Sphericity (particle physics)

In accelerator experiments in particle physics and in particular in the computer programs used for their evaluation, sphericity is used to describe the geometric shape of collision events and, for example, to filter out jet events or to indicate the proportion of transverse impulses. The following tensor (or matrix ) is used for this:

${\displaystyle S^{\alpha \beta }={\frac {\sum _{i}p_{i}^{\alpha }p_{i}^{\beta }}{\sum _{i}|p_{i}|^{2}}}}$

The numbers or (with ) location coordinates (x, y, z correspond to 1, 2, 3) of the i-th event, that is, the point in the detector where the particles created during the collision were registered. As a rule, three different positive eigenvalues ​​are obtained from the diagonalization , of which the eigenvalue i = 1 is the largest (they are normalized in such a way that the sum of the eigenvalues ​​results in 1). With the other two eigenvalues ​​i = 2,3 the "sphericity" S is formed: ${\displaystyle p_{i}^{\alpha }}$ ${\displaystyle p_{i}^{\beta }}$ ${\displaystyle \alpha ,\beta \in \{1,2,3\}}$ ${\displaystyle \lambda _{i}}$

${\displaystyle S={\frac {3}{2}}(\lambda _{2}+\lambda _{3})}$

with 0 ≤ S ≤ 1. For isotropic (spherical form) events, S is very close to 1. If there is a 2-jet event, S is close to 0.

literature

• James D. Bjorken , Stanley J. Brodsky : Statistical Model for Electron-Positron Annihilation into Hadrons. In: Physical Review D 1 ,. 1970, pp. 1416-1420

Web links

• Fermilab documentation