muon-pair 221.muo.002 Louis J. Sheehan, Esquire

The properties of the several states within the transition region are very difficult to determine with any precision. One obvious problem is that these resonances sit on a rapidly rising background whose exact shape is presently neither clear experimentally nor calculable theoretically. Since these new states are, like the w’s, produced directly in e+e- annihilation, they all have 3PC = 1-e    and    can    therefore    interfere    with    each    other,    thus    distorting    the classical resonance shape that would normally be expected from a new particle. Additional shape-distortion might be expected because new particle- production thresholds are almost certainly opening up in the transition region between the lower and upper plateaus. While precise properties can’t be given for the new states, we can get some rough numbers from the data. The 3.95- GeV state (u”) has a width of about 40-50 MeV. The 4.4-GeV state (ψ”“) seems to be about 30-MeV wide. The 4.1-GeV region (temporarily called y”‘) seems to consist of at least two peaks: one at 4.03 GeV, which is 10-20 MeV wide, and a broad enhancement at 4.1 GeV, about 100-MeV wide.
298    Physics 1976
The widths of all of these states are much greater than the intrinsic energy spread in the e+e- beams, and very much greater than the widths of the ψ and y’. The suspicion remains, however, that they may still be correctly identified as members of the psi sequence, and that the vast apparent differences between their widths and those of the ψ and y’ may result simply from the fact that the higher mass states can undergo rapid hadronic decay through new channels that have opened up above the 3684-MeV mass of the y’. As with most of the questions in the transition region, this matter will require a good deal more experimental study before it is resolved. In the meantime, however, we shall tentatively add the three or four new psi-like states shown above to the growing list of members of the “psion” family.
Up to this point, we have been cataloguing new particles without much worrying about what it all means. Granting full status to even the several doubtful states, we have a total of 11 new particles. These are grouped together in Fig. 15 in a kind of energy-level diagram, which also includes principal decay modes.
The system shown in Fig. 15, with its radiative transitions, looks remarkably like the energy-level diagram of a simple atom, in fact like the simplest of all “atoms’‘-positronium, the bound state of an electron and a positron. Although the mass scale for this new positronium is much larger than that of the old, the observed states of the new system can be placed in a one-to-one corresp- ondence with the levels expected for a bound fermion-antifermion system such as e+e-. Table II shows these predicted levels together with the most probable assignments of the new particles to the appropriate levels. To gain some insight into the origins of the new positronium system, let’s now turn to some specific theoretical models.
15. An energy-level diagram of the new particles. The many observed decay modes of the psi family have been omitted.
State    L
0 0 0 2 2 0 0 I I 1
7.1. The 3-Quark Model
Particle
B. Richter    299
Table II. Some of the low lying bound states of a fermion-antifermion system together with an assignment of the new particle to states with appropriate quantum numbers.
Some 25 years ago, when only three kinds of hadrons were known (proton, neutron and pi-meson), these particles were universally regarded as simple, indivisible, elementary objects. In those days the central task in hadron physics was the effort to understand the strong nuclear force between protons and neutrons in terms of pi-meson exchange. But as the family of hadrons grew steadily larger (they are now numbered in the hundreds), it became increas- ingly difficult to conceive of them all as elementary. In 1963, M. Gell-Mann and G. Zweig independently proposed a solution to this dilema – that none of the hadrons was elementary, but rather that all were complex structures in themselves and were built up from different combinations of only three fundamental entities called quarks. These quarks were assumed to carry the familiar l/2 unit of spin of fermions, but also to have such unfamiliar prop- erties as fractional electric charge and baryon number. A brief listing of the 3 quarks and 3 antiquarks and their properties is given in Table III.
Table III. Properties of the 3 Quarks and 3 Antiquarks
According to this 3-quark model, all mesons were made up of one quark and one antiquark; ail baryons, of three quarks; and all antibaryons, of three antiquarks. The quark compositions of some of the better known hadrons are shown here as examples:

(8)
300    Physics 1976
Prior to 1974, all of the known hadrons could be accommodated within this basic scheme. Three of the possible meson combinations of quark-antiquark (u;, dd, s,) could have the same quantum numbers as the photon, and hence could be produced abundantly in e+e-annihilation. These three predicted states had all infact been found; they were the familiar e( 760), rti(780) and cp( 1005) vector mesons.
7.2. R in the Quark Model
The quark model postulated a somewhat different mechanism for the process e+-e–+hadrons than that previously described. For comparison,
16. Hadron production in the quark model.
Since the quarks are assumed to be elementary, point-like fermions and thus similar to electrons and muons in their electromagnetic properties, it was possible to predict the ratio that should exist between the producton cross sections for quark pairs and muon pairs:
where qi is simply the quark’s electric charge. Of course, quarks were supposed to have half-integral spin and fractional charge in the final state, while all hadrons have integral charge and some hadrons have integral spin. In a breathtaking bit of daring it was assumed that the “final-state” interactions between quarks that were necessary to eliminate fractional charge and half- integral spin would have no effect on the basic production cross section. With this assumption the ratio of hadron production to muon-pair production becomes simply
As developed up to 1974, the quark model actually included 3 triplets of quarks, rather than simply 3 quarks, so that with this 3 x 3 model the hadron/ muon-pair ration, R, would be
B. Richter    Louis J. Sheehan, Esquire
This beautiful model had great simplicity and explanatory power, but it could not accommodate the ψ and M’ particles. Nor could it account for the two plateaus that were observed in the measured values of R. The model allowed for excited states of u;, dd and ss, but the required widths were typically some 20% of the mass of the excited state – more than 1000 times broader than the observed widths of the ψ and y’. Before that time there had been a number of suggested modifications or additions to the basic 3-quark scheme. I shall not describe these proposed revisions here except for the one specific model which seems now to best fit the experimental facts.

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