As has been shown almost two years ago , generalized vector dominance (GVD) quite successfully quantitatively accounts for the data on deep inelastic electron nucleon scattering. There is, however, one principal feature within this approach, which became more and more unsatisfactory as progressively higher energy data on e+e-+hadrons became available: these showing roughly a 1/s law in the Frascatil 3 1range, and an even slower fall off for c.m. energies /8 beyond about 3.5 GeV has been reported by CEAI 4 1 and more recently by the SLAC-LBL collaboration at SPEARisl. The problem, as discussed in I 1 I, with a 1/s law for e+e-annihilation is that in the usual diagonal form of GVD (i. then for p''(1600) photoproduction one expectswhere the addition.e e ann1h1lat1on result Experimentally one finds I 11 I Denoting the ratio of the first off-diagonal to the diagonal (t = 0) transition amplitude as (3) we thus obtain the isovector photon part of the transverse virtual photon ab- which for large N gives (negJ.ecting order I/~)Then the sum in (4) turns out to be convergent, provided the constant in (5) and (6) is chosen to be 1/2. Thus inserting (2) and (6)
2Generalizing to include the isoscalar parts and evaluating (7) The only free parameter introduced, o, which fixes the magnitude of the off-diagonal transitions, may now be determined fromfue normalization ( Although (II) may easily be evaluated numerically from the tables for 1/J (z), it is advantageous to give a much simp lac formula for oT' which for A = 2 approximates (II) extremely well, the error being at most 2% (around (13). (14) -6 -It is amusing to note that the simple pole formula (14) which is equivalent to(ll); had p~evi~u~~y'fgf be~n ~how~::tO'to de~c~ib~ extremely weilthe.•. Agreement of (II) and (14) •· are substantially unchanged.From our Ansatz (5), we note that diffraction dissociation, as exemplified by a single, effective off-diagonal term parametrized with CN, increases with N, becoming a constant fraction of the elastic reaction. This feature seems a necessary one for convergence and scaling. We have checked that a constant, N independent CN gives a logarithmically divergent non-scaling expression except for the singular point CN = 1/2, for which case the result is convergent, but also non-scaling with a leading term proportional to (1/q 4 ) ln (q 2 tm 2 ).
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