Quantum Chromodynamics in the presence of intense magnetic field reveals exotic phenomena
like chiral magnetic effect, magnetic catalysis, inverse magnetic catalysis, vacuum
superconductivity etc. Such a strong magnetic field is expected to be produced in non-central
relativistic heavy ion collision experiments at RHIC and LHC. So, the study of ``strongly"
interacting hot and/or dense matter under external magnetic field has become one of the
most important topics of research since a decade. In particular, the study of the
properties of mesons at finite temperature and/or density in an external magnetic field
is important in order to extract information about chiral phase transition parameters.
In this contribution, we will present the medium modification of pions and rho mesons under
an arbitrary external magnetic field. The one-loop self energies of $\pi$ and $\rho$ are calculated
using effective field theoretical techniques taking nucleon and pions as the loop particles
respectively. The proton and charged pion propagators are modified due to the magnetic field
using the full Schwinger proper time propagator. From the
in-medium self energies, we obtained the effective mass and dispersion relations for $\pi$
and $\rho$ at the pole of the complete propagator calculated from the Dyson-Schwinger equation.
We have also studied the spectral function as well as the detailed analytical structure
of the self energy function of $\rho$. A non-trivial effect of magnetic field on these mesonic
properties is observed.
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