Nucleon and Delta sigma-terms

Author(s)

Gabriel Rocha de Santana Zarnauskas

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2006-06-02

Examining board members

Manoel Roberto Robilotta; Tobias Frederico; Adilson Jose da Silva

• Advisor: Manoel Roberto Robilotta

Abstract

The nucleon sigma term, $sigma_N$, may be extracted from experimental data and allows theories and models aimed at describing chiral symmetry breaking effects to be tested. At present, chiral perturbation theory is considered the effective theory of quantum chromodynamics at low energies. With this theory, one can obtain an expansion of $sigma_N$ in terms of the pion mass, involving low energy constants, which must be obtained from experiment. In this work we present a model that yields values for both $sigma_N$ and the delta sigma term, $sigma_Delta$, as functions of known parameters only. In the case of $sigma_Delta$, this procedure is particularly relevant, because $sigma_Delta$ is an important quantity in the evaluation of theoretical amplitudes and it is impossible to take it from experimental data. Several choices for pion-baryon coupling constants were used and our results lie in the intervals 43~MeV~$leq sigma_N leq$~49~MeV e 28~MeV~$leq sigma^R_Delta leq$~32~MeV, which are compatible with values produced by other groups. As the delta can decay, its sigma term has an imaginary part that we used to test the consistency of our calculations. The power counting in the chiral limit of our results is consistent with chiral perturbation theory. (AU)