Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) we study the electronic structure of layered BaZnBi$_2$. Our experimental results show no evidence of Dirac states in BaZnBi$_2$ originated either from the bulk or the surface. The calculated band structure without spin-orbit interaction shows several linear dispersive band crossing points throughout the Brillouin zone. However, as soon as the spin-orbit interaction is turned on, the band crossing points are significantly gapped out. The experimental observations are in good agreement with our DFT calculations. These observations suggest that the Dirac fermions in BaZnBi$_2$ are trivial and massive. We also observe experimentally that the electronic structure of BaZnBi$_2$ comprises of several linear dispersive bands in the vicinity of Fermi level dispersing to a wider range of binding energy.
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