Abstract
We present a detailed study of the exclusive radiative decays $Z\to\eta^{(\prime)}\gamma$ employing the QCD factorization approach. We derive a factorization formula for the decay amplitudes valid at leading power in an expansion in $(\Lambda_{QCD}/m_Z)^2$, which includes convolutions of calculable hard-scattering kernels with the leading-twist quark and gluon light-cone distribution amplitudes of the mesons. Large logarithms arising in the evolution from the high scale $m_Z$ down to hadronic scales are resummed using the renormalization group, carefully accounting for the effects of the heavy bottom and charm quarks. Our results for the branching ratios are very sensitive to hadronic input parameters, such as the decay constants and mixing angle characterizing the $\eta-\eta'$ system. Using the most recent estimates of these parameters, we obtain the branching ratios $Br(Z\to\eta\gamma)\sim 1.6\cdot 10^{-10}$ and $Br(Z\to\eta'\gamma)\sim 4.7\cdot 10^{-9}$. A measurement of these processes at a future high-luminosity Z factory could provide interesting information on the gluon distribution amplitude.
Highlights
Is formed from two collinear gluons instead of a quark-antiquark pair
We derive a factorization formula for the decay amplitudes valid at leading power in an expansion in (ΛQCD/mZ)2, which includes convolutions of calculable hard-scattering kernels with the leading-twist quark and gluon light-cone distribution amplitudes of the mesons
In previous work the QCD factorization formula for exclusive radiative decays Z → M γ was derived for the case of flavor-nonsinglet pseudoscalar or vector mesons M = P or V, which are produced via a quark-antiquark pair [11]
Summary
In previous work the QCD factorization formula for exclusive radiative decays Z → M γ was derived for the case of flavor-nonsinglet pseudoscalar or vector mesons M = P or V , which are produced via a quark-antiquark pair [11]. A second form factor, which is allowed by Lorentz invariance, vanishes since the final-state meson P is an eigenstate of the charge-conjugation operator. At leading order in an expansion in powers of (ΛQCD/mZ), the form factor for the case of Z → π0γ decays reads [11]. The physical η and η mesons are complicated mixtures of quark-antiquark states with different flavor. More profoundly, the flavor-singlet quark-antiquark state mixes with a pure gluon state under renormalization, and the η and η mesons can be produced via a two-gluon LCDA
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