The Iwasawa μ-invariant of p-adic Hecke L-functions

For an odd prime p, we compute the mu-invariant of the anticyclotomic Katz p-adic L-function of a p-ordinary CM field if the conductor of the branch character is a product of primes split over the maximal real subfield. Except for rare cases where the root number of the p-adic functional equation is congruent to - 1 modulo p, the invariant vanishes.