Amplitude analysis of $B^+ \to ψ(2S) K^+ π^+ π^-$ decays

Abstract: The first full amplitude analysis of $B^+ \to \psi(2S) K^+ \pi^+ \pi^-$ decays is performed using proton-proton collision data corresponding to an integrated luminosity of $9\,\text{fb}^{-1}$ recorded with the LHCb detector. The rich $K^+ \pi^+ \pi^-$ spectrum is studied and the branching fractions of the resonant substructure associated with the prominent $K_1(1270)^+$ contribution are measured. The data cannot be described by conventional strange and charmonium resonances only. An amplitude model with 53 components is developed comprising 11 hidden-charm exotic hadrons. New production mechanisms for charged charmonium-like states are observed. Significant resonant activity with spin-parity $J^P = 1^+$ in the $\psi(2S) \pi^+$ system is confirmed and a multi-pole structure is demonstrated. The spectral decomposition of the $\psi(2S) \pi^+ \pi^-$ invariant-mass structure, dominated by $X^0 \to \psi(2S) \rho(770)^0$ decays, broadly resembles the $J/\psi \phi$ spectrum observed in $B^+ \to J/\psi \phi K^+$ decays. Exotic $\psi(2S) K^+ \pi^-$ resonances are observed for the first time.