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.

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ǫ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N )invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.

We use the numerical S-matrix bootstrap method to obtain bounds on the two leading Wilson coefficients (or low energy constants) of the chiral lagrangian controlling the low-energy dynamics of massless pions. This provides a proof of concept that the numerical S-matrix bootstrap can be used to derive non-perturbative bounds on massless EFTs in more than two spacetime dimensions.

Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α ′ expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O(α ′ 6 ). Thus the massless S-matrix of string theory "knows" about the presence of D-branes.