Search for direct $CP$ violation in charged charmless $B \to PV$ decays

Measurements of $CP$ asymmetry in charmless $B\to PV$ decays are presented, where $P$ and $V$ denote a pseudoscalar and a vector meson, respectively. Five different $B\to PV$ decays from four final states, $B^\pm \to \pi^\pm \pi^+ \pi^-$, $B^\pm \to K^\pm \pi^+ \pi^-$, $B^\pm \to K^\pm K^+ K^-$ and $B^\pm \to \pi^\pm K^+ K^-$ are analised. The measurements are based on a method that does not require full amplitude analyses, and are performed using proton-proton collision data at a centre-of-mass energy of 13TeV collected by LHCb between 2015 and 2018, corresponding to an integrated luminosity of 5.9 fb$^{-1}$. In the $B^\pm \to \rho(770)^0 K^\pm$ decay, a $CP$ asymmetry of $A_{CP}$ = +0.150 $\pm$ 0.019 $\pm$ 0.011 is measured, where the first uncertainty is statistical and the second is systematic. This is the first observation of $CP$ violation in this decay. For the other four decay channels, $B^\pm \to \rho(770)^0 \pi^\pm$, $B^\pm \to \overset{(-)}{K^*}(892)^0 \pi^\pm$, $B^\pm \to \overset{(-)}{K^*}(892)^0 K^\pm$ and $B^\pm \to \phi(1020) K^\pm$ decays, $CP$ asymmetries compatible with zero are measured.