π−πPhase Shifts in the Region 1.0-1.4 GeV/c2

Abstract

find a satisfactory answer to the following question: Should one parametrize the P h S, or perhaps both? Without some actual experience there is no definite answer at present. One reasonable exploratory program would be the following: Choose for S a delta-convergent sequence and parametrize it; then select a set of P f that belong to some well-defined class of geometrical objects; finally optimize the parameters with respect to the primitive function cp p . A very important example of geometrical objects is the class of all hypersurfaces. In particular, the integral of an N-dimensional function F{x) over the hyperplane x l \i l + • • • + x N n N =p is called the Radon transform of F(x). 9 Its general properties and geometrical meaning are well established. 9 Assume now that the x i9 i= 1, • • •, L, refer to the L electron-nucleus separation coordinates in a molecule. Using Eq. (2) we can construct Lcenter molecular orbitals that are completely different from the conventional linear combination of atomic orbitals ones and relate much more closely to the geometry of the molecule. Furthermore, the coalescence of the x t produces a "united-atom" atomic orbital.We have to discuss the questions of symmetry and statistics. The least sophisticated approach is to construct both the primitive function and the shape function in such a way that they are neither symmetry breaking nor statistics violating. Of course, this also imposes certain restrictions on the arguments of the P fm Another method would consist of applying symmetrization (and antisymmetrization) operators as well as the appropriate An enhancement in the rr ~7r + mass spectrum in the di-pion mass region 1.0-1.2 GeV has been reported by Whitehead etal., 1 Miller et al., 2 and projection operators at the end. The relative merits of these alternatives need further investiastion.It has to be emphasized that Eq. (2) is not the most general correlated many-particle trial function one could imagine. First, the t f need not be the scale factors. Second, the P/(f) could be made dependent also on the physical coordinates. (This would relate our functions to the more conventional collective-coordinate approach in nuclear physics. 10 ) Finally, the general delta function we use could be replaced by an arbitrary function of x and f. However, we feel that the formulation we propose combines conceptual simplicity and an appeal to geometrical intuition with the possibility of systematic classification of trial functions and computational practicability.7T7T scattering in the di-pion mass region 1.0-1.4 GeV is analyzed. It is shown that an anomaly of the TT""TT + state in the region 1.0-1.2 GeV is either an 7=0 D-wave amplitude which interferes with a nearly static 1=1 P-wave amplitude or a Breit-Wigner D wave which interferes with a moving P wave (possibly resonant). The/ 0 meson seems to show considerable inelasticity. 331