  We report shot noise measurements for a quantum dot formed in an InAs
nanowire suspended between superconducting electrodes. We find a clear
alternation for the shot noise value in the Coulomb blockade regime between
even and odd electron occupation in the dot, indicating that super-Poissonian
(Poissonian) shot noise with the Fano factor reaching around 2 (1) occurs for
even (odd) parity. With increasing magnetic field, the parity effect disappears
and all the regimes show the Fano factor of around 1. The whole observation in
our experiments quantitatively agrees with simulation obtained from
full-counting statistics of cotunneling including spin-flip relaxation process,
which corresponds to modelling electron motion in a quantum dot with strong
spin-orbit interaction.
