Probing the CPT Constraint on CP Violation with $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$ Decay

The CPT theorem, combined with S-matrix unitarity, imposes nontrivial constraints on CP asymmetries in B-meson decays ~\cite{Marshak1969}. A long-standing question is whether these constraints apply in an inclusive manner—globally across all final states—or exclusively, within a final state interaction (FSI) as argued by Wolfenstein ~\cite{Wolfenstein1991}. We present the theoretical framework underlying this relationship between CP violation and the CPT theorem (CPV/CPT), deriving the CP-violating rate differences through the S-matrix formalism with final-state interactions (FSI). We propose that a precise measurement of the integrated CP asymmetry in $B^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$ can unambiguously discriminate between the two mechanisms.