A new series by NPR seeks to answer that. Money quote from part 1:
"Sigmund Freud declared God to be a delusion, and others maintained that God, if there is such a thing, is beyond the tools of science to measure.
But now, some researchers are using new technologies to try to understand spiritual experience. They're peering into our brains and studying our bodies to look for circumstantial evidence of a spiritual world. The search is in its infancy, and scientists doubt they will ever be able to prove — or disprove — the existence of God."
Podcast is here. Oh, how I love science.