Left-right symmetric composite Higgs model

We find the exchange symmetry between left and right handed top quark in composite Higgs model with partial compositeness is efficient to soften the Higgs potential and reduce fine tuning. This symmetry can keep the Higgs potential in top sector invariant under trigonometric parity $\sin (h/f)\leftrightarrow \cos (h/f)$. Thus the Higgs quadratic divergences can be canceled entirely, resulting in a UV insensitive Higgs potential. We explicitly construct the minimal left-right symmetric model based on coset space $SO(6)/SO(5)$, which is locally isomorphic to $SU(4)/Sp(4)$ and thus has well defined fermionic UV completion. This UV completion can automatically keep Higgs potential in the gauge sector finite even the gauge sector breaks this discrete symmetry. We find that the vector mesons can be very heavy, while the colored top partners are relatively light ($>1.5\mathrm{TeV}$) to obtain a light Higgs.

Figure 1

Scatter plot for $\xi =0.03$, $m_t\in [140,170]\mathrm{GeV}$, $m_h\in [120,130]\mathrm{GeV}$ and $U(1{)}_{\eta }$ gauge boson mass $m_{B\prime }\in [\frac{125}{2},1000]\mathrm{GeV}$. In the left (right) panel we show the tuning $\mathrm{\Delta }$ as a function of $m_{\rho }$ (lightest top partner $M_T$). The red line corresponds to the estimation from Eq. (39).

Figure 2

Scatter plot of tuning ${\mathrm{\Delta }}_i$ as a function of $m_h$ with $\xi$ fixed at 0.03 for the various free input parameters $x_i$: $M_5$ (black), $M_1$ (blue), $m_{\rho }$ (red) and $g_1$ (green). We choose the range of parameters as follows: $m_t\in [140,170]\mathrm{GeV}$, $m_{\rho }\in [2.5,5]\mathrm{TeV}$, $m_{B\prime }\in [\frac{125}{2},1000]\mathrm{GeV}$ and the lightest top partner’s mass $M_T>1.5\mathrm{TeV}$.