$\mathit A_{CPT}$(t) is defined in terms of the time-dependent decay probabilities ${{\mathit P}}({{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$) and ${{\overline{\mathit P}}}({{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$) by $\mathit A_{CPT}$(t) = (${{\overline{\mathit P}}}−{{\mathit P}})/({{\overline{\mathit P}}}$ + ${{\mathit P}}$). For small mixing parameters x${}\equiv\Delta \mathit m/\Gamma $ and y${}\equiv\Delta \Gamma /2\Gamma $ (as is the case), and times t, $\mathit A_{CPT}$(t) reduces to [y $\mathit Re$(z) $−$ x $\mathit Im$(z)] $\Gamma $t, where z is the $\mathit CPT$-violating parameter. The following is actually y $\mathit Re$(z) $−$ x $\mathit Im$(z).

VALUE CL% DOCUMENT ID TECN  COMMENT $\bf{-14.6 \times 10^{-5} \text{ to 6.6 }\times 10^{-5}}$ 95 1 KRZEMIEN 2024 RVUE from LHCb data • • We do not use the following data for averages, fits, limits, etc. • • ($8.3$ $\pm6.5$ $\pm4.1$) $ \times 10^{-3}$ LINK 2003 B FOCS $\gamma $ nucleus, ${{\overline{\mathit E}}}_{\gamma }\approx{}$180 GeV 1  The constraints are derived by reinterpreting the LHCb measurement of the time-dependent asymmetry in the Cabibbo-favored ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ decay rates. These constraints can be directly translated into the flavor eigenstate decay width difference $\delta \Gamma $ = $\Gamma _{{{\mathit D}^{0}}} - \Gamma _{{{\overline{\mathit D}}^{0}}}$ by the relation $\delta \Gamma $ = (y$\mathit Re$(z) $−$ x$\mathit Im$(z)) ${\times }$ 2$\Gamma $, yielding ($-4.7$ $<$ $\delta \Gamma $ $<$ 2.1) ${\times }$ $10^{-16}$ GeV at 95$\%$ CL.

Conservation Laws:

$\mathit CPT$ INVARIANCE

References