Dr. Branch was born in Hopkinsville, Kentucky, received his M.D. from Tulane University Medical School (1935), interned at the Southern Pacific Hospital in San Francisco (1935–36), and served his residency at Mills Hospital in San Mateo, CA. Dr. Branch was a staff member of Queen of Angels Hospital in Los Angeles, CA (1937–42). He served in the U.S. Navy during WWII, and following the war, he served as Executive Officer of the Institute of Psychiatry in Philadelphia. From 1948–70, he was Chairman of Psychiatry at the Medical College of the University of Utah. He later moved to California, where he was Deputy Director of the Santa Barbara Mental Health Services (1970–71) and Emeritus Clinical Professor of Psychiatry at the University of Southern California in Los Angeles.
Dr. Branch was active in psychiatric and medical organizations. He was a member of the American Board of Psychiatry and Neurology (1954–62), President (1961–62), served on the National Advisory Board of the Mental Health Association (1952–61), President of the Research Foundation of the National Association for Mental Health (1965), a member of the Academy of Psychoanalysis, the American Association for the Advancement of Science, the American Association of Social Psychiatry, the American Geriatric Society, and the World Psychiatric Association. He gave the Ransom Memorial Lecture at Northwestern University (1951) and made many contributions to the psychiatric literature.
Dr. Branch served as Secretary-Treasurer (1958–61) of the American Psychiatric Association and President (1962–63).