Exclusive Radiative Decays of Z Bosons in QCD Factorization

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 ${\Lambda }_{\mathrm{QCD}}/m_Z$, 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 $({\Lambda }_{\mathrm{QCD}}/m_Z{)}^2$. 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 $M={\eta }^{(}{}^{\prime }{}^{)}$ 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 $\eta -{\eta }^{\prime }$ system. Future measurements of these decays could yield interesting information about these parameters and the gluon distribution amplitude.

Comments: 6 pages, 3 figures, 1 table, contribution to the proceedings of the 38th International Conference on High Energy Physics, 3-10 August 2016, Chicago, USA