Scalar resonances: dynamic relations between scattering and decay processes

Author(s)

Diogo Rodrigues Boito

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2007-10-16

Examining board members

Manoel Roberto Robilotta; Carla Göbel Burlamaqui de Melo; Rogério Rosenfeld

• Advisor: Manoel Roberto Robilotta

Abstract

The existence of a light scalar-isoscalar meson, known as ?, was suggested in the 60\'s. This particle played an important role in the theoretical construction of ?? interactions but, in spite of all experimental effort, it failed to be detected. This scenario changed radically in 2001, when a scalar-isoscalar resonance was discovered in the ?+?- channel of the D+ -> ?+?-?+ decay and was called ?(500). Nowadays, its existence is rather well established. However, in the analysis of experimental data, expressions loosely based on theory are employed and therefore its mass and width are still not well known. In this kind of decay, the production of the resonance may occur at the weak vertex. When it propagates, final state interactions take place. Usually these interactions are not properly taken into account in data analysis. In this work, we introduce a function _(s), which describes the propagation and decay of the resonance in the presence of the final state interactions. In the elastic regime, the phase of _(s) is determined by the Watson\'s theorem, which states that it must be the same as the scattering phase. We were able to establish, unambiguously, how the information from scattering should be used to determine not only the phase of _(s) but also its modulus. Our main result is an expression for _(s) in terms of the elastic phase and another one related to a well controlled loop integral. Three special cases are explored numerically, namely: the linear and non linear sigma models and a phenomenological model that takes into account the coupling between pion-pion and kaon-kaon channels. In agreement with quantum field theory, our result encompasses unitarity, treats the resonance as an explicit degree of freedom and, moreover, corresponds to a generalisation of the usual K-matrix unitarization procedure. Since it represents a clear way to relate scattering and production, our function _(s) can be useful in data analysis and may be instrumental in the determination of the pole position of the ? as well as other scalar resonances. (AU)