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We study the in-medium masses of the heavy quarkonium (charmonium andbottomonium) states in isospin asymmetric nuclear matter in presence of anexternal magnetic field. The mass modifications of the heavy quarkonia areobtained from the medium modifications of a scalar dilaton field, $\chi$,calculated within a chiral effective model. The dilaton field is introduced inthe model through a scale invariance breaking logarithmic potential, and,simulates the gluon condensates of QCD. Within the chiral effective model, thevalues of the dilaton field along with the scalar (isoscalar, $\sigma (\sim\langle \bar u u \rangle +\langle \bar d d \rangle)$, isoscalar $\zeta (\sim\langle \bar s s \rangle$) and isovector $\delta (\sim \langle \bar u u\rangle  - \langle\bar d d \rangle)$) fields, are solved from their coupled equationsof motion. These are solved accounting for the effects of the Dirac sea (DS) aswell as anomalous magnetic moments (AMMs) of the nucleons. The Dirac seacontributions are observed to lead to enhancement (reduction) of the quarkcondensates (through $\sigma$ and $\zeta$ fields) with increase in magneticfield, an effect called the (inverse) magnetic catalysis. The magnetic fieldeffects on the masses of the heavy quarkonia include the mixing of thepseudoscalar (spin 0) and vector (spin 1) states (PV mixing), as well as, theeffects from (inverse) magnetic catalysis. These effects are observed to besignificant for large values of the magnetic field. This should have observableconsequences on the production of the heavy quarkonia and open heavy flavourmesons, resulting from ultra-relativistic peripheral heavy ion collisionexperiments, where the created magnetic field can be huge.

Masses of Heavy Quarkonium states in magnetized matter -- effects of PV mixing and (inverse) magnetic catalysis