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- W2051278430 abstract "In the main part of this paper it is shown how to define other complex angular momentum trajectories which are related to, but distinct from, the usual Regge trajectory $ensuremath{alpha}$. One of these other trajectories, called here $ensuremath{gamma}$, is a zero of a function $Y$ (which is essentially the cotangent of the scattering phase shift for physical values of the angular momentum) in contrast to the Regge trajectory $ensuremath{alpha}$ which is a zero of the inverse $S$ matrix. $ensuremath{gamma}$ has simpler analyticity properties as a function of energy than $ensuremath{alpha}$. The $ensuremath{gamma}$ trajectory is, in one sense, the $ensuremath{alpha}$ trajectory with the contribution of the elastic kinematics removed; thus $ensuremath{gamma}$ is real between the elastic threshold and the inelastic threshold, unlike $ensuremath{alpha}$. The ways by which $ensuremath{gamma}$ and $ensuremath{alpha}$ produce bound states and elastic and inelastic resonances are compared and contrasted. One unusual feature of the $ensuremath{gamma}$ trajectory is that it can be purely real and still produce resonances of finite width. In the secondary part of the paper the pion-nucleon elastic-phase-shift data of the ${P}_{33}$ and ${F}_{37}$ partial waves in the regions of the ${P}_{33}(1232)$ and ${F}_{37}(1950)$ resonances are given a direct-channel complex angular momentum interpretation using a crude model based on the $ensuremath{gamma}$ trajectory. The model fitted to the data (1) provides an illustration of the use of the $ensuremath{gamma}$ trajectory, and (2) demonstrates the feasibility of a direct-channel complex angular momentum analysis of scattering data." @default.
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- W2051278430 title "Kinematics-free angular momentum trajectories. I. Theory and phenomenology" @default.
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- W2051278430 doi "https://doi.org/10.1103/physrevd.20.305" @default.
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