Collective modes of gluons in an anisotropic thermomagnetic medium

We study the collective modes of gluons in an anisotropic thermal medium presence a constant background magnetic field using hard-thermal-loop perturbation theory. The momentum space anisotropy has been incorporated through generalized Romatschke-Strickland form distribution function, whereas modification arising from quark loop contribution taken into account lowest Landau level approximation. consider two special cases: (i) spheroidal with vector orthogonal to external and (ii) ellipsoidal mutually vectors describing anisotropies along direction. general structure polarization tensor both cases is equivalent consists six independent basis tensors. find that introduction ingrains azimuthal angular dependence thermomagnetic modes. Our suggests strong can significantly reduce growth rate unstable modes, which may have important implications equilibration magnetized quark-gluon plasma.