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Articles Particle Physics Two- and Three-Point Energy Correlations in Hadronic e+e- Annihilation (1980)
TWO- AND THREE-POINT ENERGY CORRELATIONS IN HADRONIC e+e- ANNIHILATION (1980) |
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In a previous paper [1] (1) , we introduced the shape parapeters (the 
are the Legendre polynomials, and the sum runs over all pairs of particles)
which describe the distribution of energy in the final states of 
annihilation events and whose mean values may be computed from QCD perturbation theory. In this paper, we describe further methods for analyzing event shapes (2). In Sect. 2, we consider two-point energy correlations, whose mean values provide a reexpression of the information on event shapes contained in the 
. The 
were explicitly constructed to be rotationally invariant; Sect. 3 discusses a generalization of the in which measures correlations between the final state and the incoming beam direction.
We define the two-detector energy correlation function introduced in [1] and [3] by
where the 
are the sum of the moduli of the three-momenta of particles incident on two detectors covering the regions 
of total solid angle 
The rotationally-invariant observable 
is formed in each event by averaging 
over all possible positions for the detectors, while maintaining their relative orientation. 
may, therefore, be written as
where 
signifies the relative orientation of 
and 
and the averages are over all positions of and 
in a particular event which maintain this: does not depend on the orientation of the final state with respect to the beam axis. For theoretical purposes, such as those of [2] and [4], it is convenient to consider the idealized energy correlation 
between two point detectors. This has the useful property that
For large 
may be approximated by
Hence to obtain estimates for the at large 
one requires only the behavior of 
for close to 
corresponding to energy correlations between detectors which are either close together or back-to-back (anticollinear). Such estimates are given in [2,4,5].
In order to assess to what extent the various predictions presented in this paper constitute tests of QCD, one should compare them with results from other theories. Appendix B gives some predictions which would follow from a theory with colored scalar, rather than vector, gluons.
