${{\mathit D}^{\pm}}{{\mathit \chi}^{2}}$ TESTS OF $\mathit CP$-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 ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{\pm}}$

INSPIRE   PDGID:
S031L01
VALUE (%) EVTS DOCUMENT ID TECN  COMMENT
$\bf{78.1}$ 3.1M 1
AAIJ
2014C
LHCB ${{\mathit \chi}^{2}}$
1  AAIJ 2014C uses binned and unbinned methods, and finds slightly better sensitivity with the former. We took the first value in the table of results for the binned method.
Conservation Laws:
$\mathit CP$ INVARIANCE
References:
AAIJ 2014C
PL B728 585 Search for $\mathit CP$-Violation in the Decay ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$