Air Carrier Captain reported during push back operations at BOS airport; a lack of communication and visual with tug resulted in aircraft rolling into tug.

Narrative

During pushback from gate; our tug became disconnected from the tow-bar while simultaneously communication over headsets with our tug driver was lost. Just prior to this occurring; we were in a normal pushback towards taxiway Alpha; tail south and had been cleared to start engines. We had begun to start engine one but as the pushback progressed towards the service road area; it seemed that our tug driver was starting to have some difficulty maneuvering the aircraft and that they were getting some slippage which prompted us to shut the engine down. We were now well clear of the gate area with the aircraft positioned around the non-movement/movement line for taxiway Alpha across from Quebec taxiway. The tug had been maneuvering so that it was positioned to the right of the aircraft nose and was not readily visible from the flight deck when the aircraft began moving forward.The aircraft movement still felt like it was being controlled by the tug and we had not received any warning that the tug had detached. Our First Officer caught sight of the tug to the right and behind his position which was the first indication that the tug had disconnected. In response; our First Officer applied his toe brakes; the aircraft came to a stop and the parking brake was set. It wasn't immediately apparent from the flight deck that the tug had contacted the airframe as we did not feel an obvious impact. Our First Officer opened his window to get a better view and he confirmed that the tug had contacted the airframe and was resting between the fuselage and front of the right engine nacelle. We communicated this information to BOS Operations + BOS ground Control and emergency services was contacted.The impact was more readily felt from the cabin and while we were still assessing the situation we received a call from our FA 1 who stated that they were getting a fuel smell in the cabin. Still not knowing the condition of the aircraft and the source of the smell; I asked our FA 1 to have the cabin crew at stations. After communicating with emergency services personal outside; verifying we did not have a fuel leak and that we would be able to return to a gate; I contacted the cabin crew and informed them the smell was likely from the discontinued engine start; posed no danger and that we would be returning to a gate for normal deplaning. Once the tug which had impacted our aircraft was moved; we were towed back to the gate and deplaned normally. No customers or crew were injured. The incident was reported to the appropriate personnel per our Flight Operations Manual and a maintenance logbook entry was made.