On-shell electroweak sector and the Higgs mechanism

Abstract

We describe a new approach towards the development of an entirely on-shell description of the bosonic electroweak sector of the Standard Model and the Higgs mechanism. We write down on-shell three particle amplitudes consistent with Poincaré invariance and little group covariance. Tree-level, four particle amplitudes are determined by demanding consistent factorization on all poles and correct UV behaviour. We present expressions for these 2 → 2 scattering amplitudes using massive spinor helicity variables. We show that on-shell consistency conditions suffice to derive relations between the masses of the W ± , Z, the Weinberg angle and the couplings. This provides a completely on-shell description of the Higgs mechanism without any reference to the vacuum expectation value of the Higgs field.

Structure of two-loop SMEFT anomalous dimensions via on-shell methods

“…[41][42][43][44][45][46][47]). They have also been used as a convenient means for classifying interactions in EFTs such as the SMEFT [48][49][50][51][52]. In addition, general proper-JHEP10(2020)211 ties of the S-matrix, such as unitarity, causality and analyticity have been used to constrain Wilson coefficients of EFTs [53], including the SMEFT [54,55].…”

Higgs coupling measurements and the scale of new physics

“…Unitarity arguments indicated that the theory of electroweak interactions is incomplete without a Higgs sector at or below the TeV scale. It was established in the 1970s that unitarity of amplitudes at high energy requires the theory to be a spontaneously broken gauge theory [1][2][3][4] (see [5][6][7] for a modern approach). Lee, Quigg, and Thacker [8,9] turned this into a quantitative constraint, showing that tree-level unitarity of longitudinal vector boson scattering could be used to give a bound on the energy scale of the Higgs sector (see also refs.…”

Sum rules in the standard model effective field theory from helicity amplitudes

“…[23][24][25] for recent reviews), it seems much more natural to directly treat amplitudes as a description of the EFT, which are equivalent to the Wilson coefficients of the higher dimensional operators in the Lagrangian. Recent efforts have been made in parameterizing the Standard Model (SM) and its effective field theory (SMEFT) with on-shell amplitudes [26][27][28][29][30][31][32][33][34]. While the conventional parameterization, obtained by adding higher dimensional operators to the SM Lagrangian [35,36], still offers the most complete and practical description of the SMEFT, the on-shell approach does have certain advantages.…”