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

Abstract

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.