  A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed
as a Higgsed descendant of rank-2 U(1) lattice gauge theory. As noted by the
authors recently, [Y.-T. Oh, J. Kim, E.-G. Moon, and J. H. Han, Phys. Rev. B
{\bf 105}, 045128] the quasiparticles in that model shows unusual braiding
statistics that depends on the initial locations of the particles which
participate in the braiding. We show that this new kind of statistical phase
captures the total dipole moment of quasiparticles encompassed in the braiding,
in contrast to the conventional anyonic braiding seeing the total charge. An
Aharonov-Bohm interpretation of such {\it dipolar braiding statistics} is made
in terms of emergent, rank-1 vector potentials that are built out of the
underlying rank-2 gauge fields. Pertinent field theories of the quasiparticle
dynamics in the R2TC are developed, and the accompanying conservation laws
derived. A {\it dipolar BF theory} of the rank-2 gauge fields is constructed
and shown to correctly capture the dipolar braiding statistics, in contrast to
the conventional BF theory capturing the monopolar braiding statistics of
anyons in the rank-1 toric code.
