Abstract
We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from few basics assumptions such as Poincaré invariance and locality, we classify all the renormalisable and non-renormalisable interactions at lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT marginal interactions up to mass dimension 8, to linear order in the effective interactions.
Highlights
We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments
The Standard Model Effective Field Theories (SMEFT) are a systematic and model independent framework to characterise both experimental deviation from predictions of the Standard Model (SM) and possible extensions beyond it
In the previous two sections we argued that any four-point amplitude in the Standard Model can be fully determined from its factorisation channels, and we gave a general algorithm to find all the SMEFT interactions
Summary
The Standard Model Effective Field Theories (SMEFT) are a systematic and model independent framework to characterise both experimental deviation from predictions of the Standard Model (SM) and possible extensions beyond it (for a review, see [1] and references therein). A more direct way of constructing this basis has been proposed, which relies on the classification of the independent effective interactions directly from their S-matrix elements [27,28,29,30,31,32,33,34], and has been used to classify all the SMEFT operators up to mass dimension 9 [35, 36]. This algorithm is based on factorisation properties of the tree-level amplitudes, and allows to bypass the use of recursion relations which can be problematic when non-renormalisable interactions are involved. The computed amplitudes are manifestly local, which is well suited for example when computing loop-level results through generalised unitarity
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