Need help on a dimensional model scenario

Need suggestions to model the scenario explained below

I have a dimension "EXPERIMENT_DIM" which has a hierarchy Conceptual Phase -> Master Phase -> Implementation Phase. At each phase, I need to link a set of users responsible for running the phase and with a flag for one of them as primary user. The user data is available in "USER_DIM"

Do I need a bridge table between EXPERIMENT_DIM and USER_DIM to handle this scenario? Please suggest

Thanks in advance

The bridge table should be between User dim and the fact.