  The masses of the $1S$ and $1P$ states of heavy quarkonia are investigated in
the magnetized, asymmetric nuclear medium, accounting for the Dirac sea
effects, using a combined approach of chiral effective model and QCD sum rule
method. These are calculated from the in-medium scalar and twist-2 gluon
condensates, calculated within the chiral model. The gluon condensate is
simulated through the scalar dilaton field, $\chi$ introduced in the model
through a scale-invariance breaking logarithmic potential. Considering the
scalar fields to be classical, the dilaton field, $\chi$, the non-strange
isoscalar, $\sigma (\sim (\langle \bar u u\rangle +\langle \bar d d\rangle ))$,
strange isoscalar, $\zeta (\sim \langle \bar s s\rangle)$ and non-strange
isovector, $\delta (\sim (\langle\bar u u\rangle-\langle\bar d d\rangle)$)
fields, are obtained by solving their coupled equations of motion, as derived
from the chiral model Lagrangian. The effects of magnetic field due to the
Dirac sea as well as the Landau energy levels of protons, and the non-zero
anomalous magnetic moments of the nucleons are considered in the present study.
In presence of an external magnetic field, there is also mixing between the
longitudinal component of the vector meson and pseudoscalar meson (PV mixing)
in both quarkonia sectors, leading to a rise (drop) of the masses of
$J/\psi^{||}\ (\eta_c$) and $\Upsilon^{||}(1S)\ (\eta_b$) states. These might
show in the experimental observables, e.g., the dilepton spectra in the
non-central, ultra-relativistic heavy ion collision experiments at RHIC and
LHC, where the produced magnetic field is huge.
