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Full counting statistics of Kondo-type tunneling in a quantum dot: the fluctuation effect of Slave-Boson field

We study the full counting statistics (FCS) of electron tunneling through a multi-terminal quantum dot in the Kondo regime within the slave-boson mean field theory. By employing the A.O. Gogolin and A. Komnik's method of calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B {\bf 73}, 195301 (2006)], we obtain the counting field $λ$-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing perturbative expansion to the first order of $λ$, we find an extra contribution to the shot noise due to the bias-induced Bose field fluctuation, and then confirm that the nonequilibrium particle number fluctuation plays an important role in the current noise of the Kondo dot: enhancement of the current auto-correlation and a positive current cross-correlation.