Unfortunately, it's hard to answer the science piece simply because Wilder and Lehman draw from a number of different sources. The best place to start is probably with this online article by Wilder: The Theoretical Basis for the Life Model. That article will refer people to his sources, where they can explore further.
As Wilder states in that article, the main Pain Processing Pathway concept comes from Allan Schore with some modifications based on the work of Daniel Siegel. I've read Siegel's The Developing Mind and it's FULL of IP stuff in different language. But if you know the concepts, you'll recognize everything from trauma and capacity, to attunement and attachment, to awareness of body and emotion. It's not an easy read, but it covers a wide range of brain research and summarizes it in a coherent way with excellent source citation. I would probably start there before going to Schore.Lehman also adds a few more brain science details in Outsmarting Yourself, and I think he cites pretty well, at least for the brain studies that he narrates. I'm not sure how well he cites sources for the PPP and RCs, but those are rooted in the work Wilder cites in the article above. Lehman's new book on Immanuel Prayer also offers many personal testimonies and data from using IP in international settings. These aren't officially researched sources, but they give substantive evidence for the impact of IP on people's lives.
So I think those resources should be plenty of reading and lead you on to other sources along the way.