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- W2155651465 startingPage "329" @default.
- W2155651465 abstract "An infinite sequence of direct-channel resonances is explicitly summed by the Sommerfeld-Watson method. This is quite different from the problem heretofore considered of summing $t$-channel resonances and requires different physical assumptions. In fact, the parabolic mass trajectory ${ensuremath{mu}}_{J}ensuremath{propto}J$ and a slow growth of width (on resonance) ${ensuremath{Gamma}}_{J}ensuremath{propto}J$ as $Jensuremath{rightarrow}ensuremath{infty}$ are necessary to reproduce in the Regge limit the form $mathrm{const}ifmmodetimeselsetexttimesfi{}{J}_{ensuremath{Delta}ensuremath{lambda}}(Rsqrt{ensuremath{-}t})$, $Rensuremath{equiv}mathrm{interaction}mathrm{range}$, $ensuremath{Delta}ensuremath{lambda}ensuremath{equiv}mathrm{total}mathrm{helicity}mathrm{change}$, for the imaginary part of this (nondiffractive) part of the c.m. two-body reaction amplitude, in agreement with experiment, and Harari's qualitative theory, for $ensuremath{pi}N$ and $mathrm{KN}$ entrance channels. The above width ansatz is of central importance in the derivation and is also experimentally supported. Linear and parabolic mass trajectories in the direct channel are compared. Small $s$-dependent deviations from fixed crossover $ensuremath{-}tensuremath{approx}0.2$ ${(mathrm{G}mathrm{e}mathrm{V}/mathit{c})}^{2}$ and first dip $ensuremath{-}tensuremath{approx}0.6$ ${(mathrm{G}mathrm{e}mathrm{V}/mathit{c})}^{2}$ points are predicted." @default.
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- W2155651465 date "1972-07-01" @default.
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- W2155651465 title "Connection of Parabolic Mass and Width Trajectories with High-Energy Scattering" @default.
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- W2155651465 doi "https://doi.org/10.1103/physrevd.6.329" @default.
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