In this work, we present a thorough theoretical structure and spectroscopic study of the ground and low lying excited states of RbBa molecule. High-level ab-initio calculations are performed, using MCSCF/MRCI+Q level of method, based on the effective core potential (ECP) and core-polarization potential (CPP) approach. The potential energy curves, spectroscopic parameters, vibrationnel energy levels of the 16(^2,4Σ⁺,^2,4Π,^2,4Δ) first electronic states, with respect to the lowest five dissociation limits were calculated. The comparison of the spectroscopic constants of the ground state X²Σ⁺ with the available theoretical work, are in good agreement. The study of all the excited states is performed in this work for the first time. Afterwards, the spin-orbit operator is incorporated in valence MRCI calculation using optimized relativistic spin-orbit pseudo-potentials and 33 Ω states are generated and split into Λ-S states. In addition, both relativistic and non relativistic calculations of permanent and transition dipole moments are presented and discussed. Stimulated black body (T= 300 K) and spontaneous transition rates of vibrational states of X²Σ⁺ state were evaluated. The related vibrational lifetimes for RbBa are found to be in order of 10³ s which is sufficiently large for ultracold experiments. Moreover, the vibrational life-time for the A²Σ⁺(v’) and A²П (v”) states are measured and the possibility of Laser Cooling for the RbBa molecule is discussed based on Franck–Condon factors calculation of A²Σ⁺ (v’)→ X²Σ⁺(v) and A²П(v”) → X²Σ⁺(v) transition. This work represents a significant contribution for experimentalists as it provides efficient information in order to form cold alkali and alkaline-earth RbBa molecules.