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Search for $CP$ violation in the phase space of $D^0\rightarrow\pi^+\pi^-\pi^+\pi^-$ decays

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Abstract

A search for time-integrated $CP$ violation in the Cabibbo-suppressed decay $ D^0\rightarrow\pi^+\pi^-\pi^+\pi^-$ is performed using an unbinned, model-independent technique known as the energy test. This is the first application of the energy test in four-body decays. The search is performed for $P$-even $CP$ asymmetries and, for the first time, is extended to probe the $P$-odd case. Using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb$^{-1}$ collected by the LHCb detector at centre-of-mass energies of $\sqrt{s}=$7 TeV and 8 TeV, the world's best sensitivity to $CP$ violation in this decay is obtained. The data are found to be consistent with the hypothesis of $CP$ symmetry with a $p$-value of $(4.6\pm0.5)\%$ in the $P$-even case, and marginally consistent with a $p$-value of $(0.6\pm0.2)\%$ in the $P$-odd case, corresponding to a significance for $CP$ non-conservation of 2.7 standard deviations.

Figures and captions

Distribution of $\Delta m$ with fit overlaid for the selected $ D ^{*+}$ candidates in the 2012 data. The data points and the contributions from signal, background, and their total obtained from the fit are shown.

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(a,b) Distribution of permutation $T$-values fitted with a GEV function for the simulated sample and showing the measured $T$-value as a vertical line, and (c,d,e,f) local asymmetry significances. Left column plots are for a $P$-even $ C\!P$ -violation test with a $3^\circ$ phase $ C\!P$ violation introduced in the $a_1(1260)^+$ resonance (see text), projected onto the (c) $m(\pi_1 \pi_2 \pi_3)$ and (e) $m(\pi_1\pi_2)$ axes. Right column plots are for a $P$-odd $ C\!P$ -violation test with $3^\circ$ phase $ C\!P$ violation introduced in the P-wave $\rho ^0 (770) \rho ^0 (770)$ resonance projected onto the same axes. In plots (c,d,e,f) the grey area corresponds to candidates with a contribution to the $T$-value of less than one standard deviation. The pink (blue) area corresponds to candidates with a positive (negative) contribution to the $T$-value. Light, medium or dark shades of pink and blue correspond to between one and two, two and three, and more than three standard-deviation contributions, respectively.

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(a,b) Distribution of permutation $T$-values fitted with a GEV function and showing the $T$-value of the data tests as a vertical line, and (c,d,e,f) local asymmetry significances. Left column plots are for the $P$-even $ C\!P$ -violation test, projected onto the (c) $m(\pi_1 \pi_2 \pi_3)$ and (e) $m(\pi_1\pi_2)$ axes. Right column plots are for the $P$-odd $ C\!P$ -violation test projected onto the same axes. In plots (c,d,e,f) the grey area correspond to candidates with a contribution to the $T$-value of less than one standard deviation. In the $P$-even $ C\!P$ violation test the positive (negative) asymmetry significance is set for the $ D ^0$ candidates having positive (negative) contribution to the measured $T$ value. In the $P$-odd $ C\!P$ violation test the positive (negative) asymmetry significance is set for sample $I+IV$ having positive (negative) contribution to the measured $T$ value (see Sect. 5). The pink (blue) area corresponds to candidates with a positive (negative) contribution to the $T$-value. Light, medium or dark shades of pink and blue correspond to between one and two, two and three, and more than three standard deviation contributions, respectively.

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Tables and captions

The yields of signal events in the four samples that obtained from fits to the $\Delta m$ distribution.

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Overview of sensitivities to various $ C\!P$ -violation scenarios in simulation. $\Delta A$ and $\Delta \phi$ denote, respectively, the relative change in magnitude and the change in phase of the amplitude of the resonance $R$. The P-wave $\rho ^0 (770)\rho ^0 (770)$ is a $P$-odd component. The phase change in this resonance is tested with the $P$-odd $ C\!P$ -violation test. Results for all other scenarios are given with the standard $P$-even test.

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Results for the $P$-even and $P$-odd $ C\!P$ -violation tests for three different values of the effective radius $\delta$. The $p$-values obtained with both the counting and GEV fitting methods are given (see text). The counting method is the default method.

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Supplementary Material [file]

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This ZIP file contains supplementary material for the publication LHCb-PAPER-2016-044. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats

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