Acoplanarity

For a two-jet final state, a useful measure of acoplanartiy is

${\displaystyle \varphi =\pi -(\phi _{2}-\phi _{1})}$

where ${\displaystyle \phi _{i}}$ are the azimuthal angles of the final state jets with respect to the beam line.[2] An alternative measure of acoplanarity which is infrared safe and which works for broad jets of many particles is given by

${\displaystyle A=4\min {\left({\frac {\sum _{i}|p_{out}^{i}|}{\sum _{i}|p_{i}|}}\right)^{2}}}$

where ${\displaystyle p_{i}}$ are the momenta of the final state particles and ${\displaystyle p_{out}^{i}}$ are the components of these momenta perpendicular to a plane chosen such that A is minimized.[1] In the case of two coplanar final state particles, the plane which minimizes A would contain the paths of both particles and the beamline, and A would equal 0.

• Color confinement
• Asymptotic freedom