Low-virtuality splitting in the Standard Model

TL;DR

This paper computes comprehensive tree-level splitting amplitudes in the Standard Model for high-energy collisions, capturing low-virtuality regimes including collinear and soft emissions, with potential applications to future high-energy colliders.

Contribution

It introduces a complete set of splitting amplitudes for the Standard Model at high energies, using an improved bi-spinor formalism that includes the Goldstone Boson Equivalence Theorem.

Findings

Derived explicit splitting amplitude expressions for all Standard Model processes.

Unified treatment of collinear and soft emission regimes.

Potential for systematic electroweak radiation predictions at future colliders.

Abstract

When the available collision energy is much above the mass of the particles involved, scattering amplitudes feature kinematic configurations that are enhanced by the much lower virtuality of some intermediate particle. Such configurations generally factorise in terms of a hard scattering amplitude with exactly on-shell intermediate particle, times universal factors. In the case of real radiation emission, such factors are splitting amplitudes that describe the creation or the annihilation -- for initial or final state splittings -- of the low-virtuality particle and the creation of the real radiation particles. We compute at tree-level the amplitudes describing all the splittings that take place in the Standard Model when the collision energy is much above the electroweak scale. Unlike previous results, our splitting amplitudes fully describe the low-virtuality kinematic regime, which includes the region of collinear splitting, of soft emission, and combinations thereof. The splitting amplitudes are compactly represented as little-group tensors in an improved bi-spinor formalism for massive spin-1 particles that automatically incorporates the Goldstone Boson Equivalence Theorem. Simple explicit expressions are obtained using a suitably defined infinite-momentum helicity basis representation of the spinor variables. Our results, combined with the known virtual contributions, could enable systematic predictions of the leading electroweak radiation effects in high-energy scattering processes, with particularly promising phenomenological applications to the physics of future colliders with very high energy such as a muon collider.