All members of the group participated in a certain part of the experiment and helped in its successful completion. Freidler of Caltech built the triads and assisted greatly with the installation of all the instruments. Ricardo Gomez and Jerry Pihe for advice and help during the experiment, and especially Dr.
The decay of A is in good agreement with the predictions of the ro-photon analogy of Stodolsky and Sakurai. The decay angular distributions show that the reaction is dominated since at higher moments by a pion exchange mechanism. Test of A and K* density matrix elements of quark dispersion relations.
INTRODUCTION
Some of the solutions, from both energy-dependent and energy-independent analyses, show a possible resonance at the P3/2 partial wave with an incident moment between 1.3 and 1.9 GeV/c. They also suggest that the velocity, the rate of change of the phase shift with energy, is inconsistent with resonance behavior. In an earlier experiment, Bland et a1.(5), studied the production of a single pion at the incident time between 0.84 GeV/c and 1.37 GeV/c.
It is the purpose of this experiment to extend the study of the inelastic K+p responses. Quasi-two body processes contribute significantly to the pion production responses and much of the analysis will be devoted to these states. The production and decay of resonances in the quasi-two body responses are studied in Part VII.
DESCRIPTION OF THE EXPERIMENT
For each pulse, we took a picture only if there were more than five and less than fifteen numbers in the chamber. To further control the number of traces in each photo, a beam destroyer magnet was installed upstream of the production target. A curve is fitted through the measured track points using the least squares method, and the angles and curvature are determined for each track.
To properly account for the energy loss through ionization, the fit is tested for each track for each possible particle. The output of TVGP consists of azimuth, dip and inverse projected momentum at the beginning and end of each track, for each possible mass, as well as the errors for these errors. SQUAW outputs the adjusted quantities and errors for each hypothesis that reaches a confidence level greater than 10-5.
SCANNING, MEASURING AND FITTING A. Results of First Scan
This efficiency is used to correct the number of events of each topology found in the first scan. About half of the failed events have been remeasured and the pass rate is again approximately equal to that of the first pass. The proportion of events that matched the possible responses in the second measurement was in good agreement with the results of the first measurement.
To correct the cross-sections for this adaptation inefficiency, we assume that the events that were not remeasured and the events that failed in the second adaptation were distributed in the same proportion. Due to the measurement errors in the impulses and angles, many events can pass more than one reaction pass. For hypotheses with the same number of constraints, the x2 of the fit is a reliable criterion for choosing the correct response.
CROSS-SECTION DETERMINATION A. Normalization
To check this we also used a beam track count and a total cross section scan. We scanned every fifth roll of film and recorded the number of cuts in every tenth frame. Using the data from this scan, we determined the average number of tracks per frame at each momentum.
Tau decays were measured simultaneously with the reaction sample, and scanning efficiency was determined in a second pass. This includes a factor for the number of K0s that are in the K0L state and a factor for the branching ratio K0s ~ 7T+rr. Even after two stages of mass separation, there are still some pions left in the K beam. The pion contamination at each run is given.
In this experiment we measured three reactions with two pions in the final state. The diameters measured in this experiment are given in table 5 and are presented in figure 6. The threshold for two pion production is .82 GeV/c, while the threshold for the quasi-two body channel K*~ is 1.74 GeV/. c.
Assuming that these reactions are dominated by this simple condition, we can estimate, using Clebsch-Gordan coefficients, the contribution of the two unmeasured reactions.
QUASI-TWO BODY REACTIONS A. Single Pion Production
Using the Clebsch-Gordan coefficients from table 6, we also calculated the total K~ and K*N diameters, which are shown in figure 8. The behavior of the KN1T cross section is clearly dominated by these two reactions, not only in the threshold region but also at higher momenta. In this case, the Dalitz plot density is not only the sum of the squares of the production amplitude, but may include an interference term.
There appears to be no net improvement in the interference region and we will neglect interference in the discussion of the K~ and K*N final states. The only quasi-two-body reaction with a threshold in the scope of this experiment is the reaction. The ratios for the possible charge states were calculated using isotopic spin Clebsch-Gordan coefficients.
In Fig. 10 we present all available data for K*4 production up to 2.5 GeV/c, together with KNmrcross-. Again we see that the production of two pions is associated with the production of the K*b state. It is therefore interesting to see how the characteristics of the total cross section relate to the cross sections for one-pion and two-pion provocation.
The sum of the three curves is shown at the top and is compared with the measured total cross-section data. The curve illustrates the measured cross-sections very well and seems to follow the properties observed earlier. The first bulge in the overall section appears to be associated with the rapid uplift of the KN~ section.
The second hump in the total cross-section appears just above the rapid rise of the KN7T7T cross-section.
PRODUCTION AND DECAY ANGULAR DISTRIBUTIONS A. General Discussion
Data on reactions where resonances are known to be important can serve as guidelines in our discussion of K+p distribution. Both A7 and A7 change sign at about 1.5 GeV/c, indicating a rapid phase change in the dominant amplitude. In addition, high rotation increases the effect both because of the (J+t) factor and because the contribution to the expansion of the Legend is at.
However, knowledge of the inelastic differential cross-sections can provide additional limitations for the partial wave analysis of elastic differential cross-sections and polarizations, and should help reduce the number of ambiguous solutions. In the following sections we will look at each of the quasi-two body channels in turn. This, combined with the data from Bland(5), will provide a complete and model-independent description of the inelastic.
By using the spin density matrix elements, we can compare our data with data at higher momenta, and can qualitatively study the mechanisms in each of the quasi-two body channels. 6cMiss the angle of the A measured with respect to: to the incident proton in the production center of mass. The behavior of the first four coefficients from threshold to 2.17 GeV/c is shown in figure 13.
The region up to 1.58 GeV/c has been studied by Bland et al. (5) and the A production and . decay was found to be in good agreement with the predictions of the rho-photon analogy of Stodolsky and Sakurai <14). Bland has pointed out that the simple rho-photon analogy fails to explain the magnitude or energy dependence of the difference. The statistics of the experiment are not sufficient to allow meaningful comparison with possible exchange models.
In the next section, however, we will examine the relation of the exchange mechanism to the angular distribution of decay.
ILJ\
CONCLUSIONS
This final state shows strong production of the quasi-two body states KA and K*N as at lower momenta. One very useful choice of parameters is the invariant mass of the two body systems. This series is given by. where cos e 4 is the decay cosine of particle 4. measured with respect to the direction of the system of particles 3 and 4 in the production center of.
For each resonance of a specific parity, the density of points in I and II must be the same, except for . the presence of resonance in the other two particles. We will consider the effective mass distributions as we did in the case of the three-body system. there are many possible choices of effective masses. The boundaries of the plot then form a right-of-way. triangle, and the effective mass graph will be called a triangle.
We can take into account all events in the region. triangular plot where M.34 and Ms6 are within the resonance mass region for K* and L:. events from the phase space distribution can be removed by interpolation, as was done in the three-body case. A further specification of the J or 4-particle system may include the production angle of a 2-particle center-of-mass resonance. For the description of almost two reactions of the body in this paper we will always define production. the angle relative to the input particle which forms the resonance.
In describing the differential cross-section for quasi-two-body reactions, both of these descriptions are taken into account. Here we choose the positive z-axis along the direction of the incoming proton or K in the ~ or K* center of mass. y-axis is chosen as the perpendicular to the production plane, and the x-axis is defined by the right-hand side. The z-axis is chosen as the direction of motion of the resonance in the production center or mass.
In the case of the three-body final state, we have already noted that the decay angle in the Helicity frame is directly related to the effective mass of the other two-body system in the Dalitz graph.
