Amplified Isospin Breaking from Coupled-Channel Dynamics Near Threshold

Abstract

We identify the dynamical origin of amplified isospin breaking in near-threshold states. Using a pole-residue-based measure defined directly from the pole couplings, rather than from decay observables that are also affected by different final-state kinematics, we show that threshold proximity of the pole alone is insufficient: large isospin breaking requires a sizable interaction in the companion isospin channel. Applied to the $X(3872)$, the observed large isospin breaking points to a nearby partner pole, $W_{c1}$, as predicted in previous studies. In addition, we find that the $W_{c1}$ pole, which predominantly affects the line shapes near the charged threshold in the physical case, does not evolve into the pure $I=1$ eigenstate in the isospin limit; instead, that eigenstate is continuously connected to a more distant shadow pole.

11 pages,4 figures