Abstract
We calculate the low-energy constant $L_{10}$ in a two-representation SU(4) lattice gauge theory that is close to a composite-Higgs model. From this we obtain the contribution of the new strong sector to the $S$ parameter. This leads to an upper bound on the vacuum misalignment parameter $\xi$ which is similar to current estimates of this bound. Our result agrees with large-$N_c$ scaling expectations, within large systematic uncertainties.
Highlights
The composite-Higgs paradigm [1,2] provides a solution to the problem of protecting the Higgs mass from large radiative corrections by supposing that the Higgs is a pseudo Nambu-Goldstone boson of some new strong interaction, dubbed hypercolor, operative at the fewTeV scale
In this paper we focus on L10, a next-to-leading order (NLO) lowenergy constants (LECs) which, in chiral perturbation theory (ChPT) for fermions in a single representation, multiplies the operator [19,20]
In Appendix A we briefly review the embedding of the electroweak gauge fields of the Standard Model in the M6 composite-Higgs model [8,9,24,25], and calculate the contribution of the hypercolor theory to the S parameter
Summary
The composite-Higgs paradigm [1,2] provides a solution to the problem of protecting the Higgs mass from large radiative corrections by supposing that the Higgs is a pseudo Nambu-Goldstone boson (pNGB) of some new strong interaction, dubbed hypercolor, operative at the fewTeV scale. In a series of papers [11,12,13,14,15], we have studied the SU(4) gauge theory with two Dirac fermions in the fundamental representation, together with two Dirac fermions—equivalently, 4 Majorana fermions—in the sextet representation, which is a real representation. By itself, this fermion content is not enough to accommodate a composite Higgs along with a top partner. Some technical details regarding discretization effects in ChPT are relegated to Appendix B, while some further investigations of our lattice data are described in Appendix C
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