Scattering Amplitudes for Monopoles: Pairwise Little Group and Pairwise Helicity

Abstract

On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S-matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding "pairwise helicity" is identified with the quantized "cross product" of charges, $e_1{g}_2-e_2{g}_1$, for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the $2\to 2$ fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

arXiv comment45 pages

References in corpus (23)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Direct extraction of one-loop integral coefficients
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions
• The Double Copy of Electric-Magnetic Duality
• Integrability of Black Hole Orbits in Maximal Supergravity
• An $S$-Matrix for Massless Particles
• Magnetic Mixing -- Electric Minicharges from Magnetic Monopoles
• Constructing massive on-shell contact terms
• New Selection Rules from Angular Momentum Conservation
• Monopoles, strings and dark matter
• Bounding milli-magnetically charged particles with magnetars
• Dual Quantum Electrodynamics: Dyon-Dyon and Charge-Monopole Scattering in a High-Energy Approximation
• Dirac Relation and Renormalization Group Equations for Electric and Magnetic Fine Structure Constants
• Resolving the Weinberg Paradox with Topology
• Dark Monopoles and SL(2,Z) Duality
• Anomaly Constraints on Monopoles and Dyons
• S-Duality and Helicity Amplitudes
• Gravitational Wu-Yang Monopoles
• Spurious Poles in the Scattering of Electric and Magnetic Charges

Cited by in corpus (1)

• Zwanziger's pairwise little group on the celestial sphere