Toward TeV Conformality

We study the chiral properties of an $SU(3)$ gauge theory with $N_f$ massless Dirac fermions in the fundamental representation when $N_f$ is increased from 2 to 6. For $N_f=2$, our lattice simulations lead to a value of $⟨\overline{\psi }\psi ⟩/F^3$, where $F$ is the Nambu-Goldstone-boson decay constant and $⟨\overline{\psi }\psi ⟩$ is the chiral condensate, which agrees with the measured QCD value. For $N_f=6$, this ratio shows significant enhancement, presaging an even larger enhancement anticipated as $N_f$ increases further, toward the critical value for transition from confinement to infrared conformality.

Figure 1

$R_m\equiv [M_m^2/2m{F}_m{]}_{6f}/[M_m^2/2m{F}_m{]}_{2f}$, versus $\overline{m}\equiv [m_{2f}+m_{6f}]/2$, indicating enhancement of $⟨\overline{\psi }\psi ⟩/F^3$ at $N_f=6$ relative to $N_f=2$.

Figure 2

The slope of the pseudoscalar mass squared $M_m^2/2m$ in lattice units, as a function of fermion mass. The fit for $N_f=2$ is a joint fit to $M_m^2$, $F_m$ and $⟨\overline{\psi }\psi {⟩}_m$, using the (solid) points at $m_f=0.01–0.02$, constrained to match NLO $\chi \mathrm{PT}$.

Figure 3

The Goldstone-boson decay constant $F_m$ in lattice units, as a function of fermion mass. The fit for $N_f=2$ is a joint fit to $M_m^2$, $F_m$ and $⟨\overline{\psi }\psi {⟩}_m$, using the (solid) points at $m_f=0.01–0.02$, constrained to match NLO $\chi \mathrm{PT}$.

Figure 4

The chiral condensate per fermion $⟨\overline{\psi }\psi {⟩}_m$ in lattice units, as a function of fermion mass. The fit for $N_f=2$ is a joint fit to $M_m^2$, $F_m$ and $⟨\overline{\psi }\psi {⟩}_m$, using the (solid) points at $m_f=0.01–0.02$, constrained to match NLO $\chi \mathrm{PT}$.