Dilaton Chiral Perturbation Theory: Determining the Mass and Decay Constant of the Technidilaton on the Lattice

We propose a scale-invariant chiral perturbation theory of the pseudo-Nambu-Goldstone bosons of chiral symmetry (pion $\pi$) as well as the scale symmetry (dilaton $\varphi$) for large $N_f$ QCD. The resultant dilaton mass $M_{\varphi }$ reads $M_{\varphi }^2=m_{\varphi }^2+\frac{1}{4}(3-{\gamma }_m)(1+{\gamma }_m)(2N_f{F}_{\pi }^2/F_{\varphi }^2)m_{\pi }^2+(\mathrm{chiral}\log \mathrm{corrections})$, where $m_{\varphi }$, $m_{\pi }$, ${\gamma }_m$, $F_{\pi }$, and $F_{\varphi }$ are the dilaton mass in the chiral limit, the pion mass, the mass anomalous dimension, and the decay constants of $\pi$ and $\varphi$, respectively. The chiral extrapolation of the lattice data, when plotted as $M_{\varphi }^2$ versus $m_{\pi }^2$, then simultaneously determines ($m_{\varphi }$, $F_{\varphi }$) of the technidilaton in walking technicolor with ${\gamma }_m\simeq 1$. The chiral logarithmic corrections are explicitly given.

Figure 1

A plot of $M_{\varphi }^2/{\mathrm{\Lambda }}_{\chi }^2$ with respect to $m_{\pi }^2/{\mathrm{\Lambda }}_{\chi }^2(\equiv \mathcal{X})$ obtained from Eq. (8), with $N_f=8$ and $F_{\pi }=123\mathrm{GeV}$ and the chiral-limit dilaton mass $m_{\varphi }=125\mathrm{GeV}$. The slope $s\simeq r=2N_f{F}_{\pi }^2/F_{\varphi }^2$ in Eq. (8) has been taken to be 0.2 (solid black line), 0.5 (dashed black line), and 1.0 (dotted black line). The solid red line corresponds to $M_{\varphi }^2=m_{\pi }^2$. The inset figure just denotes the close-up window for the small pion mass region.

Figure 2

A plot of $M_{\varphi }^2/{\mathrm{\Lambda }}_{\chi }^2$ with respect to $m_{\pi }^2/{\mathrm{\Lambda }}_{\chi }^2(\equiv \mathcal{X})$ including the chiral logarithmic corrections in Eq. (10) for the one-family model with $N_f=8$, $F_{\pi }=123\mathrm{GeV}$, the chiral-limit mass $m_{\varphi }=125\mathrm{GeV}$, and the factor $s\simeq r=2N_f{F}_{\pi }^2/F_{\varphi }^2=(0.2,1.0)$ (solid black and blue curves). The leading-order scalings in Eq. (8) are also depicted for $s=0.2$ and 1.0 by dashed black and blue lines, respectively. The solid red line corresponds to $M_{\varphi }^2=m_{\pi }^2$.