Abstract
We describe the soft coupling of zero-mass bosons to other particles, by considering the limit of a theory with a massive boson. With the standard $S$-matrix assumptions of analyticity and crossing for four-body helicity amplitudes, we demonstrate generally that in the limit of zero mass, a vector boson (${1}^{\ensuremath{-}}$) couples to a conserved charge and a ${2}^{+}$ boson couples to the inertial mass. Bosons of other spin-parity combinations (with the exception of zero spin) have no zero-mass soft coupling. With this technique, we not only give a pedagogically interesting solution to gauge invariance and the kinematics of zero-mass particles, but suggest new applications to small-mass integral-spin systems. We speculate on the application of this technique to such problems as $\ensuremath{\rho}$ universality, the Adler-Weisberger relation, and the universality of leptonic couplings in a vector or axial-vector state.
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