Seeing your ex in the arms of another can be a truly difficult sight to have to deal with, when you love her and want nothing more than to work things out with her...but it IS possible that maybe it's not the terrifying thing it appears to be. In fact, it can actually be a positive sign for you!
Relax! It's really quite common for people just out of breakups to try to immediately give it another go out in the dating world. These are nothing but rebound relationships, and very rarely pose much of a threat to your chances of getting back together. Couples throughout history have gone through this and then still gotten back together and gone on to live very happy lives in loving relationships.
The vast majority of these relationships don't last a month...some not even two weeks! Their only purpose is to convince you that life without your ex isn't a barren wasteland without any kind of hope for the future...in fact, I tell a lot of the people in your situation that it's not necessarily a bad idea to try it themselves. It's not a betrayal (so long as it's really over as far as your ex is concerned), it helps you get back on your feet.
So you shouldn't take this as a sign that things between the two of you are permanently done with. You can still win her back, but you will have to adapt your strategy to fit this situation. A well-conceived and properly-executed plan is a powerful thing, and already essential for winning your ex back. You can get some help in forming your plan through the link in this next paragraph.