Revisiting $Zb\overline{b}$ couplings in the littlest Higgs model with $T$ parity under current experimental constraints

In the littlest Higgs model with $T$ parity (LHT), we revisited $Zb\overline{b}$ couplings under current experimental constraints including the LHC Higgs data and the precision electroweak data. We study the LHT effects in the branching ratio $R_b$, the forward-backward asymmetry $A_{FB}^b$ and the left- and right-handed couplings $g_{Lb}$, $g_{Rb}$. We find that the LHT effects in $R_b$ are sizable enough to be observed at future $Z$-factories (ILC, CEPC, FCC-ee) in the allowed parameter space, while these effects in $A_{FB}^b$ are weak so that it is difficult to detect at the future experiments. The LHT model provides the large correction to the left-handed coupling $g_{Lb}$, which can be limited by current and future experiments.

Figure 1

One-loop Feynman diagrams of the mirror quark correction to $Zb\overline{b}$.

Figure 2

One-loop Feynman diagrams of the top partner correction to $Zb\overline{b}$.

Figure 3

The scatter plots of the mirror quark one-loop effects (top left and top right), the top partner one-loop effects (bottom left) and the $R_b$ (bottom right) in two scenarios.

Figure 4

The plots of survived samples on $\delta R_b$, showing the constraint of the Higgs data in two cases and the constraint of the oblique parameters $S$, $T$, $U$, where the samples with and without the relevant constraints at $2\sigma$ level are displayed.

Figure 5

The plots of survived samples on $\delta R_b$, showing the combined constraints of the Higgs data and the oblique parameters $S$, $T$, $U$ in two cases, where the samples with and without the combined constraints at the $2\sigma$ level are displayed. In the right panel, the survived samples on the $R_b$ are displayed, where the experimental value $R_b^{\exp }=0.21629\pm 0.00066$.

Figure 6

Same as Fig. 4, but for $A_{FB}^b$.

Figure 7

Same as Fig. 5, but for $A_{FB}^b$, where the experimental value $A_{FB}^{b,\exp }=0.0992\pm 0.0016$.

Figure 8

Preferred regions in the ($\delta g_{Lb}$,$\delta g_{Rb}$) plane for case A (left) and case B (right), assuming SM central values and current precision for all measurements.

Figure 9

Correlation between $\delta R_b$ and $\delta A_{FB}^b$.