  We theoretically investigate the D'yakonov-Perel' spin relaxation properties
in diffusive wurtzite semiconductor nanowires and their impact on the quantum
correction to the conductivity. Although the lifetime of the long-lived spin
states is limited by the dominant $k$-linear spin-orbit contributions in the
bulk, these terms show almost no effect in the finite-size nanowires. Here, the
spin lifetime is essentially determined by the small $k$-cubic spin-orbit terms
and nearly independent of the wire radius. At the same time, these states
possess in general a complex helical structure in real space that is modulated
by the spin precession length induced by the $k$-linear terms. For this reason,
the experimentally detected spin relaxation largely depends on the ratio
between the nanowire radius and the spin precession length as well as the type
of measurement. In particular, it is shown that while a variation of the radius
hardly affects the magnetoconductance correction, which is governed by the
long-lived spin states, the change in the spin lifetime observed in optical
experiments can be dramatic. We compare our results with recent experimental
studies on wurtzite InAs nanowires.
