We have studied the three quark system in a relativized version of the quark potential model with chromodynamics. With parameters consistent with those of an analogous study of meson spectroscopy we obtain a successful description of the spectrum of baryons. The model naturally explains the apparent absence of spin‐orbit interactions in baryons.

Baryons in a relativized quark model with chromodynamics

The past seventeen years have witnessed tremendous progress on the experimental and theoretical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in [Phys. Rept. 639 (2016) 1-121]. In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Especially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known $XYZ$ and $P_c$ states, we shall discuss more interesting tetraquark and pentaquark systems either with one, two, three or even four heavy quarks. Some very intriguing states include the fully heavy exotic tetraquark states $QQ\bar Q\bar Q$ and doubly heavy tetraquark states $QQ\bar q \bar q$, where $Q$ is a heavy quark. The $QQ\bar Q\bar Q$ states may be produced at LHC while the $QQ\bar q \bar q$ system may be searched for at BelleII and LHCb. Moreover, we shall pay special attention to various theoretical schemes. We shall emphasize the model-independent predictions of various models which are truly/closely related to Quantum Chromodynamics (QCD). There have also accumulated many lattice QCD simulations through multiple channel scattering on the lattice in recent years, which provide deep insights into the underlying structure/dynamics of the $XYZ$ states. In terms of the recent $P_c$ states, the lattice simulations of the charmed baryon and anti-charmed meson scattering are badly needed. We shall also discuss some important states which may be searched for at BESIII, BelleII and LHCb in the coming years.

Pentaquark and Tetraquark states

Hyperspherical coordinate approach to atomic and other Coulombic three-body systems

In the framework of simple non-relativistic potential models, we examine the system consisting of two quarks and two antiquarks with equal or unequal masses. We search for possible bound states below the threshold for the spontaneous dissociation into two mesons. We solve the four body problem by empirical or systematic variational methods and we include explicitly the virtual meson-meson components of the wave function. With standard twobody potentials, there is no proliferation of multiquarks. With unequal quark masses, we obtain however exotic$\left( {\bar Q\bar Qqq} \right)$ bound states with a baryonic antidiquark-quark-quark structure very analogous to the heavy flavoured (Q′qq) baryons.

Four quark bound states

The potential harmonic expansion method

Application of the Hyperspherical Formalism to the Trinucleon Bound State Problems

Four quark states in additive potentials

In the framework of the hyperspherical formalism, we present a study of the coupled adiabatic approximation for the case of three nucleons interacting via central spindependent two-body potentials. We analyze the convergence of the ground state eigenvalues versus the grand orbital quantum number ($2K$) and compare the results to that of the coupled equations. We also compare with two simpler but less accurate approximations: the uncoupled adiabatic approximation and the extreme adiabatic approximation. The former provides an upper and the latter provides a lower bound to the ground state energy.NUCLEAR STRUCTURE Few body bound states, reduction of hyperspherical equations applied to triton, quantum few-body problem.

J.L. Ballot

Papers

Application of the Hyperspherical Formalism to the Trinucleon Bound State Problems

Four quark states in additive potentials

Coupled adiabatic approximation in the three-body problem

The four-nucleon problem with local realistic nn interactions

Contribution of two-body correlations to the wave function of many-body systems