η - η′ mixing: From electromagnetic transitions to weak decays of charm and beauty hadrons

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 nonperturbative 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 semileptonic decays of D+, D-s(+), and B+ mesons. The resulting insights will be instrumental in treating even nonleptonic B transitions involving eta and eta ' and their CP asymmetries; thus they can sharpen the case for or against new physics intervening there.