A search for timeintegrated CP violation in the Cabibbosuppressed decay $D^0\to\pi^\pi^+\pi^0$ is performed using for the first time an unbinned modelindependent technique known as the energy test. Using protonproton collision data, corresponding to an integrated luminosity of 2.0 fb$^{1}$ collected by the LHCb detector at a centreofmass energy of $\sqrt{s}$ = 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 pvalue of (2.6 +/ 0.5).
Distribution of $\Delta{}m$ with fit overlaid for the selected data set with (a) resolved and (b) merged $\pi ^0$ candidates. The lines show the fit results for total signal (dotdashed red), widest Gaussian signal component (dotted red), background (dashed green), and total (solid blue). 
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Dalitz plot of the (a) resolved, (b) merged and (c) combined $ D ^0 \rightarrow \pi ^ \pi ^+ \pi ^0 $ data sample. Enhanced event densities in the phasespace corners originate from the $\rho(770)$ resonances. 
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Distribution of permutation $T$ values fitted with a GEV function for the simulated sample and showing the nominal $T$ value as a vertical line for (a) $2\%$ $ C P$ violation in the amplitude and (b) $1^\circ$ phase $ C P$ violation of the $\rho^+$ resonance. 
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(a,c) $T_i$ value distributions, and (b,d) local asymmetry significances for (top) $2\%$ $ C P$ violation in the amplitude and (bottom) $1^\circ$ phase $ C P$ violation of the $\rho^+$ resonance. 
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The selection efficiency as a function of $m(\pi ^+ \pi ^ )$. The efficiency for the combined sample is fitted with a straight line. 
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(a) Permutation $T$ value distribution showing the fit function and the measured $T$ value as a red line. (b) Visualisation of local asymmetry significances. The positive (negative) asymmetry significance is set for the $ D ^0$ candidates having positive (negative) contribution to the measured $T$ value, respectively (see Sec.4). 
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Animated gif made out of all figures. 
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Overview of sensitivities to various $ C P$ violation scenarios. $\Delta A$ and $\Delta \phi$ denote, respectively, change in amplitude and phase of the resonance $R$. 
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Results for various metric parameter values. The $ p$ values are obtained with the counting method. 
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Created on 06 March 2021.