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[After having shown that the sum rule of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} meson can be analyzed by MEM, we in this chapter proceed to the next classic sum rule, the one of the nucleon. As will be seen, the analysis of this sum rule is more difficult compared with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} meson case, especially because the interpolating field here contains three quarks and thus has a larger mass dimension, which leads to a slower convergence and larger uncertainties of the OPE. As a consequence, we will show that the MEM analysis of the nucleon sum rule with a Borel kernel in fact does not work well. On the other hand, the sum rule with a Gaussian kernel provides reasonable results. This chapter is mainly based on K. Ohtani, P. Gubler and M. Oka, Eur. Phys. J. A 47, 114 (2011)., and its results were calculated by K. Ohtani.]
Published: Mar 30, 2013
Keywords: Gaussian sum rule; Interpolating field; Parity projection
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