Sphericty axis and thrust axis

Question

I read a paper about the detection of the gluon at DESY in the 1979. There are described two methods of evaluating the results.
I do understand that jets are measured and the momentum is pretty important. But I wonder what it means by "with respect to the sphericity axis". I can not find any definition of a sphericity axis.
I hope someone else can help.

RogerJBarlow · Accepted Answer

The sphericity axis is the direction about which the total squared transverse momentum of all the observed particles is minimum.
This is easy to determine: you take the 3 by 3 matrix of the sum of the cartesian products of the particle momenta with themselves and diagonalise it. It's the analogy of the inertia tensor.
Spherocity is slightly different: it minimises the sum of the absolute transverse momenta.
The thrust axis is the one that maximises the sum of the total absolute momenta along the axis.
Thrust and spherocity require a numerical minimisation but are 'infra-red safe' in that if a (massless) particle splits into two they do not change, whereas the sphericity does. So sphericity is easy to calculate experimentally but messy to predict theoretically.

Sphericty axis and thrust axis

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