Abstract
We calculate the complete tree and one-loop matching of the dimension-six Standard Model Effective Field Theory (SMEFT) with unbroken U(3)5 flavour symmetry to the operators of the Weak Effective Theory (WET) which are responsible for flavour changing neutral current effects among down-type quarks. We also explicitly calculate the effects of SMEFT corrections to input observables on the WET Wilson coefficients, a necessary step on the way to a well-defined, complete prediction. These results will enable high-precision flavour data to be incorporated into global fits of the SMEFT at high energies, where the flavour symmetry assumption is widespread.
Highlights
Statements which apply to the particular theories which are en vogue at the moment, and to theories which have not yet been dreamt up
An important source of precise data which should be used as much as possible is the output of the tremendous effort of the experimental flavour physics community, where measurements of a vast number of processes have been made, most of which indicate that the approximate flavour symmetry which is present in the SM must remain very nearly correct up to scales far higher than we typically expect of NP
All operators which are invariant under CP and the U(3)5 flavour symmetry are listed in tables 1 and 2, where we indicate which down-type FCNC processes are affected by each operator at one loop
Summary
Statements which apply to the particular theories which are en vogue at the moment, and to theories which have not yet been dreamt up. LHC searches have been interpreted in the SMEFT, with techniques to address the unique theoretical errors inherent in high energy searches for EFT effects recently developed [33, 34] All of these contributions will need to coalesce into a fully global fit of the SMEFT Wilson coefficients and cutoff scale, as only will it be possible to truly understand the conservative constraints which can be imposed on an arbitrary model through matching to the SMEFT and comparison of a given parameter point to the likelihood associated with all the relevant measurements. This assumption represents a “worst-case scenario” for flavour searches in the context of roughly TeV-scale NP, so this calculation will give an insight into the smallest effects we should reasonably expect to see if NP is near the TeV scale
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