Exclusive radiative Z-boson decays to mesons with flavor-singlet components

Abstract

We present a detailed study of the exclusive radiative decays Z → η ( ) γ employing the QCD factorization approach. We derive a factorization formula for the decay amplitudes valid at leading power in an expansion in (Λ 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 η −η system. Using the most recent estimates of these parameters, we obtain the branching ratios Br(Z → ηγ) ∼ 1.6 · 10 −10 and Br(Z → η γ) ∼ 4.7 · 10 −9 . A measurement of these processes at a future high-luminosity Z factory could provide interesting information on the gluon distribution amplitude.

The anomalous magnetic moment of the muon in the Standard Model

“…The first limit is commonly known as the Brodsky-Lepage (BL) limit [577,578], while the latter can be rigorously obtained from the operator product expansion (OPE) [582][583][584][585]. The η and η cases receive important α s corrections due to the anomalous dimension of the singlet axial current [586], which have been accounted for by the last factor [576,587,588]. Finally, higher-order corrections have been calculated using the OPE, which, for the π 0 , multiply Eq.…”

The anomalous magnetic moment of the muon in the Standard Model

“…The first limit is commonly known as the Brodsky-Lepage (BL) limit [600,601], while the latter can be rigorously obtained from the operator product expansion (OPE) [605][606][607][608]. The η and η ′ cases receive important α s corrections due to the anomalous dimension of the singlet axial current [609], which have been accounted for by the last factor [599,610,611]. Finally, higher-order corrections have been calculated using the OPE, which, for the π 0 , multiply Eq.…”

Exclusive weak radiative Higgs decays in the standard model and beyond

“…For the related case of Z → η ( ) γ decays these effects were studied in [18] and found to be very small. The branching ratios range from 6 · 10 −7 for the decay h → ωZ up to 1.5 · 10 −5 for the decay h → Υ(1S) Z.…”

“…For mesons containing heavy quarks, insight into the structure of the LCDAs can be obtained using heavy-quark effective theories such as NRQCD and HQET. The QCD factorization formula can be derived elegantly using soft-collinear effective theory [13][14][15][16], as has been demonstrated in [17,18].…”