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1.3 Determination of and

The decay rate contains two real functions

 

as the only unknowns. In Figs. (1.1,1.2) we display contour plots for the density distributions for . These five terms have obviously very different Dalitz plots. Therefore, in principle, one can determine the strength of each term by choosing a suitable kinematical region of observation. To pin down , it would be sufficient to measure at each photon energy the interference term INT. This has not yet

 
Figure 1.1: Contour plots for ,..., []. The numbering on the lines points towards increasing modulus. The normalization is arbitrary.  

 
Figure 1.2: Contour plots for ,..., []. The numbering on the lines points towards increasing modulus. The normalization is arbitrary.  

been achieved so far, either because the contribution of INT is too small (in ) , or because too few events have been collected (in ). On the other hand, from a measurement of SD alone one can determine A, V only up to a fourfold ambiguity:

 

In terms of the ratio

 

this ambiguity amounts to

 

Therefore, in order to pin down the amplitudes A and V uniquely, one must measure the interference terms INT as well.



Carlos E.Piedrafita