${{\mathit D}^{0}}$ TESTS OF LOCAL $\mathit CP$-VIOLATION ($\mathit CPV$)

We list model-independent searches for local $\mathit CP$ violation in phase-space distributions of multi-body decays.
Most of these searches divide phase space (Dalitz plot for 3-body decays, five-dimensional equivalent for 4-body decays) into bins, and perform a ${{\mathit \chi}^{2}}$ test comparing normalised yields ${{\mathit N}_{{{i}}}}$, ${{\overline{\mathit N}}_{{{i}}}}$ in $\mathit CP$-conjugate bin pairs ${{\mathit i}}$: ${{\mathit \chi}^{2}}$ = ${{\mathit \Sigma}_{{{i}}}}({{\mathit N}_{{{i}}}}$ $−$ ${{\mathit \alpha}}{{\overline{\mathit N}}_{{{i}}}})/{{\mathit \sigma}}({{\mathit N}_{{{i}}}}−{{\mathit \alpha}}{{\overline{\mathit N}}_{{{i}}}}$). The factor ${{\mathit \alpha}}$ = (${{\mathit \Sigma}_{{{i}}}}{{\mathit N}_{{{i}}}})/({{\mathit \Sigma}_{{{i}}}}{{\overline{\mathit N}}_{{{i}}}}$) removes the dependence on phase-space-integrated rate asymmetries. The result is used to obtain the probability (p-value) to obtain the measured ${{\mathit \chi}^{2}}$ or larger under the assumption of CP conservation [AUBERT 2008AO, BEDIAGA 2009 ]. Alternative methods obtain p-values from other test variables based on unbinned analyses [WILLIAMS 2011 , AAIJ 2014C]. Results can be combined using Fisher's method [MOSTELLER 1948 ].

Local $\mathit CPV$ in ${{\mathit D}^{0}}$, ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$

INSPIRE  
VALUE (%) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 4.9}$ OUR EVALUATION
$2.6$ 566k 1
AAIJ
2015A
LHCB unbinned method
$32.8$ 82k
AUBERT
2008AO
BABR ${{\mathit \chi}^{2}}$
1  Unusually, AAIJ 2015A assigns an uncertainty on the p value of $\pm0.5\%$. This results from limited test statistics.
Conservation Laws:
$\mathit CP$ INVARIANCE
References:
AAIJ 2015A
PL B740 158 Search for $\mathit CP$ Violation in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ Decays with the Energy Test
AUBERT 2008AO
PR D78 051102 Search for $\mathit CP$ Violation in Neutral ${{\mathit D}}$ Meson Cabibbo-suppressed Three-body Decays