QCD and Relativistic $O(\alpha_{s}v^2)$ Corrections to Hadronic Decays of Spin-Singlet Heavy Quarkonia $h_c, h_b$ and $\eta_b$

TL;DR

This paper computes QCD and relativistic corrections to the decay widths of spin-singlet heavy quarkonia, achieving predictions consistent with experimental data and highlighting the significance of these corrections, especially for charmonium states.

Contribution

It provides the first detailed calculation of $O( ext{alpha}_s v^2)$ corrections to these decay processes within nonrelativistic QCD, improving theoretical predictions.

Findings

Corrections are small for bottomonium but significant for charmonium.

Negative $O( ext{alpha}_s v^2)$ correction lowers the decay width of $h_c$.

Predictions align well with recent experimental measurements.

Abstract

We calculate the annihilation decay widths of spin-singlet heavy quarkonia $h_c, h_b$ and $\eta_b$} into light hadrons with both QCD and relativistic corrections at order $O(\alpha_{s}v^{2})$ in nonrelativistic QCD. With appropriate estimates for the long-distance matrix elements by using the potential model and operator evolution method, we find that our predictions of these decay widths are consistent with recent experimental measurements. We also find that the $O(\alpha_{s}v^{2})$ corrections are small for $b\bar{b}$ states but substantial for $c\bar{c}$ states. In particular, the negative contribution of $O(\alpha_{s}v^{2})$ correction to the $h_{c}$ decay can lower the decay width, as compared with previous predictions without the $O(\alpha_{s}v^{2})$ correction, and thus result in a good agreement with the recent BESIII measurement.