We review the status as regards the existence of three- and four-body bound states made of neutrons and $Lambda$ hyperons. For interesting cases, the coupling to neutral baryonic systems made of charged particles of different strangeness has been add
ressed. There are strong arguments showing that the $Lambda nn$ system has no bound states. $LambdaLambda nn$ strong stable states are not favored by our current knowledge of the strangeness $-1$ and $-2$ baryon-baryon interactions. However, a possible $Xi^- t$ quasibound state decaying to $LambdaLambda nn$ might exist in nature. Similarly, there is a broad agreement about the nonexistence of $LambdaLambda n$ bound states. However, the coupling to $Xi NN$ states opens the door to a resonance above the $LambdaLambda n$ threshold.
We study the coupled $LambdaLambda nn-Xi^- pnn$ system to check whether the inclusion of channel coupling is able to bind the $LambdaLambda nn$ system. We use a separable potential three-body model of the coupled $LambdaLambda nn - Xi^- pnn$ system a
s well as a variational four-body calculation with realistic interactions. Our results exclude the possibility of a $LambdaLambda nn$ bound state by a large margin. However, we have found a $Xi^- t$ quasibound state above the $LambdaLambda nn$ threshold.
We present the first full-fledged study of the flavor-exotic isoscalar $T_{bb}^-equiv b b bar u bar d$ tetraquark with spin and parity $J^P=1^+$. We report accurate solutions of the four-body problem in a quark model, characterizing the structure of
the state as a function of the ratio $M_Q/m_q$ of the heavy to light quark masses. For such a standard constituent model, $T_{bb}^-$ lies approximately 150 MeV below the strong decay threshold $B^-bar {B^*}^{0}$ and 105 MeV below the electromagnetic decay threshold $B^- bar B^0 gamma$. We evaluate the lifetime of $T_{bb}^-$, identifying the promising decay modes where the tetraquark might be looked for in future experiments. Its total decay width is $Gamma approx 87 times 10^{-15}$ GeV and therefore its lifetime $tau approx$ 7.6 ps. The promising final states are ${B^*}^{-}, {D^*}^{+} , ell^- , bar u_ell$ and $bar {B^*}^{0} , {D^*}^{0} , ell^- , bar u_ell $ among the semileptonic decays, and ${B^*}^{-} , {D^*}^{+} , {D_s^*}^-$, $bar {B^*}^{0} , {D^*}^{0} , {D_s^*}^- $, and ${B^*}^{-} , {D^*}^{+} , rho^-$ among the nonleptonic ones. The semileptonic decay to the isoscalar $J^P=0^+$ tetraquark $T_{bc}^0$ is also relevant but it is not found to be dominant. There is a broad consensus about the existence of this tetraquark, and its detection will validate our understanding of the low-energy realizations of Quantum Chromodynamics (QCD) in the multiquark sector.
We outline the most important results regarding the stability of doubly heavy tetraquarks $QQbar qbar q$ with an adequate treatment of the four-body dynamics. We consider both color-mixing and spin-dependent effects. Our results are straightforwardly
applied to the case of all-heavy tetraquarks $QQbar Qbar Q$. We conclude that the stability is favored in the limit $M_Q/m_q gg 1$ pointing to the stability of the $bbbar ubar d$ state and the instability of all-heavy tetraquarks.
It is shown that standard constituent quark models produce $(bar c c qqq)$ hidden-charm pentaquarks, where $c$ denotes the charmed quark and $q$ a light quark, which lie below the lowest threshold for spontaneous dissociation and thus are stable in t
he limit where the internal $bar c c$ annihilation is neglected. The binding is a cooperative effect of the chromoelectric and chromomagnetic components of the interaction, and it disappears in the static limit with a pure chromoelectric potential. Their wave function contains color sextet and color octet configurations for the subsystems and can hardly be reduced to a molecular state made of two interacting hadrons. These pentaquark states could be searched for in the experiments having discovered or confirmed the hidden-charm meson and baryon resonances.
We review some recent studies on the string model of confinement inspired by the strong-coupling regime of QCD and its application to exotic multiquark configurations. This includes two quarks and two antiquarks, four quarks and one antiquark, six qu
arks, and three quarks and three antiquarks with a careful treatment of the corresponding few-body problem.
