Observation and investigation of the $T_{c\bar{c}1}(4430)^{+}$ structure in $B^{+} \to \psi(2S) K_{\text{S}}^{0} \pi^{+}$ decays

The first four-dimensional amplitude analysis of the $B^{+} \to \psi(2S) K_{\text{S}}^{0} \pi^{+}$ decay is performed with proton-proton collision data collected by the LHCb experiment at $\sqrt{s} = 13~\rm{TeV}$, corresponding to an integrated luminosity of $5.4~\rm{fb^{-1}}$. The data cannot be fully explained by $B^{+} \to \psi(2S) K^{*+}$ contributions alone. A significantly better description of the data is obtained by adding a $T_{c\bar{c}}^{+}$ contribution decaying to $\psi(2S)\pi^{+}$. The properties of the $T_{c\bar{c}}^{+}$ structure are consistent with the exotic state $T_{c\bar{c}1}(4430)^{+}$ reported in the isospin-related $\bar{B}^{0} \to \psi(2S) K^{-} \pi^{+}$ decay. Effects of a possible $T_{c\bar{c}1}(4430)^{+} \to \bar{D}_{1}^{*}(2600)^{0} D^{+}$ decay mode on the $T_{c\bar{c}1}(4430)^{+} \to \psi(2S)\pi^{+}$ mass distribution are investigated through a Flatt\'e parametrization, providing constraints on the relative decay strength. A description of the $T_{c\bar{c}1}(4430)^{+}$ structure using the triangle singularity mechanism is studied and also found to be consistent with the data.