Abstract
We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons. All operators are non-Hermitian and are classified according to their baryon (∆B) and lepton (∆L) numbers violated. Including Hermitian-conjugated operators, there are in total 3168, 750, 588, 712 operators with (∆B, ∆L) = (0, 0), (0, ±2), (±1, ∓1), (±1, ±1) respectively. We perform the tree-level matching with the standard model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in both LEFT and SMEFT. As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 SMEFT operators. We compare various neutrino-photon scattering cross sections with their counterparts in the standard model and highlight the new features. Finally, we illustrate how these effective interactions could arise from ultraviolet completion.
Highlights
JHEP08(2020)162 gauge bosons W ±, Z, the Higgs boson h, and the top quark t, we arrive at the so-called low energy effective field theory (LEFT)
We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons
As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 standard model effective field theory (SMEFT) operators
Summary
In the LEFT where we are working the electroweak symmetry breakdown has already taken place, so that the gauge group is SU(3)C × U(1)EM. The reducibility of the class ψ2XD2 rests on that of the scalar bilinear operators In this case the Lorentz indices in X and D2 have to be contracted. By utilizing the Mathematica code developed in that reference, we generate all possible field configurations that can form a gauge and Lorentz invariant dim-7 operator, and count the total number of independent operators for each field configuration. This counting is done with nu up-type quarks, nf down-type quarks, and nf neutral and charged leptons, and is in accord with the counts shown in tables 1 and 2 obtained by an analysis of flavor symmetries.
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