The initial decay rate Omega((k) over bar) of the dynamical scattering
factor of a single regular star polymer is investigated with the chai
n conformational renormalization group method up to first order in eps
ilon. The reduced relaxation rate Omega((k) over bar)/k(3) is expresse
d 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 st
andard calculation in three dimensions, and the difference comes from
the effect of the epsilon-expansion on the mobility. The renormalizati
on group result at the self-avoiding fixed point describes qualitative
ly well the behavior of Omega((k) over bar)/k(3) observed in neutron s
cattering experiments for 12-arm-stars in a good solvent.