Abstract: We address the issue of the compositeness of hadronic states and demonstrate that starting with a genuine state of nonmolecular nature, but which couples to some meson-meson component to be observable in that channel, if that state is blamed for a bound state appearing below the meson-meson threshold it gets dressed with a meson cloud and it becomes pure molecular in the limit case of zero binding. We discuss the issue of the scales, and see that if the genuine state has a mass very close to threshold, the theorem holds, but the molecular probability goes to unity in a very narrow range of energies close to threshold. The conclusion is that the value of the binding does not determine the compositeness of a state. However, in such extreme cases we see that the scattering length gets progressively smaller and the effective range grows indefinitely. In other words, the binding energy does not determine the compositeness of a state, but the additional information of the scattering length and effective range can provide an answer. We also show that the consideration of a direct attractive interaction between the mesons in addition to having a genuine component, increases the compositeness of the state. Explicit calculations are done for the Tcc(3875) state, but are easily generalized to any hadronic system.

Abstract: A measurement of the polarisation of Wbosons produced in top-quark decays is presented, using proton-proton collision data at a centre-of-mass energy of v s= 13TeV. The data were collected by the ATLAS detector at the Large Hadron Collider and correspond to an integrated luminosity of 139fb(-1). The measurement is performed selecting t tevents decaying into final states with two charged leptons (electrons or muons) and at least two b-tagged jets. The polarisation is extracted from the differential cross-section distribution of the cos theta* variable, where theta(*) is the angle between the momentum direction of the charged lepton from the Wboson decay and the reversed momentum direction of the b-quark from the top-quark decay, both calculated in the Wboson rest frame. Parton-level results, corrected for the detector acceptance and resolution, are presented for the cos theta* angle. The measured fractions of longitudinal, left- and right-handed polarisation states are found to be f(0) = 0.684 +/- 0.005 (stat.)+/- 0.014 (syst.), f(L)= 0.318 +/- 0.003 (stat.)+/- 0.008 (syst.) and f(R)=-0.002 +/- 0.002 (stat.)+/- 0.014 (syst.), in agreement with the Standard Model prediction.

Abstract: We face the inverse problem of obtaining the interaction between coupled channels from the correlation functions of these channels. We apply the method to the interaction of the (DK+)-K-0, (D+K0), and D-s(+)eta channels, from where the D-s0(& lowast;)(2317) state emerges. We use synthetic data extracted from an interaction model based on the local hidden gauge approach and find that the inverse problem can determine the existence of a bound state of the system with a precision of about 20 MeV. At the same time, we can determine the isospin nature of the bound state and its compositeness in terms of the channels. Furthermore, we evaluate the scattering length and effective range of all three channels, as well as the couplings of the bound state found to all the components. Lastly, the size parameter of the source function, R, which in principle should be a magnitude provided by the experimental teams, can be obtained from a fit to the data with relatively high accuracy. These findings show the value of the correlation function to learn about the meson-meson interaction for systems which are difficult to access in other present facilities.