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

INSPIRE   PDGID:
S032L02
p-value (%) EVTS DOCUMENT ID TECN  COMMENT
$0.6$ $\pm0.2$ 1.0M 1
AAIJ
2017AE
LHCB unbinned, $\mathit P$-odd
• • We do not use the following data for averages, fits, limits, etc. • •
$4.6$ $\pm0.5$ 1.0M 2, 3
AAIJ
2017AE
LHCB unbinned, $\mathit P$-even
$41$ 330k 2, 4
AAIJ
2013BR
LHCB ${{\mathit \chi}^{2}}$, $\mathit P$-even
1  This AAIJ 2017AE value tests $\mathit CP$ Violation in $\mathit P$-odd variables.
2  This value tests $\mathit CP$ Violation in $\mathit P$-even variables.
3  Not included in average as correlation to $\mathit P$-odd measurement using the same data is unclear.
4  See AAIJ 2017AE.
Conservation Laws:
$\mathit CP$ INVARIANCE
References