Cross Sections at High Energies
Dec 15, 1961Citations per year
Abstract: (APS)
If the difference σ+(E)−σ−(E) of particle and antiparticle total cross sections changes sign at most at a finite number of energies, then the odd part f+(E)−f−(E) of the forward scattering amplitude has a very useful representation, as a rational times a "Herglotz" function. The representation implies a correlation between the high-energy asymptotic behavior of σ+(E)−σ−(E) and f+(E)−f−(E). For example, if {f+(E)−f−(E)}ElnmE is bounded, and m≤12 then we have the Pomeranchuk result that σ+(E)−σ−(E)→0. Even if m>12 it seems likely that although the difference of σ+(E) and σ−(E) may not tend to zero, their ratio does tend to one.References(5)
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