Dead nerve tooth tooth broke off to gum line in back how can i treat the infection i have no pain in tooth?

See a dentist: See a dentist to determine whether or not the tooth can be salvaged or more likely removed and replaced.

What infection ?: Are you positive you have an infection? Even if you do, a dentist needs to evaluate the fractured tooth to determine the next course of action.. restoration or extraction. Have your dentist evaluate your mouth to determine if antibiotics are necessary... not advisable to take antibiotics when not needed.

Root canal or remove: A tooth that breaks at the gum line likely had a dead nerve. That's why it doesn't hurt. If the tooth has enough structure to be restored, you would need a root canal treatment to cleanthe infection, then a post and core and a crown. If too much of it is gone affecting the root structure, it is better to remove it and consider other options to replace the lost tooth.

Fractured off tooth: Cory, you may not even have an infection but a quick xray will tell the story! In today's world, we are often less heroic with saving a damaged root that is compromised and we are placing an implant at that site, which is like giving you a new, stronger root! See your dentist immediately to discuss options!

Broken tooth: You are very fortunate. A broken tooth with the pulp exposed releases gases that cause pain. BUT seek professional attention ASAP to assess the problem. If the gases become trapped the strong unrelenting pain will surely follow.