Cannabidiol Research Expansion Act This bill requires the Drug Enforcement Administration (DEA) and the Department of Health and Human Services to each evaluate whether cannabidiol, the nonpsychoactive substance derived from marijuana or the synthetic formulation, should be a controlled substance under the Controlled Substances Act. After taking into consideration the evaluations, the DEA must initiate proceedings for classifying cannabidiol as a controlled substance if control is warranted. The bill expands the authority for: (1) conducting medical research on cannabidiol and other nonpsychoactive components of marijuana, and (2) possessing or transporting cannabidiol or any other nonpsychoactive component of marijuana for certain medicinal purposes. The Department of Justice shall register an applicant to manufacture or distribute cannabidiol or marijuana for the purpose of commercial production if approved by HHS. Physicians who are licensed under state law may discuss the potential harms and benefits of cannabidiol or those components of marijuana as a treatment with their patients or the legal guardians of underage patients. The bill terminates four years after enactment.