On this day in 1960, the biggest stars of their respective eras smiled, palled around and ‘danced’ together on television. But behind the scenes was a history of veiled insults, plus a surprising current love triangle and a tangled future.

Just two years before, Frank Sinatra had publicly blasted rock and roll: “It is the most brutal, ugly, degenerate, vicious form of expression it has been my displeasure to hear… It smells phony and false. It is sung, played and written for the most part…