Z+(4430)and analogous heavy flavor states

Abstract

The proximity of Z + (4430) to the D * D 1 threshold suggests that it may be a D * D 1 molecular state. The D * D 1 system has been studied dynamically from quark model, and state mixing effect is taken into account by solving the multichannel Schrödinger equation numerically. We suggest the most favorable quantum number is J P = 0 − , if future experiments confirm Z + (4430) as a loosely bound molecule state. More precise measurements of Z + (4430) mass and width, partial wave analysis are helpful to understand its structure. The analogous heavy flavor mesons Z + bb and Z ++ bc are studied as well, and the masses predicted in our model are in agreement with the predictions from potential model and QCD sum rule. We further apply our model to the DD * and DD * system.We find the exotic DD * bound molecule doesn't exist, while the 1 ++ DD * bound state solution can be found only if the screening mass µ is smaller than 0.17 GeV. The state mixing effect between the molecular state and the conventional charmonium should be considered to understand the nature of X(3872).

The hidden-charm pentaquark and tetraquark states

“…The interaction between a quark and an antiquark includes the short distance one-gluon exchange potential and the long distance confinement interaction [235]. After solving the multichannel Schrödinger equation, they found that the Z + (4430) can be explained as a looselyD 1 D * molecular state with J P = 0 − [235], which is consistent with the conclusion from the OPE model [203].…”

“…The authors concluded that the interaction of D * andD 1 is attractive in the J P = 0 − channel but not strong enough to form a bound state [508,509]. Both the phenomenological models [202,203,235,233] and the quenched lattice QCD calculations [508,509] indicated that the S-wave D 1D * interaction is attractive. The authors of Ref.…”

“…Ding et al [235] also studied the D * D 1 interaction in the quark model. The interaction between a quark and an antiquark includes the short distance one-gluon exchange potential and the long distance confinement interaction [235].…”

“…The proximity of their masses to the thresholds inspired molecular explanations of these structures [196,215,216,202,217,218,219,220,221,222,223,224,225,203,226,200,227,228,229,230,231,232,233,234,235,236,237,238,239]. With the refinement of the meson exchange model, many subtle aspects of this framework were investigated, such as the S-D wave mixing effect [185,197], coupled-channel effect [240,241,242], and recoil correction [243,244].…”

Bound states of the heavy flavor vector mesons andY(4008)andZ1+(4050)

“…Inspired by the nucleon-nucleon interactions, we further extended the one pion exchange model to include the short distance contributions from the heavier bosons η, σ, ρ and ω exchanges in Ref. [22]. We have also taken into account the contribution of the "δ function" term, which leads to a δ function term in the effective potential in configuration space when no regularization is used.…”