Evidence for an \(\eta _c(1S) \pi ^-\) resonance in \(B^0 \rightarrow \eta _c(1S) K^+\pi ^-\) decays

A Dalitz plot analysis of \({{B} ^0} \!\rightarrow \eta _c(1S) {{K} ^+} {{\pi } ^-} \) decays is performed using data samples of pp collisions collected with the \(\text{ LHCb } \) detector at centre-of-mass energies of \({\sqrt{s}} =7,~8\) and \(13{\,\mathrm {Te}\mathrm {V}} \), corresponding to a total integrated luminosity of \(4.7 \,\text{ fb }^{-1} \). A satisfactory description of the data is obtained when including a contribution representing an exotic \(\eta _c(1S) \pi ^-\) resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are \(4096 \pm 20~^{+18}_{-22} \,\mathrm {Me}\mathrm {V} \) and \(152 \pm 58~^{+60}_{-35} \,\mathrm {Me}\mathrm {V} \), respectively. The spin-parity assignments \(J^P=0^+\) and \(J^{P}=1^-\) are both consistent with the data. In addition, the first measurement of the \({{B} ^0} \!\rightarrow \eta _c(1S) {{K} ^+} {{\pi } ^-} \) branching fraction is performed and gives $$\begin{aligned} \displaystyle \mathcal {B}({{B} ^0} \!\rightarrow \eta _c(1S) {{K} ^+} {{\pi } ^-} ) = (5.73 \pm 0.24 \pm 0.13 \pm 0.66) \times 10^{-4}, \end{aligned}$$ where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions.