Scalar resonance: A model for Kappa

Author(s)

Patricia Camargo Magalhães

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2008-12-15

Examining board members

Manoel Roberto Robilotta; Bruto Max Pimentel Escobar; Carla Göbel Burlamaqui de Melo

• Advisor: Manoel Roberto Robilotta

Abstract

This work aims mostly at studying the $\\k$ resonance, which is still a controversial scalar meson nowadays within the scientific community. We studied the $K\\pi$ elastic scattering, because the $\\k$ appears as an intermediate state in this subsystem. From an effective chiral lagrangian $SU(3)\\times SU(3)$, involving contact terms and resonances, we calculated the $K\\pi$ amplitude projected on the $1/2$ isospin channel and then unitarized by means of mesonic {\\it loops}. The physical poles of the amplitude were investigated, given by the zeros of its denominator which are encountered on the Riemanns surface. Although these zeros can be numerically obtained, the strict analysis of this solution does not supply information about the poles producing dynamics. Alternatively, a qualitative description of the poles was obtained considering the $SU(2) \\Leftrightarrow M_\\p=0$ limit and the K matrix approximation, which corresponds to the unitarizing of the amplitude with {\\it loops} of $K\\p$ on shell. These simplifications reduce the amplitude denominator to a second grade polynomial that originates two physical poles, later identified as being $K^*_0(1430)$ and $\\k$. This simplified model allows for a good interpretation of the poles dynamic origin. The $\\k$ has been stable on the explicit resonance coupling, showing that it is produced by the contact diagram. The $K^*_0(1430)$ identified resonance, on the other hand, varies from a bounded state to a non-physical pole, depending on the resonance parameters attributed values, which strongly suggest that the nature of this poles is distinct. These different dynamic behaviors have also been observed in the numerical programs, indicating that the essence of the poles was maintained in the simplified model. With the numerical programs we obtained the position of pole $\\k$ in $(0.7505 \\pm 0.0010) - i\\, (0.2363 \\pm 0.0023)\\;$GeV, which is in accordance with various more complex chiral models. (AU)