Scaling results for charged sectors of near conformal QCD

Abstract

We provide the leading near conformal corrections on a cylinder to the scaling dimension ${\Delta }_Q^{\ast }$ of fixed isospin charge $Q$ operators defined at the lower boundary of the Quantum Chromodynamics conformal window: \begin{equation} Δ_Q = Δ_Q^\ast +\left(\frac{m_σ}{4 πν}\right)^2 \, Q^{\fracΔ{3}} B_1 + \left(\frac{m_π(θ)}{4πν} \right)^4\ Q^{\frac{2}{3}(1-γ)} B_2 + \mathcal{O}\left ( m_σ^4 , m_π^8, m_σ^2 m_π^4\right) \ . \nonumber \end{equation} The results are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale $4\pi \nu$ with the theta-angle dependence encoded directly in the pion mass. The characteristic $Q$-scaling is dictated by the quark mass operator anomalous dimension $\gamma$ and the one characterising the dilaton potential $\Delta$. The coefficients $B_i$ with $i=1,2$ depend on the geometry of the cylinder and properties of the nearby conformal field theory.

22 pages, 4 figures