Colorful imprints of heavy states in the electroweak effective theory

Abstract

We analyze heavy states from generic ultraviolet completions of the Standard Model in a model-independent way and investigate their implications on the low-energy couplings of the electroweak effective theory. We build a general effective Lagrangian, implementing the electroweak symmetry breaking SU (2) L ⊗ SU (2) R → SU (2) L+R with a non-linear Nambu-Goldstone realization, which couples the known particles to the heavy states. We generalize the formalism developed in previous works [1,2] to include colored resonances, both of bosonic and fermionic type. We study bosonic heavy states with J P = 0 ± and J P = 1 ± , in singlet or triplet SU (2) L+R representations and in singlet or octet representations of SU (3) C , and fermionic resonances with J = 1 2 that are electroweak doublets and QCD triplets or singlets. Integrating out the heavy scales, we determine the complete pattern of low-energy couplings at the lowest non-trivial order. Some specific types of (strongly-and weakly-coupled) ultraviolet completions are discussed to illustrate the generality of our approach and to make contact with current experimental searches.

Simple explanation of strong suppression offermionic EFT operators & custodial symmetry breaking

“…In an analogous way to the extension of χPT which incorporates the meson resonances as active degrees of freedom [14,15], one can include resonances to obtain their contribution to the couplings of the O(p 4 ) chiral Lagrangian operators [12,13]. Thus, one must obtain the equations of motion of the resonances and substitute the expressions for the classical fields in the Lagrangian for these resonances.…”

“…Using the equations of motion for the Goldstone and gauge bosons in L R (R class ), the contribution to the couplings of the EWET Lagrangian is obtained by making a comparison with the full O(p 4 ) basis given in reference [12,13]. Thus, the four-fermion contact interaction given in the phenomenological Lagrangian in references [2,3,4] L EW ET ⊃ L qq = 2π…”

“…With the chiral counting given in ref. [12,13], the SM operators will be given by the lowest chiral dimension Lagrangian densityd = 2.…”

“…Just as χPT can be naturally extended to include meson resonances [14,15], so can the EWET [12,13] be extended to include resonances. From the resonances Lagrangian the equations of motion (EoM) are obtained and then substituted to obtain the low-energy contribution to the couplings of the EWET theory Lagrangian density of chiral dimensiond = 4.…”

Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian

“…It can describe the SM in the limit described below in eq. (4.1), as well as composite Higgs models, as discussed in [4,5]. Parallel to the EWChL , there is an alternative EFT used to study new physics beyond the SM, the Standard Model EFT (SMEFT) [6].…”