"Accidentally"

I don't believe it's possible to cheat on someone on accident. I do think people do it and regret it right after, but that doesn't make it an accident.

Nah man. You need to let your current partner go. It's not fair to ask someone to trust you again after that, and I think it's pretty clear that you don't actually love your current partner. If you did, you wouldn't have gone and seen your ex like that. You knew what you were doing. I'm not saying you're a terrible person for doing it, but if you were willing to cheat on your partner then she's not the one and it's horribly selfish and cruel to expect her to move past your infidelity.