Abstract
Effective Field Theory (EFT) technique is one of the most elegant ways to capture the impact of high scale theory, if any, at some low energy by incorporating higher mass dimensional (≥5) effective operators ( mathcal{O} i). The low energy EFT is described in terms of only light degrees of freedom (DOF) which can appear on-shell. An essential task while developing the EFT framework is to compute these mathcal{O} i’s. Hilbert Series (HS) is a novel and mathematically robust method to construct the complete set of gauge invariant independent, effective operators. The HS requires the knowledge of the transformation properties of the light DOF and the covariant derivatives under the internal gauge symmetries and conformal groups. The Hilbert Series method, by its virtue, automatically takes care of the redundancies in the operator set due to the Equations of Motion (EOMs) of fields and Integration by Parts (IBPs) with impeccable accuracy.In this paper, we have adopted this methodology to construct the complete set of independent operators up to dimension-6 in the “Warsaw”-like basis for two different Beyond Standard Model scenarios — Two Higgs Doublet Model (2HDM) and Minimal Left-Right Symmetric Model (MLRSM). For both these cases, we have calculated the corrections to the scalar, gauge boson and fermion mass spectra due to the dimension-6 operators. The additional contributions to all the Feynman vertices are computed and their impact on different observables, namely Weak mixing angle, Fermi constant, ρ and oblique (S, T, U) parameters. We have further discussed how the magnetic moments of charged leptons and production and decay of the massive BSM particles, e.g., charged scalar and different rare processes are affected in the presence of effective operators. We have also constructed the effective scalar four-point interactions and commented on the possible reinvestigation of the theoretical constraints, e.g., unitarity and vacuum stability within these frameworks.
Highlights
In this paper, we have adopted this methodology to construct the complete set of independent operators up to dimension-6 in the “Warsaw”-like basis for two different Beyond Standard Model scenarios — Two Higgs Doublet Model (2HDM) and Minimal Left-Right Symmetric Model (MLRSM)
One can look into the refs. [45, 46] where the SM-Effective Field Theory (SMEFT) with dimension-6 operators was constructed based on this principle
We have implemented the Hilbert Series (HS) method to construct the complete set of independent effective operators up to dimension-6 for two BSM scenarios: 2HDM and MLRSM
Summary
We have briefly sketched the Hilbert Series (HS) method [9, 37, 38, 53,54,55, 57,58,59] based on which our BSM-EFT construction has been developed. We have listed all the dimension-6 operators that are computed using the Hilbert Series method These operators are computed using the information given in tables 13, and following the thumb rules mentioned in the flowchart of figure 1. Similar to the 2HDM case, the Wilson Coefficients are taken to be real for this particular scenario These operators are tabulated in tables 15–24, and schematically depicted in figure 3 where the number of operators is mentioned for each class as +4κ31(C621L4r1 +C621R4l1)+2κ22κ1(C62L41r3 +C641L41r +C641R2l1 +C641R41l)+κ32C641L2r3 +vL3 vR 2κ1(C6LlL4r1 +C6LlR4l1)+κ2C6LlR2l1 +vL4 κ1(C6{21}{LlLl} +C621LlLl)+κ2C641LlLl +κ1vR2 2κ21(C62121Rr +C62211Rr)+3κ2κ1C62141Rr +κ22(C623Rr41 +C62R21r1 +2(C64141Rr +C641R2r1)). +C6LlR4l1)+κ2C6LlR2l1 +2vL3 κ21(C6{21}{LlLl} +C621LlLl)+κ22(C6{21}{LlLl} +C6LlL21l)+2κ2κ1C641LlLl +κ1vR vR2 κ2C6RrL2r1 +κ1(C6RrL4r1 +C6RrR4l1) +2 κ2κ21C621L2r1 +κ31(C621L4r1 +C621R4l1).
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