Amplitude analysis of $B^0 \rightarrow \eta _c(1S) K^+ \pi ^- $ decays

An amplitude analysis of the ${{{B} ^0} \!\rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-}}$ decays with ${\eta _{c}} (1S) \rightarrow {p} {\overline{{p}}}$ is performed using a sample corresponding to an integrated luminosity of 9 $\,\text {fb} ^{-1}$ of $p$ $p$ collision data collected by the LHCb detector at centre-of-mass energies of $\sqrt{s}$ = 7, 8 and 13 $\,\text {Te\hspace{-1.00006pt}V}$ . The data are described with a model including only intermediate contributions from known ${K} ^{*0}$ resonances. Evidence for an exotic resonance in the ${\eta _{c}} (1S) {{\pi } ^-}$ system, reported in a previous analysis of this decay channel, is not confirmed. The inclusive branching fraction of the ${{B} ^0} \rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-}$ decays is measured to be $\begin{aligned}&\mathcal {B}({{B} ^0} \rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-}) \\&\quad = (5.82 \pm 0.20 \pm 0.23 \pm 0.55) \times 10^{-4}, \end{aligned}$ B ( B 0 → η c ( 1 S ) K + π - ) = ( 5.82 ± 0.20 ± 0.23 ± 0.55 ) × 10 - 4 , where the first uncertainty is statistical, the second systematic, and the third arises from the limited knowledge of external branching fractions.