  This is the first part of a series of two papers where we study perturbations
of divergence form second order elliptic operators
$-\mathop{\operatorname{div}} A \nabla$ by first and zero order terms, whose
coefficients lie in critical spaces, via the method of layer potentials. In
particular, we show that the $L^2$ well-posedness of the Dirichlet, Neumann and
Regularity problems for complex Hermitian, block form, or constant-coefficient
divergence form elliptic operators in the upper half-space are all stable under
such perturbations. For instance, this allows us to claim the first results in
the setting of an unbounded domain concerning the solvability of boundary value
problems for the magnetic Schr\"odinger operator $-(\nabla-i{\bf a})^2+V$ when
the magnetic potential ${\bf a}$ and the electric potential $V$ are accordingly
small in the norm of a scale-invariant Lebesgue space. In the present paper, we
establish $L^2$ control of the square function via a vector-valued $Tb$ theorem
and abstract layer potentials, and use these square function bounds to obtain
uniform slice bounds for solutions. The existence and uniqueness of solutions,
as well as bounds for the non-tangential maximal operator, are considered in
the upcoming paper.
