  We determine the largest non-trivial rate of exponential decay at infinity
for solutions to the Dirac equation
  \begin{equation*}
  \mathcal{D}_n \psi + \mathbb{V} \psi = 0
  \quad \text{ in }\mathbb{R}^n,
  \end{equation*} being $\mathcal{D}_n$ the massless Dirac operator in
dimension $n\geq 2$ and $\mathbb{V}$ a (possibly non-Hermitian) matrix-valued
perturbation such that $|\mathbb{V}(x)| \sim |x|^{-\epsilon}$ at infinity, for
$-\infty < \epsilon < 1$. Moreover, we show that our results are sharp for $n
=2,3$, providing explicit examples of solutions that have the prescripted
decay, in presence of a potential with the related behaviour at infinity.
