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Model-independent search for $CP$ violation in $D^{0} \to K^{-}K^{+}\pi^{-}\pi^{+}$ and $D^{0} \to \pi^{-}\pi^{+}\pi^{+}\pi^{-}$ decays

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Abstract

A search for CP violation in the phase-space structures of D0 and D0bar decays to the final states K-K+pi-pi+ and pi-pi+pi+pi- is presented. The search is carried out with a data set corresponding to an integrated luminosity of 1.0fb^-1 collected in 2011 by the LHCb experiment in $pp$ collisions at a centre-of-mass energy of 7TeV. For the K-K+pi-pi+ final state, the four-body phase space is divided into 32 bins, each bin with approximately 1800 decays. The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is a CP asymmetry greater than 6.5% observed. The phase space of the pi-pi+pi+pi- final state is partitioned into 128 bins, each bin with approximately 2500 decays. The $p$-value under the hypothesis of no CP violation is 41%, and in no bin is a CP asymmetry greater than 5.5% observed. All results are consistent with the hypothesis of no CP violation at the current sensitivity.

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Distributions of (\subref*{fig:mass:KKPiPi:D},\subref*{fig:mass:FourPi:D},\subref*{fig:mass:KThreePi:D}) $ m(hhhh)$ and (\subref*{fig:mass:KKPiPi:DELTAM},\subref*{fig:mass:FourPi:DeltaM},\subref*{fig:mass:KThreePi:DELTAM}) $\Delta m$ for (\subref*{fig:mass:KKPiPi:D},\subref*{fig:mass:KKPiPi:DELTAM}) $ D ^0 \!\rightarrow K ^- K ^+ \pi ^- \pi ^+ $ , (\subref*{fig:mass:FourPi:D},\subref*{fig:mass:FourPi:DeltaM}) $ D ^0 \!\rightarrow \pi ^- \pi ^+ \pi ^+ \pi ^- $ , and (\subref*{fig:mass:KThreePi:D},\subref*{fig:mass:KThreePi:DELTAM}) $ D ^0 \!\rightarrow K ^- \pi ^+ \pi ^+ \pi ^- $ candidates for magnet up polarity. Projections of the two-dimensional fits are overlaid, showing the contributions for signal, combinatorial background, and random soft pion background. The contributions from $ D ^0 \!\rightarrow K ^- \pi ^+ \pi ^- \pi ^+ \pi ^0 $ and $ D _{s}^{+}\!\rightarrow K ^- K ^+ \pi ^- \pi ^+ \pi ^+ $ contamination are also shown for the $ D ^0 \!\rightarrow K ^- K ^+ \pi ^- \pi ^+ $ sample.

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Invariant mass-squared distributions for $ D ^0$ meson (black, closed circles) and $\overline{ D }{} ^0$ meson (red, open squares) decays to the final state $ K ^- K ^+ \pi ^- \pi ^+ $ . The invariant mass-squared combinations s(1,2), s(2,3), s(1,2,3), s(2,3,4), and s(3,4) correspond to s( $ K ^-$ , $ K ^+$ ), s( $ K ^+$ , $\pi ^-$ ), s( $ K ^-$ , $ K ^+$ , $\pi ^-$ ), s( $ K ^+$ , $\pi ^-$ , $\pi ^+$ ), and s( $\pi ^-$ , $\pi ^+$ ) , respectively for the $ D ^0$ mode. The charge conjugate is taken for the $\overline{ D }{} ^0$ mode. The phase-space distribution of the $ D ^0 \!\rightarrow K ^- K ^+ \pi ^- \pi ^+ $ decay is expected to be dominated by the quasi-two-body decay $ D ^0 \!\rightarrow \phi\rho^0 $ with additional contributions from $ D ^0 \!\rightarrow K _{1}(1270)^{\pm} K ^{\mp} $ and $ D ^0 \!\rightarrow K ^{*}(1410)^\pm K ^{\mp} $ decays [10].

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Invariant mass-squared distributions for $ D ^0$ meson (black, closed circles) and $\overline{ D }{} ^0$ meson (red, open squares) decays to the final state $\pi ^- \pi ^+ \pi ^+ \pi ^- $ . The invariant mass-squared combinations s(1,2), s(2,3), s(1,2,3), s(2,3,4), and s(3,4) correspond to s( $\pi ^-$ , $\pi ^+$ ), s( $\pi ^+$ , $\pi ^+$ ), s( $\pi ^-$ , $\pi ^+$ , $\pi ^+$ ), s( $\pi ^+$ , $\pi ^+$ , $\pi ^-$ ), and s( $\pi ^+$ , $\pi ^-$ ) , respectively for the $ D ^0$ mode. The charge conjugate is taken for the $\overline{ D }{} ^0$ mode. Owing to the randomisation of the order of identical final-state particles the invariant mass-squared distributions s(2,3,4) and s(3,4) are statistically compatible with the invariant mass-squared distributions s(1,2,3) and s(1,2), respectively. As such the invariant mass-squared distributions s(2,3,4) and s(3,4) are not shown. The phase-space distribution of the $ D ^0 \!\rightarrow \pi ^- \pi ^+ \pi ^+ \pi ^- $ decay is expected to be dominated by contributions from $ D ^0 \!\rightarrow a_{1}(1260)^{+} \pi^{-} $ and $ D ^0 \!\rightarrow \rho^{0} \rho^{0} $ decays [21].

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Distributions of $ S_{\mathcal{C}_{P} }$ for \subref{fig:Toy:SCP:NoCPV} a typical pseudo-experiment with generated $ D ^0 \!\rightarrow \pi ^- \pi ^+ \pi ^+ \pi ^- $ decays without CPV and for \subref{fig:Toy:SCP:CPV} a typical pseudo-experiment with a generated 10$^{\circ}$ phase difference between $ D ^0 \rightarrow a_{1}(1260)^{+} \pi^{-}$ and $\overline{ D }{} ^0 \rightarrow a_{1}(1260)^{-} \pi^{+}$ resonant decays. The points show the data distribution and the solid line is a reference Gaussian distribution corresponding to the no CPV hypothesis. The corresponding $p$-values under the hypothesis of no asymmetry for \subref{fig:Toy:SCP:NoCPV} decays without CPV and \subref{fig:Toy:SCP:CPV} decays with a 10$^{\circ}$ phase difference between $ D ^0 \rightarrow a_{1}(1260)^{+} \pi^{-}$ and $\overline{ D }{} ^0 \rightarrow a_{1}(1260)^{-} \pi^{+}$ resonant components are 85.6% and $1.1\times10^{-16}$, respectively.

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Distributions of (\subref*{fig:SCP:KKPiPi},\subref*{fig:SCP:FourPi},\subref*{fig:control:SCP}) $ S_{\mathcal{C}_{P} }$ and (\subref*{fig:RAW:KKPiPi},\subref*{fig:RAW:FourPi},\subref*{fig:control:RAW}) local $ C\!P$ asymmetry per bin for (\subref*{fig:SCP:KKPiPi},\subref*{fig:RAW:KKPiPi}) $ D ^0 \!\rightarrow K ^- K ^+ \pi ^- \pi ^+ $ decays partitioned with 32 bins, for (\subref*{fig:SCP:FourPi},\subref*{fig:RAW:FourPi}) $ D ^0 \!\rightarrow \pi ^- \pi ^+ \pi ^+ \pi ^- $ decays partitioned with 128 bins, and for (\subref*{fig:control:SCP},\subref*{fig:control:RAW}) the control channel $ D ^0 \!\rightarrow K ^- \pi ^+ \pi ^+ \pi ^- $ partitioned with 128 bins. The points show the data distribution and the solid line is a reference Gaussian distribution corresponding to the no CPV hypothesis.

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The $\chi^2/\mathrm{ndf}$ and $p$-values under the hypothesis of no CPV for the control channel $ D ^0 \!\rightarrow K ^- \pi ^+ \pi ^+ \pi ^- $ . The $p$-values are calculated separately for data samples taken with magnet up polarity, magnet down polarity, and the two polarities combined.

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The $\chi^2/\mathrm{ndf}$ and $p$-values under the hypothesis of no CPV with three different partitions for $ D ^0 \!\rightarrow K ^- K ^+ \pi ^- \pi ^+ $ decays and $ D ^0 \!\rightarrow \pi ^- \pi ^+ \pi ^+ \pi ^- $ decays. The $p$-values are calculated for a combined data sample with both data taken with magnet up polarity and data taken with magnet down polarity.

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Supplementary Material [file]

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This ZIP file contains supplemetary material for the publication LHCb-PAPER-2013-041. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps, *.C : The figures in variuous formats

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Created on 17 December 2018.Citation count from INSPIRE on 18 December 2018.