I am working with Open Daylight Hydrogen controller and I want to know which routing protocol does it use by default to set the path for a flow. Is it possible to know those paths? What about other controllers as well like POX, Floodlight, etc?
No routing protocol is used.
The purpose of routing protocols is to tell other routers which paths are available, so the other routers can make a good forwarding decision. In SDN, the controller has a complete view of the network -- it already knows all the paths. The controller calculates the best path for a particular kind of data, and then uses a protocol like OpenFlow to tell the network devices how to forward data.
An SDN controller will utilize the openflow protocol to communicate with networking devices, whether they are physical or virtual. Openflow is not a routing protocol.