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Detailed derivation of the 3P0 strong decay model applied to baryons
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Detailed derivation of the 3P0 strong decay model applied to baryons
By using the3P0 pair creation model,we provide a detailed derivation of the transition matrix for a bary-on decaying into a meson-baryon system.This analysis was successfully conducted for a meson in[J.Segovia,D.R.Entem,and F.Fernandez,Phys.Lett.B 715,322(2012)],and we extend the same formalism to the baryon sector,focusing on the △(1232)→ πN strong decay width because all hadrons involved in the reaction are very well estab-lished,the two hadrons in the final state are stable and require no further analysis,all quarks are light and thus equi-valent,and the decay width of the process is relatively well measured.Utilizing a very common Rayleigh-Ritz vari-ational method to solve the 2-and 3-body Schödinger bound-state equation in which the hadron's radial wave func-tions 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 previ-ous 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 △(1232)→ πN decay width.Despite requiring the calculation of additional baryon strong decays,a feasible avenue towards a uni-fied 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.
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