Backward polarization as a direct experimental measure of peripherality

Striking regularities are observed in πN backward elastic scattering for p_lab ? 1 GeV. The rich structure of the polarization and differential cross section vary rapidly in both angle and energy. For a fixed energy however, the observables approximately satisfy the derivative relation $\text{P(θ)}\text{d}\text{σ}\text{d}\text{θ}\text{∝}\text{?}\text{t6θ}\text{(}\text{d}\text{σ}\text{d}\text{θ}\text{)}$. This empirical relation is shown to be the consequence of the peripheral nature of the interaction at high energies and the dominance of successive partial waves with increasing energy W = √s at lower energies: l = 2,3,4 … for W = 1.68, 1.95, 2.18 … GeV, respectively. $\text{“l-}\text{dominance}\text{”}$ suggests a pattern where N,Δ and Δ,Δ states appear in nearly degenerate pairs with the same l and parity but with $\text{J = l +}\text{1}\text{2}\text{and}\text{J = l ?}\text{1}\text{2}$. The observed regularities are consistent with measurements in the inelastic channel π^?p → ΛK⁰ and could provide a useful tool for an extension of phase-shift analyses to higher energies where no prominent peaks in the total cross section constrain the solution. At the highest energy (p_lab = 6 GeV/c) a possible deviation from the derivative rule implies the onset of a non-peripheral contribution not present at lower energies.