A Geometric Framework for CPT Violation in Neutral Meson Mixing Using Biorthogonal Bargmann Invariants

We develop a geometric framework for characterizing CPT violation in neutral meson systems using Bargmann invariants formulated within a biorthogonal description of the non-Hermitian effective Hamiltonian governing neutral meson mixing. Interpreting CPT violation as a relative geometric deformation of the heavy- and light-state mixing directions in projective flavor space, we construct a fourth-order Bargmann invariant together with its CP-conjugate counterpart involving the physical mass eigenstates and experimentally accessible decay channels. From the phase of a rephasing-invariant product of these invariants, we define a geometric observable that isolates the CPT-violating contribution. The resulting formalism identifies the channel dependence of the geometric response and yields a selection criterion for decay-mode combinations exhibiting linear sensitivity to CPT violation. We further relate the geometric deformation to the Lorentz-violating coefficients of the Standard-Model Extension, showing that the resulting observable inherits the characteristic sidereal modulation of the SME framework. The present work provides a complementary geometric perspective on CPT violation in neutral meson mixing and establishes a foundation for future phenomenological studies of geometric signatures of CPT and Lorentz violation.