Zero-Mass Bosons inS-Matrix Theory

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 ($1^{-}$) 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 $\rho$ universality, the Adler-Weisberger relation, and the universality of leptonic couplings in a vector or axial-vector state.