Universality classes of absorbing phase transitions in generic branching-annihilating particle systems

We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one dimensional ring, where the walkers hop to their nearest neighbor with a bias $\epsilon$. For $\epsilon=0$, three universality classes: directed percolation (DP), parity conserving (PC) and pair contact process with diffusion (PCPD) are typically observed in such systems. We find that the introduction of $\epsilon$ does not change the DP universality class but alters the other two universality classes. For non-zero $\epsilon$, the PCPD class crosses over to DP and the PC class changes to a new universality class.