A femtoscopic tale of two $C$-parities: the $Z_c(3900)$ and the isovector partner of the $X(3872)$

Abstract

Understanding the nature of the exotic $Z_c(3900)$ and $Z_{cs}(3985)$ states, and searching for the predicted isovector partner $W_{c1}$ of the $X(3872)$, remain central challenges in exotic-hadron spectroscopy. We investigate the femtoscopic correlation functions (CFs) of the $D^{(\ast)0}D_{(s)}^{(\ast)-}$ systems. Since these charm-meson--antimeson pairs are not $G$-parity eigenstates, their CFs contain contributions from both the $C$-odd and $C$-even sectors, providing direct access to the dynamics underlying the $Z_c$, $Z_{cs}$, and the predicted isovector exotic $W_{c1}$. Within a heavy-quark-spin-symmetric coupled-channel framework, we show that the $C$-even admixture enhances the low-momentum CFs by more than $2.5σ$ in the vicinity of their thresholds. Free from Coulomb distortions and accessible in high-multiplicity $pp$ collisions at the LHC, these channels offer the first direct femtoscopic probe of the isovector $C$-even sector and of the elusive $W_{c1}$ state.