Exotic four quark matter: $Z_1(4475)$

Motivated by the LHCb’s recent confirmation of $Z_1(4475)$ as the $J^P=1^{+}$ resonance, we investigate various exotic interpretations of $Z_1(4475)$, which may be an axial vector tetraquark state, the P-wave excitation of the S-wave $D_1{\overline{D}}^{*}$ or $D_2{\overline{D}}^{*}$ molecule, the S-wave molecule composed of a $D$ or $D^{*}$ meson and a D-wave vector $D$ meson, or the cousin molecular state of $Z_c(3900)$ and $Z_c(4020)$ composed of a $D$ or $D^{*}$ meson and their radial excitations. With the help of the heavy quark symmetry, we predict the typical radiative and hidden-charm and open-charm strong decay patterns of $Z_1(4475)$, which are crucial to further identify the molecular state assignment of $Z_1(4475)$.