Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

A bstract On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, which there is no local Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S -matrix particles, without ever having refer Dirac string. key ingredient revision our fundamental understanding multi-particle representations Poincaré group. Surprisingly, asymptotic states electric-magnetic transform with an additional little group phase, associated pairs particles. The corresponding “pairwise helicity” identified quantized “cross product” charges, e 1 g 2 ? , every charge-monopole pair, represents extra angular momentum stored in electromagnetic field. We define new kind pairwise spinor-helicity variable, serves as building block amplitudes. then most general 3-point elements, well full partial wave decomposition ? fermion-monopole -matrix. particular, derive famous helicity flip lowest simple consequence generalized spin-helicity selection rule, dependence higher waves. Our construction provides significant achievement on-shell program, succeeding where description has so far failed.