${{\mathit D}^{0}}$ $\mathit CP$-VIOLATING DECAY-RATE ASYMMETRIES

This is the difference between ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ partial widths for the decay to state ${{\mathit f}}$, divided by the sum of the widths:$
$ $\mathit A_{CP}({{\mathit f}}$) = [$\Gamma $( ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit f}}$ ) $−$ $\Gamma $( ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\overline{\mathit f}}}$ )] $/$ [$\Gamma $( ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit f}}$ ) + $\Gamma $( ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\overline{\mathit f}}}$ )].

$\mathit A_{\mathit CP}$( ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ) in ${{\mathit D}^{0}}$, ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$

INSPIRE   PDGID:
S032A12
VALUE (%) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.4 \pm0.4 }$ OUR AVERAGE
$+0.6$ $\pm0.9$ $\pm0.4$ 12.8k
ABLIKIM
2022BG
 BES3 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at 3.773 GeV
$0.43$ $\pm1.30$ 123k
ARINSTEIN
2008
BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$
$0.31$ $\pm0.41$ $\pm0.17$ 80k 1
AUBERT
2008AO
 BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10.6 GeV
$1$ ${}^{+9}_{-7}$ $\pm5$
CRONIN-HENNES..
2005
CLEO ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10 GeV
1  AUBERT 2008AO report their result using a different sign convention.
Conservation Laws:
$\mathit CP$ INVARIANCE
References:
ABLIKIM 2022BG
PR D106 092005 Absolute measurements of branching fractions of Cabibbo-suppressed hadronic D0(+) decays involving multiple pions
ARINSTEIN 2008
PL B662 102 Measurement of the Ratio B( ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ )/B( ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ) and the Time-Integrated $\mathit CP$ Asymmetry in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
AUBERT 2008AO
PR D78 051102 Search for $\mathit CP$ Violation in Neutral ${{\mathit D}}$ Meson Cabibbo-suppressed Three-body Decays
CRONIN-HENNESSY 2005
PR D72 031102 Searches for $\mathit CP$ Violation and ${{\mathit \pi}}{{\mathit \pi}}$ $\mathit S$ wave in the Dalitz-Plot analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$