The past decade witnessed a remarkable proliferation of exotic charmonium-like resonances discovered at accelerators. In particular, the recently observed charged states are clearly not interpretable as qq mesons. Notwithstanding the considerable advances on the experimental side, conflicting theoretical descriptions do not seem to provide a definitive picture about the nature of the so called XY Z particles. We present here a comprehensive review about this intriguing topic, discussing both those experimental and theoretical aspects which we consider relevant to make further progress in the field. At this state of progress, XY Z phenomenology speaks in favour of the existence of compact four-quark particles (tetraquarks) and we believe that realizing this instructs us in the quest for a firm theoretical framework.

We consider the S-matrix bootstrap of four-dimensional scattering amplitudes with Oð3Þ symmetry and no bound states. We explore the allowed space of scattering lengths which parametrize the interaction strength at threshold of the various scattering channels. Next we consider an application of this formalism to pion physics. A signature of pions is that they are derivatively coupled leading to (chiral) zeros in their scattering amplitudes. In this work we explore the multidimensional space of chiral zeros positions, scattering length values, and resonance mass values. Interestingly, we encounter lakes, peninsulas, and kinks depending on which sections of this intricate multidimensional space we consider. We discuss the remarkable location where QCD seems to lie in these plots, based on various experimental and theoretical expectations.

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The nature of the so-called X Y Z states is a long-standing problem. It has been suggested that such particles may be described as compact four-quark states or loosely bound meson molecules. In the present work we analyze the Z ( ) c → η c ρ decay using both approaches. Such channel might provide useful insights on the nature of the Z ( ) c , helping discriminating between the two different models.

The high prompt production cross section of Xð3872Þ at hadron colliders has shown to be very informative about the quark nature of the X, Y, Z states. We present here a number of results on X production in ppðpÞ collisions obtained with Monte Carlo hadronization methods and illustrate what can be learned from their use to improve our understanding of exotic states. In particular, a comparison between antideuteron and X production cross sections is proposed. Hadronization might be the key to solve the problem of the extra states expected in diquark-antidiquark models which are naturally favored after the recent confirmation of the Zð4430Þ tetraquark, together with its lower partners Z c ð3900Þ and Z 0 c ð4020Þ.