2011

Complex 2D Matrix Model and Geometrical Map on Complex-Nc Plane

Nawa, Kanabu, Ozaki, Sho, Nagahiro, Hideko et al.

Understand

We study the parameter dependence of the internal structure of resonance states by formulating Complex two-dimensional (2D) Matrix Model, where the two dimensions represent two-levels of resonances.

We calculate a critical value of the parameter at which "nature transition" with character exchange occurs between two resonance states, from the viewpoint of geometry on complex-parameter space.
Such critical value is useful to know the internal structure of resonance states with variation of the parameter in the system.
We apply the model to analyze the internal structure of hadrons with variation of the color number Nc from infinity to a realistic value 3.

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If N c N_{c} -dependent cut-off [ 13 ] is considered, G π ρ G_{\pi\rho} would have complicated N c N_{c} -dependence (even in a non-analytic way). In our present study, to simply perform the analytic continuation into the complex- N c N_{c} plane, we alternatively use N c N_{c} -independent cut-off corresponding to the mass scale of q q ¯ q\bar{q} meson, which is also suggested as another candidate in Ref. [ 13 ]
Cited in the paper.

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