Amplitude analysis of $B^0$ decays to $J/\psi\pi^-K^+$ and $\psi(2S)\pi^-K^+$

Amplitude analyses of $B^0\to J/\psi(1S)\pi^-K^+$ and $B^0\to\psi(2S)\pi^-K^+$ decays are presented. The data correspond to the full LHCb Run 1 and Run 2 samples, which are much larger than previously analyzed by the Belle and LHCb experiments in similar analyses. Many more exotic $\psi(nS)\pi^-$ states are required for a good description of the data than disclosed by the previous amplitude analyses. For the first time, significant contributions from exotic $\psi(nS)K^+$ states are observed. The $J^P=1^+$ $Z(4200)^-$ state, previously established only in the $J/\psi(1S)\pi^-$ mode, is confirmed and observed with the consistent mass and width in the $\psi(2S)\pi^-$ mode. However, there are also a number of inconsistencies between the exotic states required by the two data sets which point to theoretical limitations of modelling these decays as a collection of resonances decaying only to $K^+\pi^-$, $\psi(nS)\pi^-$ or $\psi(nS)K^+$. Possible future directions in amplitude analyses of these decays are discussed.