Question for parents: If your kids are fighting do you get involved or let them work it out

My two older teens haven't spoken to each other in almost 2 weeks. This all started over a rumor. Sorry if this gets confusing. I'll try to keep it simple. My son's best friend Anthony, dated a girl named Adeline. Anthony and Adeline broke up. My kids went to a summer party for a friend. Adeline asked to talk to my son in private. According to my son she just wanted to know if my son's best friend cheated on her. My daughter and her friends saw them leave and go into a room. They assumed they were hooking up. Daughter started a rumor that my son and Adeline hooked up. My son said they never hooked up. Adeline said they never hooked up. Anthony found out about the rumor because it got around and now Adeline is being bullied and called a "homie hopper". First day of school Anthony clocks my son in the face and gave him a really bad black eye. Fight breaks out. Idk what's going on. I have to pick him up. I ask what happened. He said "Trisha and her stupid fucking rumors!" Talked to my daughter when she got home. She said she just assumed they hooked up. My son said he did not hook up with Adeline. He's never been with any girl. They were arguing because my daughter said it's not her fault that Anthony hit him. My son blamed her for starting a rumor and now his best friend hates him over something that never happened. Now they won't talk to each other. I've also received calls from Adelines mom that my daughter has spread rumors and causing bullying. At this point do I just let my kids work it out or step in?