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In particle physics, the acoplanarity of a scattering experiment measures the degree to which the paths of the scattered particles deviate from being coplanar. Measurements of acoplanarity provide a test of perturbative quantum chromodynamics, because QCD predicts that the emission of gluons can lead to acoplanar scattering events.[1]
Measures of acoplanarity

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

\( \varphi = \pi-( \phi_2 - \phi_1 ) \)

where \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

\( A = 4 \min{ \left( \frac{ \sum_i |p_{out}^i| }{ \sum_i |p_i| } \right)^2} \)

where p_i are the momenta of the final state particles and \( p_{out}^i \) 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.

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Acoplanarity