phenomenon 320.phe.003 Louis J. Sheehan, Esquire

5. Hadron. μ+μ- and e+e- pair production cross section in the regions of the ψ and 11”. The curves arc fits to the data using the energy spread in the colliding beams as the determinant of the widths.
narrowness of the peaks implies that these two states are very long-lived, which is the principal reason why they could not be accounted for by the previously successful model of hadronic structure. In Fig. 5 we show the ψ and vj’ peaks on a greatly expanded energy scale, and also as they are measured for three different decay modes: y, y’+hadrons; y, v’+/li /cm; and y, y’+e+em. In this figure the ψ and y’ peaks can be seen to have experimental widths of about 2 MeV and 3 MeV, respectively. These observed widths are just about what would be expected from the intrinsic spread in energies that exists within the positron and electron beams alone, which means that the true widths of the two states must be very much narrower. The true widths can be determined accurately from the areas that are included under the peaks in Fig. 5 and are given by the following expression:
where pi is the cross section to produce final state i, Bi is the branching fraction to that state, B is the branching fraction to e+e-, M is the mass of the state,
e
and r is its total width. The analysis is somewhat complicated by radiative corrections but can be done, with the result that [9]
(3)
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290 Physics 1976
The widths that would be expected if the psi particles were conventional hadrons are about 20% ( of their masses. Thus the new states are several thousand times narrower than those expected on the basis of the conventional model.
4.2. Psi Quantum Numbers
The quantum numbers of the new psi states were expected to be .yPc = l-- because of their direct production in e+e- annihilation and also because of the equal decay rates to e+e-and /LT/CC. In so new a phenomenon, however, anything can go, and so that assumption needed to be confirmed. In particular, one of the tentative explanations of the psi particles was that they might be related to the hypothetical intermediate vector boson, a particle that had long been posited as the carrier of the weak force. Such an identification would permit the psi’s to be a mixture of JPC = l-- and 1+-. These quantum numbers can be studied by looking for an interference effect between on- and off-peak production of muon pairs, since the latter is known to be pure 1 --. If
- the new particles were also 1 --, then an interference should occur and produce
two recognizable effects: a small dip in the cross section below the peak, and an apparent shift in the position of the peak relative to that observed in the hadron channels. In addition, any admixture of l+- could be expected to show up as a forward/backward asymmetry in the observed angular distri- bution.
This analysis was carried out as soon as there were sufficient data available for the purpose. The postulated interference effect was in fact observed, as shown in Fig. 6, while no angular asymmetry was seen [8, 9]. Thus both of the psi states were firmly established as 3P” = 1-m.