Helicity selection rules and noninterference for BSM amplitudes

Precision studies of scattering processes at colliders provide powerful indirect constraints on new physics. We study the helicity structure of scattering amplitudes in the standard model (SM) and in the context of an effective Lagrangian description of beyond-the-SM (BSM) dynamics. Our analysis reveals a novel set of helicity selection rules according to which, in the majority of $2\to 2$ scattering processes at high energy, the SM and the leading BSM effects do not interfere. In such situations, the naive expectation that dimension-6 operators represent the leading BSM contribution is compromised, as corrections from dimension-8 operators can become equally (if not more) important well within the validity of the effective field theory approach.

Figure 1

When the factorization channel goes on shell, it propagates a well-defined helicity eigenstate and Eq. (3) holds.

Figure 2

A schematic representation of the relative size of different contributions to the $VVVV$ scattering cross sections, with polarization LLLL (left panel), LLTT (central panel) and TTTT (right panel). LO and NLO denote the leading and next-to-leading contributions to the cross section, respectively. In the white region the SM dominates and the leading BSM correction comes from the ${\mathrm{BSM}}_6\text{−}\mathrm{SM}$ interference (denoted as ${\mathrm{BSM}}_6$). BSM noninterference is responsible for the light-shaded blue and orange regions, where the BSM, although it is only a small perturbation around the SM, is dominated by terms of order $E^4/{\mathrm{\Lambda }}^4$, either from ${({\mathrm{BSM}}_6)}^2$ or from the ${\mathrm{BSM}}_8\text{−}\mathrm{SM}$ interference (denoted as ${\mathrm{BSM}}_8$).