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Articles Particle Physics Observables for the Analysis of Event Shapes in e+e- Annihilation and Other Processes (1978)
OBSERVABLES FOR THE ANALYSIS OF EVENT SHAPES IN e+e- ANNIHILATION AND OTHER PROCESSES (1978) |
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(1) See, for example, B. H. Wiik and G. Wolf, DESY Report No. 78-23, 1978 (to be published).
(2) G. Sterman and S. Weinberg, Phys. Rev. Lett. 39, 1436 (1977); G. Sterman, Phys. Rev. D 17, 2789 (1978).
(3) H. Georgi and M. Machacek, Phys. Rev. Lett. 39, 1237 (1977); E. Farhi, Phys. Rev. Lett. 39, 1587 (1977); A. De Rújula, J. Ellis, E. G. Floratos, and M. K. Gaillard, Nucl. Phys. B138, 387 (1978); S.-Y. Pi, R. L. Jaffe, and F. E. Low, Phys. Rev. Lett. 41, 142 (1978). These observables appear to be inconvenient to measure experimentally [S. Brandt and H. D. Dahmen, Seigen Report No. SI-78-8, 1978 (to be published)].
(4) The 
may be generalized by taking 
multipole moments of 
and combining them to give scalars under the rotation group using 3-
symbols. The set of all such observables determines up to an overall rotation. As we shall describe elsewhere, these observables allow precise tests for planes of particles in events. An obvious application is to 
.
(5) The mean values of the 
and 
for 
have also been considered from a rather different point of view in C. L. Basham L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 17, 2298 (1978), and Phys. Rev. Lett. 41, 1585 (1978) (this issue).
(6) G. C. Fox and S. Wolfram, California Institute of Technology Report No. CALT-68-678, 1978 (to be published).
(7) R. D. Field and R. P. Feynman, Nucl. Phys. B136, 1 (1978).
(8) The model was adjusted so as to agree with observed single-hadron momentum distributions. Limited experimental tests of its predictions for the detailed structure of jets [W. G. Scott, in ``Neutrinos-78,'' edited by Earle C. Fowler (Purdue Univ. Press, to be published)] have proved successful.
(9) The division between configurations of quarks and gluons which give two- and three-jet events is determined by the details of their fragmentation to hadrons. At present the division must be made almost arbitrarily, but our results are not sensitive to the choice (see Ref. 6).
(10) If incomplete final states are considered then only a fraction of the true energy of the event will be measured, so that it is convenient to use the effective 
rather than for this case.
(11) All processes of 
, including those involving extra initial-state particles (e.g., 
), must be added in order to obtain an infrared-finite result. To , however, only the three-jet parts of 
and 
contribute to 
and 
. 
gives an insignificant contribution.
(12) One may also define two-dimensional analogs of the . These provide an improved formulation of the tests of QCD proposed by H. Georgi and H. D. Politzer, Phys. Rev. Lett. 40, 3 (1978).
