G. Hanson, G. S. Abrams, A. M. Boyarski, M. Breidenbach, F. Bulos, W. Chinowsky, G. J. Feldman, C. E. Friedberg, D. Fryberger, G. Goldhaber, D. L. Hartill, B. JeanMarie, J. A. Kadyh, R. R. Larsen, A. M. Litke, D. Lüke, B. A. Lulu, V. Lüth, H. L. Lynch, C. C. Morehouse, J. M. Paterson, M. L. Perl, F. M. Pierre, T. P. Pun, P. A. Rapidis, B. Richter, B. Sadoulet, R. F. Schwitters, W. Tanenbaum, G. H. Trilling, F. Vannucci, J. S. Whitaker, F. C. Winkelmann, and J. E. Wis
Lawrence Berkeley Laboratory and Department of Physics, University of California, Berkeley, California 94720, and Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305
(Received 8 October 1975)
We have found evidence for jet structure in e^{+}e^{}hadrons at centerofmass energies of 6.2 and 7.4 GeV. At 7.4 GeV the jetaxis angular distribution integrated over azimuthal angle was determined to be proportional to 1 + (0.78 ± 0.12) cos^{2} .
In quarkparton constituent models of elementary particles, hadron production in e^{+}e^{} annihilation reactions proceeds through the annihilation of the e^{+} and e^{} into a virtual photon which subsequently produces a quarkparton pair, each member of which decays into hadrons. At sufficiently high energy the limited transversemomentum distribution of the hadrons with respect to the original parton production direction, characteristic of all strong interactions, results in oppositely directed jets of hadrons.^{14} The spins of the constituents can, in principle, be determined from the angular distribution of the jets.
In this Letter we report the evidence for the existence of jets and the angular distribution of the jet axis.
The data were taken with the Stanford Linear Accelerator CenterLawrence Berkeley Laboratory magnetic detector at the SPEAR storage ring of the Stanford Linear Accelerator Center. Hadron production, muon pair production, and Bhabha scattering data were recorded simultaneously. The detector and the selection of events have been described previously.^{5,6} The detector subtended 0.65 x 4 ¼ sr with full acceptance in azimuthal angle and acceptance in polar angle from 50° to 130°. We have used the large blocks of data at centerofmass energies (E_{c.m.}) of 3.0, 3.8, 4.8, 6.2, and 7.4 GeV. We included only those hadronic events in which three or more particles were detected in order to avoid background contamination in events with only two charged tracks due to beamgas interactions and photonphoton processes.
To search for jets we find for each event that direction which minimizes the sum of squares of transverse momenta.^{7} For each event we calculate the tensor
(1) 
where the summation is over all detected particles and and _{} refer to the three spatial components of each particle momentum . We diagonalize _{} to obtain the eigenvalues _{1}, _{2}, and _{3} which are the sums of squares of transverse momenta with respect to the three eigenvector directions. The smallest eigenvalue (_{3}) is the minimum sum of squares of transverse momenta. The eigenvector associated with _{3} is defined to be the reconstructed jet axis. In order to determine how jetlike an event is, we calculate a quantity which we call the sphericity (S):
(2) 
S approaches 0 for events with bounded transverse momenta and approaches 1 for events with large multiplicity and isotropic phasespace particle distributions.
The data at each energy were compared to Monte Carlo simulations which were based on either an isotropic phasespace (PS) model or a jet model. In both models only pions (charged and neutral) were produced. The total multiplicity was given by a Poisson distribution. The jet model modified phase space according to the square of a matrix element of the form
(3) 
where _{} is the momentum perpendicular to the jet axis.
The angular distribution for the jet axis is expected to have the form
(4) 
where is the polar angle of the jet axis with respect to the incident positron direction, is the azimuthal angle with respect to the plane of the storage ring, = (_{T}  _{L})/(_{T} + _{L}) with _{T} and _{L} the transverse and longitudinal production cross sections, and P is the polarization of each beam. (The polarization termwill be discussed later.) The angular distribution given by Eq. (4) was used in the jetmodel simulation. The simulations included the geometric acceptance, the trig ger efficiency, and all other known characteristics of the detector. The total multiplicity and the chargedneutral multiplicity ratio for both models were obtained by fitting to the observed chargedparticle mean multiplicity and mean momentum at each energy. In the jet model the parameter b was determined by fitting to the observed mean S at the highest energy (7.4 GeV). For lower energies the value of b was determined by requiring that the mean _{} in the jet model be the same (315 MeV/c) as at 7.4 GeV.




The distribution shown in Fig. 3(b) and the value for P^{2} (0.47 ± 0.05) measured simultaneously by the reaction^{9} e^{+}e^{} µ^{+}µ^{} were used to determine the parameter of Eq. (4). The value obtained for the observed jet axis is = 0.45 ± 0.07. This observed value of will be less than the true value which describes the production of the jets because of the incomplete acceptance of the detector, the loss of neutral particles, and our method of reconstructing the jet axis. We have used the jetmodel Monte Carlo simulation to estimate the ratio of observed to produced values of and find this ratio to be 0.58 at 74 GeV. Thus the value of describing the produced jet axis angular distribution is = 0.78 ± 0.12 E_{c.m.} = 7.4 GeV. The error in is statistical only; we estimate that the systematic errors in the observed can be neglected. However, we have not studied the model dependence of the correction factor relating observed to produced values of .
The sphericity and the value of as determined above are properties of whole events. The simple jet model used for the sphericity analysis can also be used to predict the singleparticle inclusive angular distributions for all values of the secondary particle momentum. In Fig. 4 values for the inclusive hadron as a function of x at 7.4 GeV^{9} are compared with the jetmodel calculation. The model assumed the value = 0.78 ± 0.12 for the jetaxis angular distribution. The prediction agrees well with the data for all values of x.
We conclude that the data strongly support the jet hypothesis for hadron production in e^{+}e^{} annihilation. The data show a decreasing mean sphericity with increasing E_{c.m.} and the sphericity distributions peak more strongly at low values as E_{c.m.} increases. Both of these trends agree with a jet model and disagree with an isotropic PS model. The mean transverse momentum relative to the jet axis obtained using the jetmodel Monte Carlo simulation was found to be 315 ± 2 MeV/c. At E_{c.m.} = 7.4 GeV the coefficient for the jetaxis angular distribution in Eq. (4) has been found to be nearly + 1 giving a value for _{L}/_{T} of 0.13 ± O.07. The jet model also reproduces well the inclusive hadron versus x. All of this indicates not only that there are jets but also that the helicity along the jet axis is ± 1. In the framework of the quarkparton model, the partons must must have spin 1/2 rather than spin 0.