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The Gribov-Froissart projection treats even angular momentum differently from odd angular momentum. But in QCD, I believe that the odd trajectories interpolate the even trajectories--- the two trajectories are degenerate. Is there a way of understanding why the even-odd trajectories are degenerate? Is is a symmetry argument? Can you find a natural system where they are not degenerate?

A quick google search revealed this reference, which doesn't answer the question, but gives an experimental signature for the degeneracy: http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-0576.pdf , There is probably excellent data by now on this.

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You might also want to take a look at the closely related concept of parity doubling in hadron spectrum, see e.g. this review: arxiv.org/abs/arXiv:0704.1639 –  Igor Ivanov Oct 7 '11 at 12:01
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