Higgs boson as a top-mode pseudo-Nambu-Goldstone boson

In the spirit of the top-quark condensation, we propose a model which has a naturally light composite Higgs boson, “tHiggs” ($h_t^0$), to be identified with the 126 GeV Higgs discovered at the LHC. The tHiggs, a bound state of the top quark and its flavor (vectorlike) partner, emerges as a pseudo-Nambu–Goldstone boson (NGB), “top-mode pseudo-Nambu-Goldstone boson,” together with the exact NGBs to be absorbed into the $W$ and $Z$ bosons as well as another (heavier) top-mode pseudo-Nambu-Goldstone bosons ($CP$-odd composite scalar, $A_t^0$). Those five composite (exact/pseudo-) NGBs are dynamically produced simultaneously by a single supercritical four-fermion interaction having $U(3)\times U(1)$ symmetry which includes the electroweak symmetry, where the vacuum is aligned by a small explicit breaking term so as to break the symmetry down to a subgroup, $U(2)\times U(1{)}^{\prime }$, in a way not to retain the electroweak symmetry, in sharp contrast to the little Higgs models. The explicit breaking term for the vacuum alignment gives rise to a mass of the tHiggs, which is protected by the symmetry and hence naturally controlled against radiative corrections. Realistic top-quark mass is easily realized similarly to the top-seesaw mechanism by introducing an extra (subcritical) four-fermion coupling which explicitly breaks the residual $U(2{)}^{\prime }\times U(1{)}^{\prime }$ symmetry with $U(2{)}^{\prime }$ being an extra symmetry besides the above $U(3{)}_L\times U(1)$. We present a phenomenological Lagrangian of the top-mode pseudo-Nambu-Goldstone bosons along with the Standard Model particles, which will be useful for the study of the collider phenomenology. The coupling property of the tHiggs is shown to be consistent with the currently available data reported from the LHC. Several phenomenological consequences and constraints from experiments are also addressed.

Figure 1

Left panel: The $S,T$ constraints from Eqs. (75) and (76) on the $t^{\prime }$-quark mass in the $(S,T)$ plane for $G^{\prime \prime }/G=0.3$ (dotted), 0.5 (dashed), 0.7 (solid). The 95% C.L. allowed region corresponds to an area lower than the solid curve (inside the $S$-$T$ ellipsis). The regions of $S<0$ and $T<0$ are not displayed due to $c_L^t\le 1$. Right panel: The $t^{\prime }$-quark mass vs $G^{\prime \prime }/G$ allowed by the $S,T$ constraints of the left panel. The 95% C.L. allowed region corresponds to an area upper than the blue curve.

Figure 2

The one-loop diagrams contributing to $h_t^0,A_t^0$ masses as the quadratic divergent corrections up to $\mathcal{O}((G^{\prime \prime }/G{)}^2)$.