Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-01-25
Eur.Phys.J.C47:697-701,2006
Physics
High Energy Physics
High Energy Physics - Phenomenology
9 pages, 1 postscript figure; redone for clarity, removal of typos, changing reference; figure replaced
Scientific paper
10.1140/epjc/s2006-02605-8
We here comment on a series of recent papers by Igi and Ishida[K. Igi and M. Ishida, Phys. Lett B 622, 286 (2005)] and Block and Halzen[M. M. Block and F. Halzen, Phys. Rev D 72, 036006 (2005)] that fit high energy $pp$ and $\bar pp$ cross section and $\rho$-value data, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. These authors used Finite Energy Sum Rules and analyticity consistency conditions, respectively, to constrain the asymptotic behavior of hadron cross sections by anchoring their high energy asymptotic amplitudes--even under crossing--to low energy experimental data. Using analyticity, we here show that i) the two apparently very different approaches are in fact equivalent, ii) that these analyticity constraints can be extended to give new constraints, and iii) that these constraints can be extended to crossing odd amplitudes. We also apply these extensions to photoproduction. A new interpretation of duality is given.
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