Abstract
We present a complete basis of dimension-8 operators in the Standard Model Effective Field Theory. Attention is paid to operators that vanish in the absence of flavor structure. The 44,807 operators are encoded in 1,031 Lagrangian terms. We also briefly discuss a few aspects of phenomenology involving dimension-8 operators, including light-by-light scattering and electroweak precision data.
Highlights
Terms; see [3] for earlier work
In this work we presented a complete basis of dimension-8 operators in the Standard Model Effective Field Theory
There are 1031 Lagrangian terms, 38 of which vanish in the absence of flavor structure
Summary
We start by considering the various uses of the word operator. See ref. [23] for further discussion. We a define operator to be a gauge and Lorentz invariant contraction of fields and derivatives with specific flavor indices. [23] defines a type of operator as the collection of terms with the combination of fields (and derivatives) with conjugate counted separately. For types of operators with a single Lagrangian term we label them as follows. The type of operator is denoted as the fields and the derivatives in the operator raised to the power of the number of times that type of object appears in the operator, e.g. the label leBH3 indicates that this term has one left-handed lepton field, one right-handed electron field, one hypercharge field strength, and three Higgs fields. If a type of operator has multiple terms, not counting Hermitian conjugates, we instead label the operators as nterm.
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