  We prove the scattering for the defocusing generalized Benjamin-Ono equation
in the energy space $H^{\frac{1}{2}}(\mathbb{R})$. We first establish the
monotonicity formula that describes the unidirectional propagation. More
precisely, it says that the center of energy moves faster than the center of
mass. This type of monotonicity was first observed by Tao (DCDS 2007) in the
defocusing gKdV equations.
  We use the monotonicity in the setting of compactness-contradiction argument
to prove the large data scattering in the energy space
$H^{\frac{1}{2}}(\mathbb{R})$. On the way, we extend critical local theory of
Vento (IMRN 2010) to the subcritical regime. Indeed, we obtain subcritical
local theory and global well-posedness in the energy space.
