On-shell Higgsing for EFTs

Abstract

We study the on-shell version of the Higgs mechanism in effective theories (EFTs) containing particles of different spins, focusing on contact terms as a simple starting point. We derive the massive contact terms and their coefficients from the massless amplitudes of the EFT above the symmetry breaking scale, by covariantizing the massless contact terms under the massive little group. In the little-group-covariant massive-spinor formalism, this notationally amounts to bolding spinor labels. Mass-suppressed contributions to the contact-term coefficients arise from higher-point contact terms with additional soft Higgs legs. We apply this procedure to obtain massive four-point amplitudes featuring scalars, spin 1/2 fermions and vectors, in the standard-model EFT. The subleading helicity-flipped components of each massive contact term, which are dictated by little-group covariance, are associated with the residues of factorizable massless amplitudes. Extra “frozen” Higgses emitted from each leg of a massless contact term supply the additional light-like momentum component, needed to form a massive leg of the same polarization. As another application, we derive various components of massive three-point amplitudes from massless amplitudes with up to three additional Higgses, in a standard-model-like toy model.

An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes

“…Two examples of four-point dimension ≤8 SMEFT amplitudes, namely W W hh and ūdW h were derived in [45]. Here we extend these results to all the SM particles, but only include dimension-six contributions.…”

“…Indeed, on-shell methods have emerged in recent years as a powerful alternative to EFT Lagrangian constructions [29][30][31][32][33][34][35][36][37][38][39][40]. Bottom-up constructions of SM, or SM like amplitudes were discussed in [41,42,31,[43][44][45][46][47]. The emergence of symmetry from the amplitude bootstrap, and its relation to the geometry of field space was studied for instance in [48][49][50].…”

“…To recover all the SMEFT relations from this bottom-up approach, however, one needs to consider a sufficiently large set of amplitudes, including in particular higherpoint amplitudes. Instead, one can start from the massless SMEFT contact terms and "Higgs" these to obtain the massive contact terms [45]. In the little group-covariant massive spinor formalism, massless SCTs featuring just fermions and vectors are simply bolded into massive SCTs.…”

Amplitude bases in generic EFTs

“…The classification program was carried out mainly in four dimensions where we take advantage of the simplicity of both massless [65][66][67][68] and massive [69] spinor helicity formalism. In particular, recent works on various aspects of this classification and applications to the SMEFT are [70][71][72][73][74][75][76][77][78][79][80]. Generic techniques to classify fully massless interactions have been worked out in these works, while a general method for massive particles with any mass, spin and at any multiplicity is still lacking.…”

Amplitude bases in generic EFTs

“…The classification programme was carried out mainly in four dimensions where we take advantage of the simplicity of the massless [66][67][68][69] and massive [70] spinor helicity formalism. In particular, recent works on various aspects of this classification and applications to the SMEFT are [71][72][73][74][75][76][77][78][79][80][81][82][83]. Generic techniques to classify fully massless interactions have been worked out in these works, while a general method for massive particles with any mass, spin, and multiplicity is still lacking.…”