Abstract
The Standard Model Effective Field Theory (SMEFT) theoretical framework is increasingly used to interpret particle physics measurements and constrain physics beyond the Standard Model. We investigate the truncation of the effective-operator expansion using the geometric formulation of the SMEFT, which allows exact solutions, up to mass-dimension eight. Using this construction, we compare the exact solution to the expansion at mathcal{O} (v2/Λ2), partial mathcal{O} (v4/Λ4) using a subset of terms with dimension-6 operators, and full mathcal{O} (v4/Λ4), where v is the vacuum expectation value and Λ is the scale of new physics. This comparison is performed for general values of the coefficients, and for the specific model of a heavy U(1) gauge field kinetically mixed with the Standard Model. We additionally determine the input-parameter scheme dependence at all orders in v/Λ, and show that this dependence increases at higher orders in v/Λ.
Highlights
With the proliferation of precise experimental results at the Large Hadron Collider (LHC) and other facilities, and the lack of observed particles beyond the Standard Model (SM), data analysis and theoretical developments in the framework of the Standard Model Effective Field Theory (SMEFT) are of increasing interest
We investigate the truncation of the effective-operator expansion using the geometric formulation of the SMEFT, which allows exact solutions, up to massdimension eight
We have provided numerical expressions to this order for the operator dependence of the partial widths Γ(h → γγ), Γ(h → Z γ), and Γ(Z → ψψ), for both the m W and αew input-parameter schemes
Summary
With the proliferation of precise experimental results at the Large Hadron Collider (LHC) and other facilities, and the lack of observed particles beyond the Standard Model (SM), data analysis and theoretical developments in the framework of the Standard Model Effective Field Theory (SMEFT) are of increasing interest. The truncation of the effective field theory (EFT) typically leads to relative errors of O(Q2/Λ2) on the operator coefficients, where Q2 is the square of the momentum transfer in a process. Given the wide range of Q2 probed by LHC measurements, a systematic accounting of these errors is central to the result [1,2,3,4,5,6,7] They are relevant even when purely resonance observables are considered (Q2 v2), as the measurements typically constrain scales only within an order of magnitude of the process. We further match the SMEFT coefficients to an underlying U(1) kinetic mixing model up to dimension eight, quantifying the differences in inferred model parameters using different EFT truncation prescriptions
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