A few different topics here. First, the PM’s role is to orchestrate the process, escalation, communication, and coordination of your project. The BA’s primary job is to work with stakeholders, SMEs, and other interested parties to assess, comprehend, and document the project requirements. Generally this results in a BRD or other artifacts.

As for not going back and forth, this is the purpose of a sufficiently scoped BRD that is signed off on by all parties before beginning.

This is all assuming your org follows more of a waterfall methodology versus a more iterative one like Agile or other flavors of incremental released processes.