# $\vert$q/p$\vert$ INSPIRE search

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 This would include as-yet-unpublished results, see the note on ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing.''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
$\bf{ 0.92 {}^{+0.12}_{-0.09}}$ OUR EVALUATION  HFAG fit; see the note on ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing.''
$\bf{ 0.97 {}^{+0.14}_{-0.12}}$ OUR AVERAGE
$1.05$ ${}^{+0.22}_{-0.17}$ 2.3M 1
 2019 X
LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
2
 2018 K
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$0.90$ ${}^{+0.16}_{-0.15}$ ${}^{+0.08}_{-0.06}$ 3
 2014
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
4
 2013 CE
LHCB Repl. by AAIJ 2018K
$0.86$ ${}^{+0.30}_{-0.29}$ ${}^{+0.10}_{-0.08}$ 5
 2007 B
BELL Repl. by PENG 2014
1  AAIJ 2019X ${{\mathit D}^{0}}$ 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.
2  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ .
3  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 $\Delta \mathit m$.
4  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 ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$ .
5  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 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