We calculate the width $2Delta_{text{CT}}$ and intensity of the charge-transfer peak (the one lying at the on-site energy $E_d$) in the impurity spectral density of states as a function of $E_d$ in the SU($N$) impurity Anderson model (IAM). We use the dynamical density-matrix renormalization group (DDMRG) and the noncrossing-approximation (NCA) for $N$=4, and a 1/$N$ variational approximation in the general case. In particular, while for $E_d gg Delta$, where $Delta$ is the resonant level half-width, $Delta_{text{CT}}=Delta$ as expected in the noninteracting case, for $-E_d gg N Delta$ one has $Delta_{text{CT}}=NDelta$. In the $N$=2 case, some effects of the variation of $% Delta_{text{CT}}$ with $E_d$ were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. Konemann textit{et al.}, Phys. Rev. B textbf{73}, 033313 (2006)]. More dramatic effects are expected in similar experiments, that can be carried out in systems of two quantum dots, carbon nanotubes or other, realizing the SU(4) IAM.
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