Although we will briefly explore some forces in other Jp states by looking at the OPE. Most of the work done in the 600 MeV region has been carried out in the Soviet Union using the 6-meter synchrocyclotron at Dubna. However, due to the wide width of the N, we see that the ic elastic amplitude takes on a kink.
The influence of the LV channel on the LV s.cattering was also discussed by Leung26. The analytical structure of NN ~NN partial wave amplitudes is described and the occurrence of complex singularities is observed. Due to the Pauli principle, there cannot be any transitions between the two spin states.
On the sides of the matrix we have listed the initial and final helicity states. 1 n partial amplitudes the results are summarized in the following table, the energy dependence of the leading term for W ~ 00 (S. 1he only states for which the rise of the amplitudes from the inelastic threshold was investigated were J.
A more general discussion of the properties of output amplitudes is given by Cook and.
UNITARITY OF HELICITY AMPLITUDES IN THE ISOBAR MODEL
Since in our approximation we have (pseudo) two- . particle channels) the solution of the discontinuity equations can be expressed in terms of the usual multi-channel ND-l method37. With the matrix B(W) defined as the integral of the distribution over the force intercepts of the true F. Because the force cut (in OPE amplitude) intersects the unitarity cut (see Fig. 21) the integration contour U must be deformed to avoid protruding singularities.
Although (for reasons to be given in Section VI) we ignore the presence of a strange singularity in ours. For a more complete discussion of the ND -1 method, including its properties and some examples of how the calculations are performed, the reader is referred to references 37 and 34 and other references cited therein. 34;kinematic" singularities (which we assumed were not contained .. in F) and to ensure the "correct behavior of the threshold • 2,t+l.
In non-. of relativistic scattering, the usual threshold behavior can be derived if the potential is properly bounded. And because of their W ~ - W behavior, they have the same momentum dependence at negative W thresholds. The placement of this zero is quite arbitrary except for the feeling that it should be reasonably far from the area of physical interest.
Since we decided to ignore the integrations above the negative cut of unity W (see below) it does not matter that we have broken the threshold behavior at the threshold W = - 2M. Input NN ~NN Amplitude born in the region between the elastic and inelastic thresholds.
W (BEV)
RESULTS AND CONCLUSIONS
As the width of the letter N increases, the tips become less pronounced - they are "woolier" (more rounded). Amplitude of elastic NN scattering squared with width N 125 MeV for different values of ~NN * coupling constant. Flexible squared NN scattering amplitude with width N 1 Mev and coupling constant A = .5 for different values of subtraction.
Elastic NN scattering amplitude squared with width N 1 MeV and coupling constant A= .7 for different subtraction values. Amplitude of elastic LV scattering squared with width N 1 MeV for different threshold energy values. In Section V, we discussed the behavior of the Born amplitude near W = 2.033, where the irregular cut crosses the physical region.
For large widths, most of the differences are hidden because the tops are so wide and flat. Reduction of WO also tends to shift the position of the peak to slightly lower energies (see Fig. 17). But again, we must admit that the rather strong dependence of the solutions on the value of w0 is a rather serious weakness of the deterministic method.
We can probably conclude from this that modifying the high energy behavior of the input amplitudes (for example, a la Reggeism) would have very little effect on our results. However, when more detailed experimental results are available, we may find that the detailed form of the ID. In performing the dynamic calculation it combines all (four) inelastic amplitudes into an "average".
In Table IV we have listed the predicted octet division for each member of the enhancement 2 7. 2 we expect that the other members 27 will also be associated with thresholds for the inelastic reaction. If we assume that the masses of the 27 members will lie close to one of the thresholds for the coupled 8 + 10 countries, then.
We choose the three by looking for (Y,I) states in which the allowed 8 + 10 thresholds have a narrow energy spread and then use the average of the inelastic threshold energies. Apart from differences in i-spin factors, some amplitudes are the same as those for the.
Nrr 3
We now mention some of the quantities used in the calculation of the helicity amplitudes. Some of the relations used in creating the partial wave expansions (both for NN ~ NN* and NN* ~ NN~ are: .. a) The well-known recurrence relations and symmetry properties of the d-functions (see reference 29) . The resulting NN ~NN partial wave amplitudes of final parity (calculated according to the procedure described in Chapter II) will now be reported. where T.J is defined in Section I).
In this section, we add a few details to our discussion in Section IV (see also Section VI) on how the ND-1 equations are modified due to the presence of a complex singularity that intersects the unit section. Additionally, we will discuss only those modifications that are appropriate for our calculation of determinant methods and not those required in the full ND -1 equations. The deformed contour of integration around the unit cut starting at the elastic NN threshold.
21, we symbolically indicated how the integration contour should be deformed around the unitary cut, which starts at WNN. avoid protruding singularities of NN -7NN Born amplitudes. Of course there is a synnetric situation in the left plane of W, but we omit the integrals over the left unitary cut.). Let us denote the contribution of the contour (let's call it C) around the abnormal cuts z.
Instead, we'll just make a few observations and a rough guess on the order of 6. What is needed is a much more satisfactory.. treatment of the three-particle nature of the NN state and a more accurate evaluation of the integrals over such complex singularities when they are present*).
