η - η' Mixing -- From Electromagnetic Transitions to Weak Decays of Charm and Beauty Hadrons (presented at Hadron 2011)

It has been realized for a long time that knowing the \eta and \eta' wave functions in terms of quark and gluon components probes our understanding of non-perturbative QCD dynamics. Great effort has been given to this challenge -- yet no clear picture has emerged even with the most recent KLOE data. We point out which measurements would be most helpful in arriving at a more definite conclusion. A better knowledge of these wave functions will significantly help to disentangle the weight of different decay subprocesses in semi-leptonic decays of D^+, D_s^+ and B^+ mesons. The resulting insights will be instrumental in treating even non-leptonic B transitions involving $\eta$ and $\eta^{\prime}$ and their CP asymmetries; thus they can sharpen the case for or against New Physics intervening there.