Spin Dependence of High-Energy Scattering Amplitudes. II. Zero-Mass Particles

The discussion of spin dependence at high energy is extended to the case of zero-mass particles. Crossing relations for zero-mass particles are derived, showing that the helicity of massless particles is simply reversed under crossing. These are used by way of a Pomeranchuk-Martin-type theorem to obtain restrictions on the high-energy spin dependence. The problem of fixed poles in the angular-momentum plane and the coupling of the Pomeranchuk trajectory to photons is discussed. It is shown that if there are no fixed poles at positive integers for any Compton amplitude, one obtains the (presumably ridiculous) result that the asymptotic total cross section for photons on any particle is proportional to the square of its charge. An approximate dynamical calculation is given which relates the coupling of photons to the Pomeranchuk trajectory with the derivative of the trajectory at $t=0\mathrm{}$. This yields a prediction for the high-energy total cross section of photons on protons which is consistent with present data. The convergence of the Drell-Hearn sum rule is discussed; it is argued that even with cuts in the angular momentum, the sum rule will converge. Certain sum rules of Bég and of Pagels and Harari are discussed briefly.