  We investigate the effects of general non-magnetic quenched disorder on a
two-dimensional spin-density-wave (SDW) quantum critical metallic system and
discuss how a clean SDW non-Fermi liquid state becomes modified, based on a
renormalization group (RG) method. We consider (i) all possible scattering
channels by a random charge potential for fermion fields and additionally (ii)
a random mass term for a SDW boson order parameter as effects of the
non-magnetic quenched disorder. From the one-loop analysis, we find a weakly
disordered non-Fermi liquid metallic fixed point(interacting long-range ordered
fixed point) when only the random boson mass vertex is considered. However, in
the general case where all disorder vertices are considered, it turns out that
there is no stable fixed point and the low-energy RG flows are governed by the
large random charge potential vertices especially channels in a `Direct'
category with an interplay of an effective Yukawa interaction. Focusing on the
physical meanings of the low-energy RG flows, we provide a detailed explanation
of the one-loop results. Beyond the one-loop level, we first discuss partial
two-loop corrections to the random charge potential vertices. Furthermore, we
examine the possibility of different low-energy RG flows compared to that of
the one-loop results by considering the two-loop corrections to the random
boson mass vertex and, discuss low energy properties in relation to the random
singlet phase. For physical properties, we calculate asymptotic forms of the
two-point Green's functions and anomalous dimensions of the four
superconducting channels in the one-loop level.
