# Angular distance

At hadron colliders, the angular distance is usually defined in a way that is invariant under longitudinal boosts. This is achieved by using the pseudorapidity difference $\Delta\eta$ of the objects rather than an actual angle. In the transverse plane, the momentum of the initial state is (essentially) zero, so the azimuthal angle difference $\Delta\phi$ can be used directly. This gives the definition:
$\Delta R = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}.$