Pion-nucleon charge-exchange polarization by gribov reggeon calculus and the derivative rule

Abstract

Polarization measurements in u + p + u ~ indicate the presence of a relative phase between the nonflip and the flip helicity amplitudes. Corrections to the single Reggeon exchange can, in principle, generate such a relative phase. These corrections are cuts in the complex j-plane whose strength can be calculated by means of the absorption model. This model (1) describes the polarization data for very small momentum transfers but for larger values it fails entirely giving a tremendous negative peak where the experimental data are consistent with zero. The polarization obtained from the absorption model changes sign at t -~ _~ 0.20 (GeV/c) 2 as a direct consequence of the fact that the relative phase between the absorption cut and the pole of the nonfiip helicity amplitude reaches 180 ~ I t is an inevitable feature of the tradit ional absorption model tha t this relative phase can never be much larger than 180 ~ at t = 0 (GeV/c) 2. Since the cut rotates very slowly in comparison with the pole, any modification of the model has to considerably increase the starting point of the cut. The phase-modified absorption model (2) is the most extreme version of a successful modification. This model pushes the cut right into the fourth quadrant by multiplying the nourotat ing part of the cut by a factor of i and therefore absorbs the imaginary part of the amplitude total ly at the expense of the real part. The zero of the imaginary part of the helicity nonflip amplitude has to occur before the zero of the real part of this amplitude. Unless the cut is modified, the relative positions of these zeros are interchanged and the amplitude therefore rotates incorrectly in a counterclockwise manner around the origin of the Argand diagram (3). In order to achieve the needed modification in a less arbitrary way, one can do the traditional absorption model convolution, but with a pomeron which has a real and a more detailed structure (4).