Abstract
The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as ΔB = ±ΔL = ±1, ΔL = ±2, and ΔL = ±4 operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order 1/Λ2 is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.
Highlights
At dimension five, Standard Model Effective Field Theory (SMEFT) contains a single lepton-number-violating ∆L = 2 operator and its Hermitian conjugate ∆L = −2 operator, each in a single irreducible flavor representation
In addition to the 2499 dimension-six operators, there are 273 dimension-six ∆B = ∆L = 1 operators (7 irreducible flavor representations), and their Hermitian conjugates [1, 2, 4,5,6,7]. These operators are important because they are the leading operators that permit proton decay in SMEFT. It is natural for both the scales of baryon-number violation and lepton-number violation, ΛB/ and ΛL/, to be much larger than Λ, so these operators can be very suppressed in comparison to the dominant 2499 dimension-six operators that do not violate baryon and lepton number
We stress that low-energy EFT (LEFT) is the correct low-energy theory even in the case where the highenergy EFT is not given by SMEFT but by Higgs Effective Field Theory (HEFT) [36, 37], which relaxes the assumption that the Higgs particle is part of a fundamental electroweak doublet
Summary
Electroweak symmetry breaking in SMEFT is modified by the presence of dimension-six operators. Which contribute to the scalar potential and kinetic energy terms. The fermion mass matrices in the SMEFT are modified by dimension-six operators [3]. An important feature of SMEFT is that the dimension-six operators QψH generically lead to h boson Yukawa couplings that are no longer proportional to the fermion Dirac masses. The left-handed neutrinos acquire a Majorana mass matrix upon spontaneous symmetry breakdown from the dimension-five Lagrangian L(5), L [Mν. Is proportional to the Majorana-neutrino mass matrix when keeping only operators up to dimension six in SMEFT. It is important to note, that dimension-seven operators contribute a correction to the above equation at relative order v2, which generically results in a Majorana-neutrino Yukawa coupling Y5 that is not proportional to the Majorananeutrino mass matrix
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