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An overview of current experimental bounds on $CPT$ violation in neutralmeson mixing is given. New values for the $CPT$ asymmetry in the $B^0$ and$B_s^0$ systems are deduced from published BaBar, Belle and LHCb results. Withdedicated analyses, LHCb will be able to further improve the bounds on $CPT$violation in the $D^0$, $B^0$ and $B_s^0$ systems. Since $CPT$ violationimplies violation of Lorentz invariance in an interacting local quantum fieldtheory, the observed $CPT$ asymmetry will exhibit sidereal- and boost-dependentvariations. Such $CPT$-violating and Lorentz-violating effects are accommodatedin the framework of the Standard-Model Extension (SME). The large boost of theneutral mesons produced at LHCb results in a high sensitivity to thecorresponding SME coefficients. For the $B^0$ and $B_s^0$ systems, usingexisting LHCb results, we determine with high precision the SME coefficientsthat are not varying with sidereal time. With a full sidereal analysis, LHCbwill be able to improve the existing SME bounds in the $D^0$, $B^0$ and $B_s^0$systems by up to two orders of magnitude.

Status and prospects for $CPT$ and Lorentz invariance violation searches in neutral meson mixing