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We study non-equilibrium current fluctuations through a quantum dot, whichincludes a ferromagnetic Hund's rule coupling $J$, in the low-energy Fermiliquid regime using the renormalized perturbation theory. The resultingcumulant for the current distribution in the particle-hole symmetric case,shows that spin-triplet and spin-singlet pairs of quasiparticles are formed inthe current due to the Hund's rule coupling and these pairs enhance the currentfluctuations. In the fully screened higher-spin Kondo limit, the Fano factortakes a value $F_b = (9M+6)/ (5M+4)$ determined by the orbital degeneracy $M$.We also investigate crossover between the small and large $J$ limits in thetwo-orbital case M=2, using the numerical renormalization group approach.

Full counting statistics for orbital-degenerate impurity Anderson model with Hund's rule exchange coupling