Next-to-next-to-leading-order QCD corrections to hadronic width of pseudoscalar quarkonium

TL;DR

This paper calculates NNLO QCD corrections to pseudoscalar quarkonium decay rates, verifies NRQCD factorization at this order, and compares predictions with experimental data, revealing tensions especially for ηc decays.

Contribution

First verification of NRQCD factorization at NNLO for inclusive quarkonium decay and derivation of the RGE for the leading 4-fermion operator.

Findings

Severe tension between NRQCD predictions and ηc decay data.

NRQCD predictions for ηb decay are consistent with measurements.

Refined prediction for ηb to gamma gamma branching ratio: (4.8±0.7)×10^{-5}.

Abstract

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of NRQCD factorization for inclusive quarkonium decay process, for the first time, is verified to relative order $\alpha_s^2$. As a byproduct, the renormalization group equation (RGE) of the leading NRQCD 4-fermion operator ${\cal O}_1({}^1S_0)$ is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured $\eta_c$ hadronic width, and in particular the branching fraction of $\eta_c\to \gamma\gamma$. NRQCD appears to be capable of accounting for $\eta_b$ hadronic decay to a satisfactory degree, and our most refined prediction is ${\rm Br}(\eta_b\to \gamma\gamma) = (4.8\pm 0.7)\times 10^{-5}$.