  Spurred by an experimental controversy in the literature, we investigate the
end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic
simulations and dynamic mean-field theory. Precise experimental observations
over the last few years of end-monomer dynamics in the diffusion of
double-stranded DNA have given conflicting results: one study indicated an
unexpected Rouse-like scaling of the mean squared displacement (MSD) r^2(t) ~
t^(1/2) at intermediate times, corresponding to fluctuations at length scales
larger than the persistence length but smaller than the coil size; another
study claimed the more conventional Zimm scaling r^2(t) ~ t^(2/3) in the same
time range. We find a novel intermediate dynamical regime where the effective
local exponent of the end-monomer MSD, alpha(t) = d log r^2(t)/ d log t, drops
below the Zimm value of 2/3 for sufficiently long chains. The deviation from
the Zimm prediction increases with chain length, though it does not reach the
Rouse limit of 1/2. The qualitative features of this intermediate regime, in
particular the variation of alpha(t) with chain and persistence lengths, can be
reproduced through a heuristic scaling argument. Anomalously low values of the
effective exponent alpha are explained by hydrodynamic effects related to the
slow crossover from dynamics on length scales smaller than the persistence
length to dynamics on larger length scales.
