  Pitch angles $p$ of the large-scale magnetic fields $\overline{\bf{\it{B}}}$
of spiral galaxies have previously been inferred from observations to be
systematically larger in magnitude than predicted by standard mean-field dynamo
theory. This discrepancy is more pronounced if dynamo growth has saturated,
which is reasonable to assume given that such fields are generally inferred to
be close to energy equipartition with the interstellar turbulence. This 'pitch
angle problem' is explored using local numerical mean-field dynamo solutions as
well as asymptotic analytical solutions. It is first shown that solutions in
the saturated or kinematic regimes depend on only five dynamo parameters, two
of which are tightly constrained by observations of galaxy rotation curves. The
remaining 3-dimensional (dimensionless) parameter space can be constrained to
some extent using theoretical arguments. Predicted values of $|p|$ can be as
large as $\sim40^\circ$, which is similar to the largest values inferred from
observations, but only for a small and non-standard region of parameter space.
We argue, based on independent evidence, that such non-standard parameter
values are plausible. However, these values are located toward the boundary of
the allowed parameter space, suggesting that additional physical effects may
need to be incorporated. We therefore suggest possible directions for extending
the basic model considered.
