Walking technipions in a holographic model

We calculate masses of the technipions in the walking technicolor model with the anomalous dimension ${\gamma }_m=1$, based on a holographic model which has a naturally light technidilaton $\varphi$ as a composite Higgs with mass $m_{\varphi }\simeq 125\mathrm{GeV}$. The one-family model (with four weak doublets) is taken as a concrete example in such a framework, with the inputs being $F_{\pi }=v/2\simeq 123\mathrm{GeV}$ and $m_{\varphi }\simeq 125\mathrm{GeV}$ as well as ${\gamma }_m=1$. It is shown that technipion masses are enhanced by the large anomalous dimension to typically $O(1)\mathrm{TeV}$. We find a correlation between the technipion masses and $S^{(\mathrm{TC})}$, the $S$ parameter arising only from the technicolor sector. The current LHC data on the technipion mass limit thus constrains $S^{(\mathrm{TC})}$ to be not as large as $O(1)$, giving a direct constraint on the technicolor model building. This is a new constraint on the technicolor sector alone, quite independent of other sectors connected by the extended-technicolor-type interactions—in sharp contrast to the conventional $S$ parameter constraint from the precision electroweak measurements.

Figure 1

${\mathrm{\Pi }}_V(Q^2)-{\mathrm{\Pi }}_A(Q^2)$ calculated from the holographic WTC model for the case of $N_{\mathrm{TC}}=4$. Solid, dashed, and dotted curves correspond to the cases of $S=0.1$, 0.3, and 1.0, respectively.

Figure 2

${\mathrm{\Pi }}_V(Q^2)-{\mathrm{\Pi }}_A(Q^2)$ in real-life QCD obtained from the holographic calculation with the input parameters shown in Eq. (a2).

Figure 3

${\mathrm{\Pi }}_V(Q^2)-{\mathrm{\Pi }}_A(Q^2)$ calculated from the holographic WTC model for the case of $N_{\mathrm{TC}}=3$, compared with that calculated from the inhomogeneous BS equation with the improved ladder approximation in Ref. [18]. Solid, dashed, and dotted (red) curves correspond to the cases of $S=0.1$, 0.3, and 1.0 obtained from the holographic calculation, while the dash-dotted (blue) curve is the one calculated from the ladder BS equation. Both the vertical and the horizontal axes are normalized by $F_{\pi }^2$.