Is there a relation between the PF and the motor efficiency, Motor load , and would PF correction reduce the Green House Gases (GHG) to the atmosphere.

I would really appreciate it if you can provide me with real examples and case
studies in that field or if you can tell me here to find it over the net.

I read too many articles over the internet that impoving the PF will
improve the efficiency and reduce the GHG , but I am not convienced.

Thanks