There is a moment in the making of “I Want to Hold Your Hand” that Paul McCartney later described with unusual economy. He hit a chord. John Lennon turned. “That’s it,” he said. “Do that again.” The two were writing nose to nose, guitars ringing against each other, in the kind of close-quarters alchemy that had already propelled them through three UK number ones in 1963.

That run had taught them to trust speed. “From Me to You” topped the first official UK singles chart. “She Loves You” smashed sales records and bent pop convention by delivering the story through a friend’s reported speech. But the ambition had been lit long before. Lennon used to rally the band in grim dressing rooms with a question: “Where are we going, fellas?” The answer, in mock American voices, came back: “To the toppermost of the poppermost.”

By February 1964, when they stepped off the Pan Am jet at JFK, the chaos that greeted them wasn’t spontaneous. It had been primed, weeks earlier, by a single that reset the transatlantic pop current. “I Want to Hold Your Hand” wasn’t just a hit. It was the exact frequency America was waiting to pick up, and the Beatles knew it before the plane left the ground.