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We investigate out of equilibrium transport through an orbital Kondo systemrealized in a single quantum dot, described by the multiorbital impurityAnderson model. Shot noise and current are calculated up to the third order inbias voltage in the particle-hole symmetric case, using the renormalizedperturbation theory. The derived expressions are asymptotically exact at lowenergies. The resulting Fano factor of the backscattering current $F_b$ isexpressed in terms of the Wilson ratio $R$ and the orbital degeneracy $N$ as$F_b =\frac{1 + 9(N-1)(R-1)^2}{1 + 5(N-1)(R-1)^2}$ at zero temperature. Then,for small Coulomb repulsions $U$, we calculate the Fano factor exactly up toterms of order $U^5$, and also carry out the numerical renormalization groupcalculation for intermediate $U$ in the case of two- and four-fold degeneracy($N=2,\,4$). As $U$ increases, the charge fluctuation in the dot is suppressed,and the Fano factor varies rapidly from the noninteracting value $F_b=1$ to thevalue in the Kondo limit $F_b=\frac{N+8}{N+4}$, near the crossover region$U\sim \pi \Gamma$, with the energy scale of the hybridization $\Gamma$.

The Kondo crossover in shot noise of a single quantum dot with orbital degeneracy