Compositeness of chi_c1(3872) from its line shape
In plain words
The chi_c1(3872), also called $X(3872)$, lies within about 0.2 MeV of the combined mass of two charmed mesons, $D0$ and anti-D*0. Measuring its exact position and line shape decides how much of it is a loose two-meson molecule.
Precise statement
Determine the pole position of chi_c1(3872) relative to the D0 anti-$D*0$ threshold, including the finite D*0 width, and its Weinberg compositeness $1 - Z$ ($Z = 0\ \text{pure molecule}, Z = 1\ \text{compact state}$) from the $D0\ \text{anti-D0}\ \pi0\ \text{and}\ J/\psi\ \pi+\ \pi-$ line shapes. Answer: binding energy with about $10\,\mathrm{keV}$ precision and Z with uncertainty below 0.1.
What would settle it
A direct energy scan in antiproton-proton annihilation (PANDA at FAIR) or high-statistics D0 anti-D0 pi0 line shapes at LHCb or Belle II.
Status in the literature
LHCb line-shape analyses (2020) placed the pole very close to threshold, consistent with a quasi-bound state, without fixing Z.