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The LHCb experiment has recorded the world's largest sample of charmed mesondecays. This paper presents a study of a $D^0$ meson decaying into a finalstate containing a neutral pion in LHCb. The search for $CP$ violation exploitsa novel model-independent unbinned technique to assign a $p$-value for the no$CP$ violation hypothesis. With a data sample size exceeding that of previousmeasurements by almost an order of magnitude the world's best sensitivity isobtained. The $p$-value of no CP violation hypothesis given data of$D^0\rightarrow \pi^-\pi^+\pi^0$ decay analysed is found to be $(2.6 \pm0.5)\times 10^-2$.

Search for $CP$ violation in $D^0\rightarrow \pi^-\pi^+\pi^0$ decays at LHCb