Abstract
We perform a study of the D_s^+ rightarrow a_0(980)(f_0(980)) e^+ nu _e reactions investigating the different sources of isospin violation which make the production of the a_0(980) possible. We find that loops involving kaons in the production mechanism provide a source of isospin violation since they do not cancel due to the different mass of charged and neutral kaons, but we also find that the main source comes from the breaking of isospin in the meson-meson transition T matrices, which contain information on the nature of the low lying scalar mesons. The reaction is thus very sensitive to the nature of the a_0(980) and f_0(980) resonances. Our results are consistent with the present upper bound for a_0(980) production and only a factor three smaller, indicating that future runs with more statistics should find actual numbers for this reaction from where we can learn more about the origin of the scalar resonances and their nature.
Highlights
The nature of the low lying scalar mesons has been a subject of continuous debate [1,2,3,4,5,6,7]
While the a0(980) was early advocated as a K Kmolecule [8], the consideration of chiral dynamics for the interaction of mesons by means of chiral Lagrangians [9,10], and the subsequent unitarization with coupled channels introduced with the chiral approach [11,12,13,14], allows one to make this idea more quantitative and it is found that the f0(500), f0(980), a0(980) resonances are dynamically generated from the interaction of pairs of mesons, π π, K K, ηη, π η with the dynamics dictated by the chiral Lagrangians
We have studied in detail the Ds+ → a0(980)( f0(980))e+νe reactions from the perspective that the two resonances are dynamically generated from the interaction of pseudoscalar mesons
Summary
The nature of the low lying scalar mesons has been a subject of continuous debate [1,2,3,4,5,6,7]. One of the issues which has been advocated as a way to find information on the nature of the low lying scalar mesons is the one of the a0(980) − f0(980) mixing This occurs in reactions where the production of one of the states is allowed by isospin conservation and the other meson is observed in an isospin violating mode. We will present results on the π 0η mass distribution in Ds+ → a0(980)0e+νe; a0 → π 0η versus the π +π − mass distribution in Ds+ → f0(980)0e+νe; f0 → π +π −, and will show that the ratio obtained for the integrated mass distributions is consistent with the present upper bound for the reaction [58] and not too far, giving incentives for an improved measurement with more statistics, which, together with other cases already studied in the literature will provide good information concerning the nature of the low lying scalar mesons
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