${{\mathit D}^{\pm}}{{\mathit \chi}^{2}}$ 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 ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{\pm}}$

INSPIRE   PDGID:
S031L02
VALUE (%) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 31}$ OUR EVALUATION
$72$ 224k
LEES
2013F
BABR ${{\mathit \chi}^{2}}$
$12.7$ 370k 1
AAIJ
2011G
LHCB ${{\mathit \chi}^{2}}$
1  AAIJ 2011G publishes results for several binning schemes. We picked the first value in their table of results.
Conservation Laws:
$\mathit CP$ INVARIANCE
References:
LEES 2013F
PR D87 052010 Search for Direct $\mathit CP$ Violation in Singly Cabibbo-Suppressed ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{\pm}}$ Decays
AAIJ 2011G
PR D84 112008 Search for $\mathit CP$ violation in ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit \pi}^{+}}$ Decays