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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.

Color confinement
Asymptotic freedom

References

De Rújula, A.; Ellis, J.; Floratos, E. G.; Gaillard, M. K. (1978). "QCD predictions for hadronic final states in e +e - annihilation". Nuclear Physics B 138 (3): 387–429. Bibcode:1978NuPhB.138..387D. doi:10.1016/0550-3213(78)90388-7.

Bordes, G.; Nicolaidis, A. (1980). "Acoplanarity distributions at large transverse momenta". Physical Review D 22 (9): 2152–2156. Bibcode:10.1103/PhysRevD.22.2152. doi:10.1103/PhysRevD.22.2152.

Physics Encyclopedia