Top quark induced effective potential in a composite Higgs model

We consider nonperturbative aspects of a composite Higgs model that serves as a prototype for physics beyond the Standard Model, in which a new strongly interacting sector undergoes chiral symmetry breaking, and generates the Higgs particle as a pseudo-Nambu-Goldstone boson. In addition, the top quark couples linearly to baryons of the new strong sector, thereby becoming partially composite. We study the dynamics leading to the top quark Yukawa coupling as well as the top quark contribution to the effective potential for the Higgs, obtaining expressions for these couplings in terms of baryonic correlation functions in the underlying strongly interacting theory. We then show that a large-$N$ limit exists in which the top quark contribution to the Higgs effective potential overcomes that of the weak gauge bosons, inducing electroweak symmetry breaking. The same large-$N$ limit also suggests that the baryons that couple to the top quark may be relatively light. This composite Higgs model, and similar ones, can be studied on the lattice with the methods developed for lattice QCD.

Figure 1

The three possible Majorana-fermion contractions contributing to Eq. (4.28), corresponding to (a) $C_{\text{top}}$, (b) $C_1$, and (c) $C_2$. Only the top quark (solid lines) and Majorana fermions (dashed lines) are shown. The vertices $x_1,\dots ,x_4$ of Eq. (4.28) correspond to a clockwise motion starting at the lower left corner.

Figure 2

A hyperbaryon in large $N$: diagrams without hypergluons (a, b) and with them (c, d). Diagrams (a) and (c) are leading, while (b) and (d) are subleading.

Figure 3

Different large-$N$ contributions to Fig. 1. The curved lines at the top and the bottom represent the two top quark propagators. The diagrams scale like (a) $N^4$, (b) $N^2$, and (c) $N^3$.