I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
If she has no witnesses to you making the alleged statements, that may work in your favor. HR will talk to you and the other person involved to try to get to the root of what happened. If they're trying to say you don't like black people, then it may help to have pictures of your family handy so you can show how ridiculous that statement is.
As far as legal action goes, it's defamation of character to make untrue statements against someone that harm your reputation. Telling everyone you made racist comments that you did not make cold fall within that category. You have the burden of proving she said you did that (if HR has records of a complaint or grievance process, or if anyone who overheard her statements, that would help). If you wind up losing your job (and I hope you don't), you may also have a case for intentional interference with employment. But you can get damages for defamation from small claims if anyone heard her comments and thought less of you.
Also, is this an ongoing issue with that particular co-worker? Hostile work environments based on someone's race don't have to be just the employee's race. if your co-worker is subjecting you to negative treatment because of the race of your wife and children, then that's discrimination and you may have a claim. The company, once they're aware of the behavior, is supposed to take steps to stop it. That may be something else to talk to HR about.
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