By Francis Halzen (auth.), David Speiser, Francis Halzen, Jacques Weyers (eds.)
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Additional resources for Particle Interactions at Very High Energies: Part A
In other words, the slope of the absorptive part of the high energy amplitude assumes its lowest possible value for a parabolic impact parameter distribution of Im F(s,t). Recently attention was called to the fact that NAL-ISR data actually saturate this bound (DIs 73). One has, however, to be extremely careful with the interpretation of this fact. Indeed in the table below we list a few typical impact profiles and their corresponding value for the slope of the absorptive amplitude. d Slope c = dtlog ImF(s,t) t=O Impact Profile Im arb) c 9 8 1 for b < b b 0 for b > b b o c 0 9 c 8 0 0 0 0 -1J e The calculation of the entries in the right hand side of the above table is straightforward.
An upward curvature for t + 0 resulting in a tail of high partial waves ((Hog 72) and (Bar 72)) analogous to the p T' I 17' I ' p \ 17' \ ~ p p (0) Fig. 14. n p (b) Two-pion-exchange correction to the Pomeron amplitude io proton-proton scattering (a) and the p-amplitude in TIN charge exchange (b). F. HALZEN 42 one discussed here for Pomeron exchange. 3 s-Channel Unitarity and the Overlap Function We show next how the s-channel unitarity relation provides an alternative (and phenomenologically very useful) way of looking at the geometrical or impact parameter structure of the proton.
But that we can decide as well from the observed ~hape of So the only thing we learn perhaps. from this "insensitive" bound is that the scattering is mainly absorptive as crD ~ crel' which precludes the existence of a big real part at present energies or a sizeable deviation from Eq. 102). We know this. however. by direct measurement (see Sec. 3). 0%. 2) can be understood in terms of a saturated unitarity bound. 103) (II,1 04) The distinctive feature of the differential cross section in the forward peak is the gradual decrease in slope (or derivative in t) for increasing values of It I as can be seen in Fig.
Particle Interactions at Very High Energies: Part A by Francis Halzen (auth.), David Speiser, Francis Halzen, Jacques Weyers (eds.)