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A Dalitz plot analysis of $B^0 \to \eta_c(1S) K^+\pi^-$ decays is performedusing data samples of $pp$ collisions collected with the LHCb detector atcentre-of-mass energies of $\sqrt{s}=7,~8$ and $13$ TeV, corresponding to atotal integrated luminosity of $4.7~\text{fb}^{-1}$. A satisfactory descriptionof the data is obtained when including a contribution representing an exotic$\eta_c(1S) \pi^-$ resonant state. The significance of this exotic resonance ismore than three standard deviations, while its mass and width are $4096 \pm20~^{+18}_{-22}$ MeV and $152 \pm 58~^{+60}_{-35}$ MeV, respectively. Thespin-parity assignments $J^P=0^+$ and $J^{P}=1^-$ are both consistent with thedata. In addition, the first measurement of the $B^0 \to \eta_c(1S) K^+\pi^-$branching fraction is performed and gives $\displaystyle \mathcal{B}(B^0 \to\eta_c(1S) K^+\pi^-) = (5.73 \pm 0.24 \pm 0.13 \pm 0.66) \times 10^{-4}$, wherethe first uncertainty is statistical, the second systematic, and the third isdue to limited knowledge of external branching fractions.

Evidence for an $\eta_c(1S) \pi^-$ resonance in $B^0 \to \eta_c(1S) K^+\pi^-$ decays