Shadow Higgs from a scale-invariant hidden $U(1)_s$ model

TL;DR

This work studies a scale-invariant extension of the SM with a hidden gauge group $U(1)_s$, communicating with the visible sector through Higgs mixing and gauge kinetic mixing. The Coleman–Weinberg mechanism radiatively breaks the symmetry, producing a heavy SM-like Higgs $H_2$ and a light shadow Higgs (scalon) $H_1$, with couplings to SM fields suppressed by $1/(1+r)$. Experimental constraints from LEP, flavor physics, muon g-2, and stellar cooling impose stringent lower bounds on $r$ that depend on $m_{H_1}$, ranging from $r\gtrsim 10$ to as high as $10^5$–$10^{16}$ in extreme light cases; nevertheless, a shadow Higgs in the few-to-tens of GeV range could be discovered through precision top-quark decays at the LHC, especially for modest $r$, offering a potential collider signal of radiative conformal symmetry breaking. The model thus provides a minimal, testable link between conformal symmetry breaking and observable Higgs-sector phenomenology, with implications for dark matter candidates in ultra-light regimes.

Abstract

We study a scale invariant $SU(2)\times U(1)_Y \times U(1)_s$ model which has only dimensionless couplings. The shadow $U(1)_s$ is hidden, and it interacts with the Standard Model (SM) solely through mixing in the scalar sector and kinetic mixing of the U(1) gauge bosons. The gauge symmetries are broken radiatively by the Coleman-Weinberg mechanism. Lifting of the flat direction results in a light shadow Higgs or "scalon", and a heavier scalar which we identify as the SM Higgs boson. The phenomenology of this model is discussed. It is possible that shadow Higgs boson can be discovered in precision $t$-quark studies at the LHC. The conditions that it be a dark matter candidate is also discussed.

Figures (8)

• Figure 1: The parameter $r$ as a function of $g_s$ for $m_{Z_s}$ fixed at $250$ (bottom line), $500$, $750$, and $1000$ (top line) GeV.
• Figure 2: Relationships between $r$, $g_s$, and $m_{Z_s}$. In \ref{['subfig:rmZsgs1']}, the contour lines are for fixed value of $g_s = 1$ (bottom line), $0.9$, $0.8$, $0.7$, and $0.6$ (top line).
• Figure 3: Contours of $|\kappa|$ as a function of $g_s$, $m_{H_2}$, and $m_{Z_s}$ individually. In \ref{['subfig:kgs1']} and \ref{['subfig:kmZs']}, $m_{H_2}$ is fixed at $120$ (bottom line), $160$, and $200$ (top line) GeV. In \ref{['subfig:kgs2']} and \ref{['subfig:kmH']}, $m_{Z_s}$ is fixed at $250$ (top), $500$, $750$, and $1000$ (bottom) GeV.
• Figure 4: The mass of shadow Higgs, $m_{H_1}$, as a function of $g_s$ for $m_{H_2} = 200$ GeV and $m_{Z_s}$ fixed at $250$ (bottom line), $500$, $750$, and $1000$ (top line) GeV.
• Figure 5: Contours of $m_{H_1}$ as a function of $g_s$ and $\kappa$ for fixed values of $\xi_1^2 = (1+r)^{-1}$.