  We consider the effective field theory (EFT) treatment of two-body systems
with narrow resonances. Within this approach, an $s$-wave scattering amplitude
can be expanded in powers of a typical momentum scale of a system $Q\ll
\Lambda$, where $\Lambda$ represents a hard scale of a scattering system and an
energy difference $\delta \epsilon=|E-\epsilon_0|\ll \epsilon_0$, where
$\epsilon_0$ is a resonance peak energy. It is shown that at leading order in
the double expansion a universal form of a two-body scattering amplitude is a
sum of a Breit-Wigner term of order $Q^{-1}$, a smooth background term of order
$Q^0$, and an interference term of order $Q^0$. The techniques developed in
this paper can be used to investigate the properties of narrow resonances that
are produced by short-distance dynamics.
