The vanishing of anticyclotomic μ-invariants for non-ordinary modular forms

Let K be an imaginary quadratic field where p splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic Zp-extension of K, showing that one inclusion of an Iwasawa main conjecture involving the p-adic L-function of Bertolini–Darmon–Prasanna implies that their μ-invariants vanish. This gives an alternative method to reprove a recent result of Matar on the vanishing of the μ-invariants of plus and minus signed Selmer groups for elliptic curves.