Under the extreme density and temperature of the medium produced in heavy-ion collisions, the properties of hadrons, for example, in-medium masses and decay width may change significantly. Along with finite density and temperature, the finite strong magnetic field is expected to produce in the non-central heavy-ion collisions and can also have important consequences. In this thesis, we investigate the mass and decay width of different mesons in the hot and dense hadronic matter using the effective mean-field chiral SU(3) hadronic model along with other non-perturbative approaches such as QCD sum rules and chiral perturbation theory. The effect of isospin asymmetry has also been accounted for in the present work. The in-medium properties such as mass shift, optical potential, and decay width of mesons are observed to change significantly. 

Using the combined approach of chiral SU(3) model and QCD sum rules, we start with the study of in-medium mass shift of charmonia (J/ψ, ηc, χc0, χc1 ) and bottomonia (Υ, ηb, χb0, χb1 ) in the presence of asymmetric magnetized hot and dense nuclear matter. In QCD sum rules, the various properties of hadrons are expressed in terms of quark and gluon condensates. The magnetic field dependence of quark condensate, scalar gluon condensate as well as twist-2 gluon condensate, are calculated from the chiral SU(3) model. Within the chiral model, these condensates are evaluated from the in-medium values of scalar-isoscalar fields σ and ζ, scalar-isovector field δ, and scalar glueball field χ. The medium-modified condensates are used as input in QCD sum rules.

We extended the same combined approach to investigate the in-medium mass and shift in decay constants of open charm mesons (D,D0,D∗,D1). As an application, using the 3P0 model, we obtain the magnetic field-induced decay width of heavy charmonia decaying into D ¯D pairs. Furthermore, the decay width of D∗s meson decaying to D∗K is also calculated using the same 3P0 model. 

Further, we investigate the η-baryons interactions employing the chiral SU(3) model solely as well as jointly using the chiral SU(3) model and chiral perturbation theory. In the former approach, the in-medium attributes of pseudoscalar η-mesons are incorporated from the first range, mass, and d term of the chiral ηN Lagrangian. Besides, in the joint approach, the next-to-leading order contributions are computed from the ηN Lagrangian of chiral perturbation theory, in which the in-medium effects are introduced through scalar densities of the chiral SU(3) model.

The in-medium mass of ϕ meson at the one-loop level is studied using the in-medium values of K ¯K mass in asymmetric strange hadronic matter calculated within the chiral model. The ultraviolet divergence is regularized through the dipole form factor with  cut-off mass parameter Λc=1-4 GeV. Besides, the mass and decay width of ϕ meson are also calculated using the self-consistent Lagrangian approach in the strange hadronic matter.

The masses, optical potential, and decay width of these mesons modify appreciably in the presence of different medium attributes such as density, temperature, isospin asymmetry, strangeness fraction, and magnetic field. The results of the present investigation may be helpful to understand the experimental observables arising from the various experimental facilities such as CBM, PANDA, NICA, Jefferson lab, and, J-PARC.