  A new solution to the strong CP problem with distinct experimental signatures
(long-lived particles) at the LHC is proposed. It is based on the Yukawa
interactions between mirror quarks, Standard Model (SM) quarks and Higgs
singlets. (Mirror quarks and leptons which include non-sterile right-handed
neutrinos whose Majorana masses are proportional to the electroweak scale, form
the basis of the EW-$\nu_R$ model.) The aforementioned Yukawa couplings can in
general be complex and can contribute to $Arg\, Det M$ ($\bar{\theta} =
\theta_{QCD} + Arg\, Det M$) at tree-level. The model contains a
Peccei-Quinn-type global symmetry which allows it to rotate away
$\theta_{QCD}$.The crux of matter in this manuscript is the fact that {\em no
matter how large} the CP-violating phases in the Yukawa couplings might be,
$Arg\, Det M$ can remain small i.e. $\bar{\theta} < 10^{-10}$ for reasonable
values of the Yukawa couplings and, in fact, vanishes when the VEV of the Higgs
singlet (responsible for the Dirac part of the neutrino mass in the seesaw
mechanism) vanishes. The smallness of the contribution to $\bar{\theta}$ is
{\em principally due} to the smallness of the ratio of the two mass scales in
the seesaw mechanism: the Dirac and Majorana mass scales.
