The initial decay rate Omega((k) over bar) of the dynamical scattering factor of a single regular star polymer is investigated with the chain conformational renormalization group method up to first order in epsilon. The reduced relaxation rate Omega((k) over bar)/k(3) is expressed as the ratio of the mobility to the static structure factor, and we have analyzed the two contributions separately. At the Gaussian fixed point we have found a qualitatively different result to that of the standard calculation in three dimensions, and the difference comes from the effect of the epsilon-expansion on the mobility. The renormalization group result at the self-avoiding fixed point describes qualitatively well the behavior of Omega((k) over bar)/k(3) observed in neutron scattering experiments for 12-arm-stars in a good solvent.