical quark flavor number.

## Key findings

- Good agreement with Upsilon-based calculations
- Discrepancy in $eta$ between systems disappears with flavor extrapolation
- Systematic errors in $eta$ determination analyzed

## Abstract

NRQCD results for Upsilon and Charmonium using both dynamical and quenched configurations are presented. We investigate dependence on the light dynamical quark mass. Preliminary dynamical ($n_f = 2$) Charmonium data are combined with quenched results to extract the strong coupling constant $\alpha_P^{(n_f)}$ for the physical number of light dynamical quarks, $n_f = 3$. Good agreement is found with calculations based on the Upsilon system. We show that a discrepancy in $\alpha_P^{(n_f=0)}$, found between the Upsilon and Charmonium systems in the quenched theory, disappears upon extrapolating to the physical number of flavors. Results for the strong coupling constant $\alpha_{\overline{MS}}$ are presented and sources of systematic error investigated.