Your value will drop immediately, even if the girl is the kindest unicorn virgin herself.
Having a gf = you have a high value and you're desirable, raising the social status of those around you
No gf = you're an undesirable outcast with issues and you drag everyone down next to you
That's how it works.
You have to lie and come up with a fake story about your ex-gf. Keep it to a minimum and say you broke up because she moved, or because you didn't like her personality (it was you who initiated the break up, remember that)
Be smart not stupid. You must lie and adapt in this word, and if your lie doesn't hurt anyone else then it's cool.