# Exclusive Radiative Decays of Z Bosons in QCD Factorization

## TL;DR

This paper analyzes the rare Z boson decays into a meson and a photon using QCD factorization, showing that power corrections are negligible and that measurements can test theoretical predictions and probe meson structure.

## Contribution

It demonstrates that power corrections are negligible in Z boson decays to mesons and photons, and highlights the importance of renormalization-group effects for precise theoretical predictions.

## Key findings

- Power corrections are negligible due to suppression by (_{
m QCD}/m_Z)^2.
- Renormalization-group effects reduce sensitivity to hadronic uncertainties.
- Future measurements can test QCD factorization and explore meson-gluon structure.

## Abstract

We discuss the very rare, exclusive hadronic decays of a Z boson into a meson and a photon. The QCD factorization approach allows to organize the decay amplitude as an expansion in powers of $\Lambda_{\rm QCD}/m_Z\,$, where the leading terms contain convolutions of perturbatively calculable hard functions with the leading-twist light-cone distribution amplitudes of the meson. We find that power corrections to these leading terms are negligible since they are suppressed by the small ratio $(\Lambda_{\rm QCD}/m_Z)^2\,$. Renormalization-group effects play a crucial role as they render our theoretical predictions less sensitive to the hadronic input parameters which are currently not known very precisely. Thus, measurements of the decays $Z\to M\gamma$ at the LHC or a future lepton collider provide a theoretically very clean way to test the QCD factorization approach. The special case where $M=\eta^({}'{}^)$ is complicated by the fact that the decay amplitude receives an additional contribution where the meson is formed from a two-gluon state. The corresponding branching ratios are very sensitive to the hadronic parameters describing the $\eta-\eta'$ system. Future measurements of these decays could yield interesting information about these parameters and the gluon distribution amplitude.