The mass eigenstates ${{\mathit D}_{{1}}^{0}}$ and ${{\mathit D}_{{2}}^{0}}$ are related to the $\mathit C$ = $\pm1$ states by $|{{\mathit D}_{{1,2}}}>$ = p$~|{{\mathit D}^{0}}>$ + q $|{{\overline{\mathit D}}^{0}}>$. See the note on “${{\mathit D}^{0}}--{{\overline{\mathit D}}^{0}}$ Mixing” above.

“OUR EVALUATION” comes from CPV allowing averages provided by the Heavy Flavor Averaging Group. This would include as-yet-unpublished results, see the note on “${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing.''

VALUE EVTS DOCUMENT ID TECN  COMMENT $\bf{ 0.995 \pm0.016}$ OUR EVALUATION  HFLAV fit; see the note on ``${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing.'' $\bf{ 0.99 \pm0.05}$ OUR AVERAGE $0.996$ $\pm0.052$ 30.6M 1 AAIJ 2021 AB LHCB ${{\mathit p}}{{\mathit p}}$ at 13 TeV $1.05$ ${}^{+0.22}_{-0.17}$ 2.3M 2 AAIJ 2019 X LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV 3 AAIJ 2018 K LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV $0.90$ ${}^{+0.16}_{-0.15}$ ${}^{+0.08}_{-0.06}$ 4 PENG 2014 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ • • We do not use the following data for averages, fits, limits, etc. • • 5 AAIJ 2013 CE LHCB Repl. by AAIJ 2018K $0.86$ ${}^{+0.30}_{-0.29}$ ${}^{+0.10}_{-0.08}$ 6 ZHANG 2007 B BELL Repl. by PENG 2014 1  AAIJ 2021AB result comes form analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ events. 2  AAIJ 2019X measurement comes form analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays. ${{\mathit D}^{0}}$ come from ${{\mathit D}^{*+}}$ and ${{\overline{\mathit B}}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \mu}^{-}}{{\mathit X}}$ decays (and c.c.) in ${{\mathit p}}{{\mathit p}}$ collisions at 7 and 8 TeV. 3  Based on 5 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7, 8, 13 TeV. Allowing for $\mathit CP$ violation, the direct $\mathit CP$ violation in mixing is reported 1.00 $<$ $\vert $q/p$\vert $ $<$ 1.35 at the 68.3$\%$ CL for the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 4  The time-dependent Dalitz-plot analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ is employed. Decay-time information and interference on the Dalitz plot are used to distinguish doubly Cabibbo-suppressed decays from mixing and to measure the relative phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ . This value allows $\mathit CP$ violation and is sensitive to the sign of $\Delta \mathit m$. 5  Based on 3 fb${}^{-1}$ of data collected at $\sqrt {s }$ = 7, 8 TeV. Allowing for $\mathit CP$ violation, the direct $\mathit CP$ violation in mixing is reported 0.75 $<$ $\vert $q/p$\vert $ $<$ 1.24 at the 68.3$\%$ CL for the ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ . 6  The phase of p/q is ($-14$ ${}^{+16}_{-18}$ $\pm5)^\circ{}$. The ZHANG 2007B value is from the time-dependent Dalitz-plot analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ . Decay-time information and interference on the Dalitz plot are used to distinguish doubly Cabibbo-suppressed decays from mixing and to measure the relative phase between ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{*+}}{{\mathit \pi}^{-}}$ . This value allows $\mathit CP$ violation.

Conservation Laws:

$\mathit CP$ INVARIANCE

References:

AAIJ 2021AB PRL 127 111801 Observation of the Mass Difference Between Neutral Charm-Meson Eigenstates AAIJ 2019X PRL 122 231802 Measurement of the mass difference between neutral charm-meson eigenstates AAIJ 2018K PR D97 031101 Updated determination of $D^0$-$\overline{D}{}^0$ mixing and CP violation parameters with $D^0\to K^+\pi^-$ decays PENG 2014 PR D89 091103 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing and Search for Indirect $\mathit CP$ Violation using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays AAIJ 2013CE PRL 111 251801 Measurement of ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing Parameters and Search for $\mathit CP$ Violation using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ Decays ZHANG 2007B PRL 99 131803 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing Parameters in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays