Angular distance

The angular distance (or angular separation) between two objects tells how much two objects are moving in the same direction. It is usually denoted ΔR (delta R).

At hadron colliders

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:

$\Delta R = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}.$

At lepton colliders

At lepton colliders, the vector angle between the object momenta may be used directly.