Search for violations of Lorentz invariance and $CPT$ symmetry in $B_{(s)}^0$ mixing

Violations of $CPT$ symmetry and Lorentz invariance are searched for by studying interference effects in $B^0$ mixing and in $B_s^0$ mixing. Samples of $B^0\to J\mathrm{/}\psi K_{\mathrm{S}}^0$ and $B_s^0\to J\mathrm{/}\psi K^{+}{K}^{-}$ decays are recorded by the LHCb detector in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb${}^{-1}$. No periodic variations of the particle-antiparticle mass differences are found, consistent with Lorentz invariance and $CPT$ symmetry. Results are expressed in terms of the Standard Model Extension parameter $\mathrm{\Delta }{a}_{\mu }$ with precisions of $\mathcal{O}({10}^{-15})$ and $\mathcal{O}({10}^{-14})$ GeV for the $B^0$ and $B_s^0$ systems, respectively. With no assumption on Lorentz (non-)invariance, the $CPT$-violating parameter $z$ in the $B_s^0$ system is measured for the first time and found to be $ $\mathcal{R}$e(z) = -0.022 \pm 0.033 \pm 0.005$and$ $\mathcal{I}$m(z) = 0.004 \pm 0.011\pm 0.002$, where the first uncertainties are statistical and the second systematic.