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We perform a systematic analysis of the J/ψ→γπ0π0 and →γKS0KS0 partial waves measured by BESIII. We use a large set of amplitude parametrizations to reduce the model bias. We determine the physical properties of seven scalar and tensor resonances in the 1–2.5GeV mass range. These include the well known f0(1500) and f0(1710), that are considered to be the primary glueball candidates. The hierarchy of resonance couplings determined from this analysis favors the latter as the one with the largest glueball component.

Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B→ψπK and B→D¯ππ decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

We discuss the differences between several partial-wave analysis formalisms used in the construction of three-body decay amplitudes involving fermions. Specifically, we consider the decay \\[\\Lambda _b \\rightarrow \\psi \\,p K^-\\], where the hidden charm pentaquark signal has been reported. We analyze the analytical properties of the amplitudes and separate kinematical and dynamical singularities. The result is an amplitude with the minimal energy dependence compatible with the S-matrix principles.

A bstract We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular the one-pion-exchange process. It is demonstrated that unitarity demands a specific functional form of the amplitude with a clear interpretation: the bare three-particle resonances are dressed by the initial- and final-state interaction, in a way that is consistent with the considered long-range forces. We postulate that the resonance kernel admits a factorization in the energy variables of the initial- and the final-state particles. The factorization assumption leads to an algebraic form for the unitarity equations, which is reminiscent of the well-known two-body-unitarity condition and approaches it in the limit of the narrow-resonance approximation.

Using effective Lagrangians constrained by the heavy quark spin symmetry and chiral symmetry, for the light quarks, we analyze the D 0 D 0 π + , D ¯ 0 D 0 π 0 and D 0 D ¯ ∗ 0 invariant mass spectra. Performing a simultaneous analysis of the doubly charmed and charm-anti-charm states gives further insights into the nature of the T cc + and χ c 1 0 ( 3872 ) , exotic hadrons. It is confirmed that both states should lie below their respective D D ∗ / D D ¯ ∗ thresholds. Also, the contributions of the triangle and box diagrams are negligible.

We show that the cross section of the Δ(1230) production in the γp → pπ + π − reaction at forward angles and with unpolarized photons can be described in terms of gauge invariant one pion t -channel exchange amplitudes. Proper description of the polarized cross sections requires, however, the inclusion of contributions from the baryon exchanges.

In this talk I discuss aspects of hadron physics, which soon are expected to shed new light on the fundamental QCD phenomena. In the analysis of hadron reactions and their propertieds I emphasize similarities to the nuclear many body problem.

The production of η(′)π pairs constitutes one of the golden channels to search for hybrid exotics, with explicit gluonic degrees of freedom. Understanding the dynamics and backgrounds associated to η(′)π production above the resonance region is required to impose additional constraints to the resonance extraction. We consider the reaction π-p→η(′)π-p measured by COMPASS. We show that the data in 2.4

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