Abstract: We study the behavior of the chi(c1) (3872), also known as X(3872), in dense nuclear matter. We begin from a picture in vacuum of the X(3872) as a purely molecular (D (D) over bar*-c.c.) state, generated as a bound state from a heavy-quark symmetry leading-order interaction between the charmed mesons, and analyze the D (D) over bar* scattering T matrix (T-D (D) over bar*) inside of the medium. Next, we consider also mixed-molecular scenarios and, in all cases, we determine the corresponding X(3872) spectral function and the D (D) over bar* amplitude, with the mesons embedded in the dense environment. We find important nuclear corrections for T-D (D) over bar* and the pole position of the resonance, and discuss the dependence of these results on the D (D) over bar* molecular component in the X(3872) wave function. These predictions could be tested in the finite-density regime that can be accessed in the future CBM and PANDA experiments at the Facility for Antiproton and Ion Research (FAIR).

Abstract: We study the B+J/K+ reaction, and show that it is driven by the presence of two resonances, the X(3940) and X(3930), that are of molecular nature and couple most strongly to D*D*, but also to J/. Because of that, in the J/ mass distribution we find a peak related to the excitation of the resonances and a cusp with large strength at the D*D* threshold.

Abstract: We study systematically the decomposition of the Weinberg operator at three-loop order. There are more than four thousand connected topologies. However, the vast majority of these are infinite corrections to lower order neutrino mass diagrams and only a very small percentage yields models for which the three-loop diagrams are the leading order contribution to the neutrino mass matrix. We identify 73 topologies that can lead to genuine three-loop models with fermions and scalars, i.e. models for which lower order diagrams are automatically absent without the need to invoke additional symmetries. The 73 genuine topologies can be divided into two sub-classes: normal genuine ones (44 cases) and special genuine topologies (29 cases). The latter are a special class of topologies, which can lead to genuine diagrams only for very specific choices of fields. The genuine topologies generate 374 diagrams in the weak basis, which can be reduced to only 30 distinct diagrams in the mass eigenstate basis. We also discuss how all the mass eigenstate diagrams can be described in terms of only five master integrals. We present some concrete models and for two of them we give numerical estimates for the typical size of neutrino masses they generate. Our results can be readily applied to construct other d = 5 neutrino mass models with three loops.

Abstract: We study in detail the method proposed recently to study the vector-vector interaction using the N/D method and dispersion relations, which concludes that, while, for J = 0, one finds bound states, in the case of J = 2, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for N and D and a subtracted dispersion relation for D is used, with subtractions made up to a polynomial of second degree in s – s(th), matching the expression to 1 – VG at threshold. We study this in detail for the rho rho interaction and to see the convergence of the method we make an extra subtraction matching 1 – VG at threshold up to (s – s(th))(3). We show that the method cannot be used to extrapolate the results down to 1270 MeV where the f(2)(1270) resonance appears, due to the artificial singularity stemming from the “on-shell” factorization of the rho exchange potential. In addition, we explore the same method but folding this interaction with the mass distribution of the rho, and we show that the singularity disappears and the method allows one to extrapolate to low energies, where both the (s – s(th))(2) and (s – s(th))(3) expansions lead to a zero of Re D(s), at about the same energy where a realistic approach produces a bound state. Even then, the method generates a large Im D(s) that we discuss is unphysical.

Abstract: We study here the A(b)(0) -> J/psi p pi(-) reaction in analogy to the A(b)(0) -> J/psi pK(-) one, and we note that in both decays there is a sharp structure (dip or peak) in the J/psi p mass distribution around 4450 MeV, which is associated in the A(b)(0) -> J/psi pK(-) experiment to an exotic pentaquark baryonic state, although in J/psi p pi(-) it shows up with relatively low statistics. We analyze the A(b)(0) -> J/psi p pi(-) interaction along the same lines as the A(b)(0) -> J/psi pK(-) one, with the main difference stemming from the reduced Cabibbo strength in the former and the consideration of the pi(-)p final state interaction instead of the K(-)p one. We find that with a minimal input, introducing the pi(-)p and J/psi p interaction in S-wave with realistic interactions, and the empirical P-wave and D-wave contributions, one can accomplish a qualitative description of the pi(-)p and J/psi p mass distributions. More importantly, the peak structure followed by a dip of the experimental J/psi p mass distribution is reproduced with the same input as used to describe the data of A(b)(0) -> J/psi pK(-) reaction. The repercussion for the triangular singularity mechanism, invoked in some works to explain the pentaquark peak, is discussed.