On the chiral covariant approach to ρρ scattering

Abstract

We examine in detail a recent work (D. Gülmez, U.-G. Meißner and J. A. Oller, Eur. Phys. J. C 77:460 (2017)), where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J = 2 state disappears with a potential which is much more attractive than for J = 0, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J = 2 around the energy of the f2(1270). In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q 2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy. *

Disclosing $$D^*\bar{D}^*$$ D ∗ D ¯ ∗ molecular states in the $$B_c^- \rightarrow \pi ^- J/\psi \omega $$ B c - → π - J / ψ ω decay

“…Using the 3 P 0 model to implement the qq hadronization [30] and Racah algebra one can relate the states for scalar and vector or tensor production. This exercise is done in [31] to relate pseudoscalar and vector pro- [10][11][12]. They are the equivalent in the light sector to the X (3940) and X (3930) studied here in the heavy quark sector.…”

“…[9]). Actually, the interaction between mesons, particularly vector mesons in spin two, is very strong [10][11][12], even stronger than between nucleons, and the only limit to the formation of multi-meson states is that we do not have the meson number conservation, unlike baryon number conservation for the nucleons forming nuclei. This allows the multi-meson states to decay in states of fewer, or lighter mesons, the width increases with the number of mesons of the cluster, and at some point they are no longer identifiable experimentally.…”

ρρ scattering revisited with coupled channels of pseudoscalar mesons

“…However, this conclusion was not agreed upon by Ref. [11] in which the non-relativistic assumption was dropped by evaluating exactly the loops with full    .…”

Interactions between vector mesons and dynamically generated resonances

“…Ref. [42], the authors examine the the relativistically covariant ρρ interaction and argue that the disappearance of the tensor bound state in Ref. [36] is due to the on-shell factorization of the potential done in the region where an "unphysical" discontinuity (imaginary part) is developed by the left-hand cut.…”

“…The authors of Ref. [42] argue that the one-loop integrals for the t-channel ρ-exchange triangle and box diagrams do not have an imaginary part and thus the left-hand cut s ≤ 3M 2 ρ would be unphysical. The singularities of the triangle and box diagrams by putting at least two intermediate ρ mesons on shell are the triangle and box Landau singularities [43], and they indeed do not appear in the physical Riemann sheet for the processes in the energy region of interest according to the Coleman-Norton theorem [44].…”