  The diffusion of chiral active Brownian particles in three-dimensional space
is studied analytically, by consideration of the corresponding Fokker-Planck
equation for the probability density of finding a particle at position
$\boldsymbol{x}$ and moving along the direction $\hat{\boldsymbol{v}}$ at time
$t$, and numerically, by the use of Langevin dynamics simulations. The analysis
is focused on the marginal probability density of finding a particle at a given
location and at a given time (independently of its direction of motion), which
is found from an infinite hierarchy of differential-recurrence relations for
the coefficients that appear in the multipole expansion of the probability
distribution which contains the whole kinematic information. This approach
allows the explicit calculation of the time dependence of the mean squared
displacement and the time dependence of the kurtosis of the marginal
probability distribution, quantities from which the effective diffusion
coefficient and the "shape" of the positions distribution are examined.
Oscillations between two characteristic values were found in the time evolution
of the kurtosis, namely, between the value that corresponds to a Gaussian and
the one that corresponds to a distribution of spherical shell shape. In the
case of an ensemble of particles, each one rotating around an
uniformly-distributed random axis, it is found evidence of the so called effect
"anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian
distribution for the positions yet the mean squared displacement is a linear
function of time.
