  We present arguments regarding diquarks possible role in low-energy hadron
phenomenology that escaped theorists' attention so far. Good diquarks, i.e. the
$0^{+}$ states of two quarks, are argued to have a two-component structure with
one of the components peaking at distances several times shorter than a typical
hadron size (a short-range core). This can play a role in solving two old
puzzles of the 't Hooft 1/N expansion: strong quark mass dependence of the
vacuum energy density and strong violations of the Okubo-Zweig-Iizuka (OZI)
rule in the quark-antiquark $0^\pm$ channels. In both cases empiric data defy
't Hooft's 1/N suppression. If good diquarks play a role at an intermediate
energy scale they ruin 't Hoofts planarity because of their mixed-flavor
composition. This new scale associated with the good diquarks may be related to
a numerically large scale discovered in [V. Novikov, M. Shifman, A. Vainshtein
and V. Zakharov, Nucl. Phys. B 191, 301 (1981)] in a number of phenomena mostly
related to vacuum quantum numbers and $0^\pm$ glueball channels. If SU(3)$_{\rm
color}$ of bona fide QCD is replaced by SU(2)$_{\rm color}$, diquarks become
well-defined gauge invariant objects. Moreover, there is an exact symmetry
relating them to pions. In this limit predictions regarding good diquarks are
iron-clad. If passage from SU(2)$_{\rm color}$ to SU(3)$_{\rm color}$ does not
lead to dramatic disturbances, these predictions remain qualitatively valid in
bona fide QCD.
