  The pair contact process with diffusion (PCPD) has been recently investigated
extensively, but its critical behavior is not yet clearly established. By
introducing biased diffusion, we show that the external driving is relevant and
the driven PCPD exhibits a mean-field-type critical behavior even in one
dimension. In systems which can be described by a single-species bosonic field
theory, the Galilean invariance guarantees that the driving is irrelevant. The
well-established directed percolation (DP) and parity conserving (PC) classes
are such examples. This leads us to conclude that the PCPD universality class
should be distinct from the DP or PC class. Moreover, it implies that the PCPD
is generically a multi-species model and a field theory of two species is
suitable for proper description.
