Speaker
Description
In 2020-24, the observation of $c\bar c c\bar c$ exotic hadrons (di-$J/\psi$) was reported by LHCb, CMS, and ATLAS. Their energies are above the 2$m(J/\psi)$ threshold, $X(6200, 6600, 6900)$. Here, we investigate these states, focusing on the quark-Pauli blocking effect. We show that this effect can make a structure in the S-wave $c\bar c c\bar c$ systems. The Pauli blocking over the quarks should exist in these fermion composite systems but has not yet been investigated from this viewpoint.
We employ the quark-hadron hybrid model, which has a short-range four-quark part with a two-$c\bar c$-meson tail. The quark Pauli-principle 'blocks' the two quarks from occupying the same state, leading to the effect of moving one of the (anti)quarks from the $0s$- to the $1s$-level when two mesons come close. Thus, the two-hadron nonlocal potential that arises from the quark Pauli-blocking effect can be written as $v_0( \phi_{0s}(r)\phi_{1s}(r')+\phi_{1s}(r)\phi_{0s}(r'))$, with the $\phi_{ns}$ being the harmonic oscillator wave function for the relative coordinate of the two mesons $r$.
The obtained potential has a repulsion in the intermediate range and a strong attraction at $\sqrt{r^2+r'{}^2}\sim <$ 0.4fm. This feature gives rise to a shape resonance with a node at E = 6600 MeV that causes a dip in the cross-section. We discuss that this can give the observed structures in the di-$J/\psi$ spectrum.
