  Two-parametric variation over the aspect ratio of each disk and distance
between disks gives rise to numerous events of avoided crossing of resonances
of individual disks. For these events the hybridized anti-bonding resonant
modes can acquire a morphology close to the Mie resonant mode with high orbital
momentum of equivalent sphere. The $Q$ factor of such resonance can exceed the
$Q$ factor of isolated disk by two orders in magnitude. We show that dual
incoherent counter propagating coaxial Bessel beams with power $1mW/\mu m^2$
with frequency resonant to such a anti-bonding modes result in unprecedented
optical binding forces up to decades of nano Newtons for silicon micron size
disks. We show also that a magnitude and sign of optical forces strongly depend
on the longitudinal wave vector of the Bessel beams.
