A Seiberg Dual for the MSSM: Partially Composite W and Z

TL;DR

The paper investigates whether the SM $W$ and $Z$ can be realized as (partially) composite gauge bosons within a supersymmetric framework using Seiberg duality. It argues that fully composite $W$ and $Z$ are generically incompatible with SM couplings, and proposes partial compositeness achieved via mixing a magnetic $SU(2)$ sector with an elementary gauge group to reproduce weak-scale interactions; the low-energy theory is NMSSM-like with a composite Higgs/top and a meson-derived singlet, accommodating a Higgs mass up to $m_H \lesssim 400$ GeV in a fat-Higgs, RS-like 4D realization. Two minimal fermion-structure realizations are explored: (i) MSSM $SU(2)_L$ doublets as magnetic quarks with meson singlets and elementary-right Yukawa mixing; (ii) all light fermions elementary with masses from couplings to a Higgs sector connected to the composite sector. Overall, the work provides a concrete, UV-complete 4D framework that mirrors RS-type models with bulk gauge fields and can alleviate the little hierarchy problem while supporting a relatively heavy Higgs.

Abstract

We examine the possibility that the SU(2) gauge group of the standard model appears as the dual "magnetic" gauge group of a supersymmetric gauge theory, thus the W and Z (and through mixing, the photon) are composite (or partially composite) gauge bosons. Fully composite gauge bosons are expected to interact strongly at the duality scale, and a large running is needed to match the electroweak gauge couplings. Alternatively one can mix the composite "magnetic" gauge bosons with some elementary ones to obtain realistic models. In the simplest and most compelling example the Higgs and top are composite, the W and Z partially composite and the light fermions elementary. The effective theory is an NMSSM-type model where the singlet is a component of the composite meson. There is no little hierarchy problem and the Higgs mass can be as large as 400 GeV. This "fat Higgs"-like model can be considered as an explicit 4D implementation of RS-type models with gauge fields in the bulk.

Figures (1)

• Figure 1: Values of the one-loop gauge couplings $\alpha =g^2/4 \pi$, as functions of the renormalization scale $\mu$, for $\Lambda = 1.5\, \Lambda_{\rm el}$ on the left and $\Lambda = 0.8\, \Lambda_{\rm el}$ on the right. The "electric" coupling (shaded in blue for 6 colors and 8 flavors) is positive for $\mu > \Lambda_{\rm el}$, while the "magnetic" coupling (shaded in red) is positive for $\mu < \Lambda_{\rm mag}$.