Sharon & Ozzy Osbourne Lunch Date in Beverly Hills

5/18/2013 2:09 PM PDT

Sharon & Ozzy Osbourne -- Lunch Date in Beverly Hills

In what appears to be their first public out since they split last month, Sharon and Ozzy Osbourne had lunch together today in Beverly Hills ... TMZ has learned.

According to our sources, the two dined at the Polo Lounge at the Beverly Hills Hotel. We're told Ozzy arrived first, accompanied by another man, and Sharon arrived a short time later.

The three dined at a booth inside, with our sources saying Sharon and Ozzy did not appear "romantic" ... rather more like a business lunch ... but the two were definitely talking.

As TMZ first reported, Sharon has been telling friends she would not consider getting back together with Ozzy until he proves he's sober for good this time. Last month, Ozzy wrote on Facebook that he had been sober since early March ... so if he has stayed clean, he'd be about 2.5 months sober now.

Time will tell if that's proof enough for Sharon that Ozzy has changed his ways.

UPDATE 2:20 PM PT -- One source tells us that by the end of the lunch, Ozzy and Sharon were "cozying up together in the booth."