In fact, if you're lucky enough to live in the US, the hit is already happening: Problem came out there on Monday, and has knocked Pharrell's Happy off the top of the iTunes chart. It's number one in 29 other countries, too.
In the UK, though, it's not out until 6 July - for complicated music biz reasons about promotional "windows". This is happening increasingly often and it's a ridiculous state of affairs: The British system increasingly looks antiquated to an instant-gratification, on-demand generation of music consumers.
A six week gap between the US and UK release dates - during which time any idiot with an internet connection can stream or illegally download the song - unavoidably kills its chart performance (just ask Rihanna and Shakira). If the situation is allowed to continue, artists will start asking why they bother promoting their music in the UK at all.
That said, Ariana could make the gap work in her favour. Despite being a major star at home, all of the 20-year-old's singles have narrowly missed the top 40 over here. If she wraps up the US promo tour and gives Problem a real push in the UK, she could easily break that streak of bad luck.