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). 
DeltaM[..].pdf [23 KiB] HiDef png [310 KiB] Thumbnail [81 KiB] *.C file 

DeltaM[..].pdf [23 KiB] HiDef png [304 KiB] Thumbnail [78 KiB] *.C file 

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. 
Fig2a_.png [113 KiB] HiDef png [476 KiB] Thumbnail [58 KiB] *.C file 

Fig2b_.png [99 KiB] HiDef png [543 KiB] Thumbnail [60 KiB] *.C file 

Fig2c_.png [132 KiB] HiDef png [480 KiB] Thumbnail [55 KiB] *.C file 

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. 
Fig3_sub1a.pdf [28 KiB] HiDef png [148 KiB] Thumbnail [54 KiB] *.C file 

Fig3_sub1b.pdf [28 KiB] HiDef png [153 KiB] Thumbnail [55 KiB] *.C file 

(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. 
Fig3_sub2a.png [60 KiB] HiDef png [407 KiB] Thumbnail [66 KiB] *.C file 

Fig3_sub2b.png [47 KiB] HiDef png [300 KiB] Thumbnail [60 KiB] *.C file 

Fig3_sub2c.png [58 KiB] HiDef png [395 KiB] Thumbnail [66 KiB] *.C file 

Fig3_sub2d.png [46 KiB] HiDef png [301 KiB] Thumbnail [61 KiB] *.C file 

The selection efficiency as a function of $m(\pi ^+ \pi ^ )$. The efficiency for the combined sample is fitted with a straight line. 
acceptance.pdf [17 KiB] HiDef png [190 KiB] Thumbnail [79 KiB] *.C file 

(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). 
Fig5a_.pdf [29 KiB] HiDef png [195 KiB] Thumbnail [64 KiB] *.C file 

SigLev[..].png [38 KiB] HiDef png [304 KiB] Thumbnail [62 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2014054.gif Thumbnail 
Overview of sensitivities to various $ C P$ violation scenarios. $\Delta A$ and $\Delta \phi$ denote, respectively, change in amplitude and phase of the resonance $R$. 
Table_1.pdf [53 KiB] HiDef png [129 KiB] Thumbnail [22 KiB] tex code 

Results for various metric parameter values. The $ p$ values are obtained with the counting method. 
Table_2.pdf [42 KiB] HiDef png [79 KiB] Thumbnail [13 KiB] tex code 
Created on 15 June 2019.Citation count from INSPIRE on 15 June 2019.