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Detailed derivation of the 3P0 strong decay model applied to baryons

Abstract:

By using the pair creation model, we provide a detailed derivation of the transition matrix for a baryon decaying into a meson-baryon system. This analysis was successfully conducted for a meson in [J. Segovia, D. R. Entem, and F. Fernández, Phys. Lett. B 715, 322 (2012)], and we extend the same formalism to the baryon sector, focusing on the strong decay width because all hadrons involved in the reaction are very well established, the two hadrons in the final state are stable and require no further analysis, all quarks are light and thus equivalent, and the decay width of the process is relatively well measured. Utilizing a very common Rayleigh-Ritz variational method to solve the 2- and 3-body Schödinger bound-state equation in which the hadron’s radial wave functions are expanded in terms of a Gaussian basis, we can relate the expression of the invariant matrix element with the mean-square radii of hadrons involved in the decay. We use their experimental measures in such a way that only the strength of the quark-antiquark pair creation from the vacuum is a free parameter. This is then taken from our previous study on strong decay widths in the meson sector [J. Segovia, D. R. Entem, and F. Fernández, Phys. Lett. B 715, 322 (2012)], and the obtained results are compatible with the experimental results for the calculated decay width. Despite requiring the calculation of additional baryon strong decays, a feasible avenue towards a unified description of both baryon and meson strong decay widths within a single constituent quark model framework may be attainable. Finally, this research has been developed to lay the foundation for a novel raft of applications to exotic hadrons, i.e., the description of the baryon’s coupling to meson-baryon thresholds, one of the mechanisms that is considered to be responsible for providing either a large renormalization to naive states or genuine dynamically-generated meson-baryon molecules.