Automated one-loop computations in the standard model effective field theory

We present the automation of one-loop computations in the standard-model effective field theory at dimension 6. Our general implementation, dubbed smeft@nlo, covers all types of operators: bosonic and two- and four-fermion ones. Included ultraviolet and rational counterterms presently allow for fully differential predictions, possibly matched to the parton shower, up to the one-loop level in the strong coupling or in four-quark operator coefficients. Exact flavor symmetries are imposed among light quark generations, and an initial focus is set on top-quark interactions in the fermionic sector. We illustrate the potential of this implementation with novel loop-induced and next-to-leading-order computations relevant for top-quark, electroweak, and Higgs-boson phenomenology at the LHC and future colliders.

Figure 1

$t\overline{t}$ invariant-mass distribution of the interference between four-heavy-quark operators and the SM.

Figure 2

$K$-factors (NLO/LO) of the linear $({\mathrm{\Lambda }}^{-2})$ and quadratic $({\mathrm{\Lambda }}^{-4})$ contributions to pair and triple weak-boson production at the LHC $\sqrt{s}=13\mathrm{TeV}$. Charge-conjugated final states are summed over. $O_W$ values at $\mathcal{O}({\mathrm{\Lambda }}^{-2})$ are divided by 10 and negative for empty markers.

Figure 3

Linear and quadratic contributions of the five relevant operators to $H$, $HH$, and $HHH$ production at a future 100 TeV $pp$ collider, normalized by the corresponding SM predictions, for $c_i/{\mathrm{\Lambda }}^2=1{\mathrm{TeV}}^{-2}$.