B737 Captain reported during push back from gate; the tow bar broke away and the aircraft rolled back. Captain applied brakes and stopped the aircraft.

Narrative

After before push checklist and brake release push (RP) clearance was received off [Gate] XX. Communication with pushback crew/tug was spotty at best due to wireless connection. Approximately half way thru push a faint and scratchy verbiage of aaahhhh; stop" was expressed from push crew. At that time a breakaway from the tug had taken place and the airplane was moving on its own with no link/control from tug. I followed procedure and gently applied brakes to prevent tail stand and bring airplane to a stop which I estimate took 10-20 feet of roll. At that time I asked the ground crew if the airplane had broken away and a very timid voice was heard saying "yeah". Parking brake was applied and brake pressure verified. Note: Cleared to start engines was not given prior to this event. Ground crew members approached airplane and began to work in nose wheel area out of sight to myself and FO (First Officer). After a period of time Ramp Management and aircraft maintenance also approached airplane.After a period of time in an attempt to gain further situational awareness all while preserving two way comms with push crew I instructed FO to suspend push with Ramp Control and contact ZZZ Operations. Due to complexity of what was needed for my own SA (Situational Awareness) I monitored both radio frequencies. At that time; in an admitted stern voice I requested push crew to get a non wireless headset to communicate with me as there were still challenges with poor comms due to wireless connection. Operations advised over radio that the tow bar was a clean break and Maintenance verified no damage and no break in Maintenance Release. What I think to be a new tow bar was hooked up and comms verified with push crew. At that time a new wired headset was given to push at our request with much clearer audio resulting in enhanced SA and communication ability. Pushback verbiage was commenced again; clearance was received and airplane was pushed back successfully to normal ramp position. During push engine start clearance was received. After complete pushback was accomplished normal parking brake procedures and disconnect was actioned. I noticed after an abnormal amount of time that the airplane was not disconnected from tug. At that moment push advised that they were having a difficult time disconnecting tow bar from plane. A number of personnel approached nose of airplane and I witnessed a member of management walk to airplane then back away from airplane and utilize his phone in some way. Once again Operations was contacted on frequency and advised me that Ramp Maintenance and Aircraft Maintenance were inbound to plane. After 5-7 minutes tow bar was finally able to be disconnected. I was given a thumbs up by Maintenance as I requested once again a visual inspection by them thru Operations. Airplane was cleared and disconnect headset command was given. Remainder of ground operation proceeded normally.Note: Engine 2 (Right) was running as start was underway before disconnect issue was realized. Comments:Air Carrier X is a safety focused and threat forward airline with the principle of Safety being paramount to this specific event. Our communication system during today's event was grossly inadequate at a moment when the flight crew required the need to have clear communications with ground crew. The wireless option available as a whole is very poor in audio and scratchy/intermittent in voice ability.Manual verbiage needs to be available and present to fight crew with how to handle these types of event along with considerations to possibly apply to aide such events. I as a Captain almost felt backed into a corner communications wise.Yes; non-standard phraseology was utilized today from push crew attempting to tell me that the airplane had broken away from tug. While this may be an example of what not to say as the term "stop" is ambiguous at that point I am proud of that push crew member for stating a more serious word to get theflight crew attention. The words "breakaway" used multiple times is a trigger word that needs to be conveyed to all push crews as it is clear and direct and will lead crew to regain control of airplane without having to think; much like other trigger words in our policies. Air Carrier X is an airline that thrives on timing performance and for good reason as it keeps our customers happy and coming back to us for their travel needs. I have noticed that ZZZ Ramp push crews push airplanes back much faster than other hubs or stations. Perhaps a feeling on complacency is apparent as those crews only push straight back in ZZZ. There may be a feeling that pushing us back fast is helping the operations. I would also like to think that high pushback speeds create much higher stress loads on equipment. Perhaps an exercise of evaluating breakaways between stations can show some parallels to certain stations habits. Close:I am thankful that not a single person or airplane was hurt in this event. A push crew member did a good job even though it wasn't standard and the airplane was able to depart without additional stress to passengers and their schedule even though we took a 20 minute arrival delay initially; some time was made up in air.Communication equipment needs to be evaluated on a Threat and Error Management basis but also as a way to apply safety principles. Procedures may need to be reviewed. I as Captain reflected on the event and know that I am going to manage certain aspect differently should this type of event happen again."