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 $\mathbb{Z}_p$-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 $\mu $-invariants vanish. This gives an alternative method to reprove a recent result of Matar on the vanishing of the $\mu $-invariants of plus and minus signed Selmer groups for elliptic curves.