Abstract
We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.
Highlights
The first step in tackling these matching problems is to construct a complete basis of dimension-8 LEFT operators, which is the goal of this work
In this work we constructed a complete basis of dimension-8 operators in the LEFT
In addition to the operator counting, the construction of the LEFT operator basis was aided by the existence of the dimension-8 bases of SMEFT operators as all of the LEFT dimension-8 operator classes are found in the SMEFT
Summary
The LEFT consists of all the gauge invariant, non-redundant operators of dimension-3 and higher that can be formed out of the subset of SM fields whose masses are parametrically smaller than the electroweak scale. Some LEFT operators involving four fermions can violate lepton number while preserving baryon number, but in the SMEFT even mass dimensions operators (below d = 10) conserve baryon minus lepton number, ∆B − ∆L = 0 [36, 37]. For operators that conserve both baryon and lepton number we again start from the SMEFT operators of ref. For operators that violate baryon and/or lepton number we start from our operator counting and instead use set of Lorentz structures for each subclass of operator from ref. The baryon and lepton number conserving operators of class ψ4X and subclass ψL2 ψR2 X are enumerated in tables 8, 9, 10, and 11, while table contains the ψL4 XL +h.c. operators. The baryon and lepton number conserving operators of class ψ4D2 and subclass ψL2 ψR2 D2 are given in tables and 14, whereas table lists the ψL4 D2 + h.c. operators.
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