Resonance recognition in a Veneziano model

Abstract

Suppose we agree that a resonance is a second-sheet pole in s of a partial wave amplitude T J T J ( s ) = B J ( s ) + R J / ( s R J − s ) . Here s R is the pole position (Im s R < 0, R J is the residue and B J (s) is everything else (‘background’). A narrow resonance gives a circular arc (Adair 1969) in the Argand plot of T J (s) . Similar arcs are found experimentally, but it is still not agreed exactly how to get resonance parameters from them. Many criteria have been suggested. (i) Top of the loop . The maximum of Im T give the resonance mass s = Re s R provided R is real and positive. The condition holds for elastic scattering if B is negligible (by unitarity), and is sometimes assumed more widely. For inelastic amplitudes, if R is real (but of either sign), s = Re s R may be correlated with either the top or the bottom of a loop.