= Adjoint Dirac contribution to the Yang-Mills beta function
{title2=$\beta_{\mathrm{Dirac,ad}}(g)=4C_Ag^3/[3(4\pi)^2]$}
One adjoint <Dirac spinor> contributes the displayed screening term to the four-dimensional <renormalization-group beta function> in the <modified minimal subtraction scheme>. The fermion contribution to the gluon <self-energy> insertion has pole $-8g^2C_A(k^2\delta_{\mu\nu}-k_\mu k_\nu)/(3\epsilon(4\pi)^2)$. The corresponding background gauge-field <counterterm> is $\delta Z_A=-8g^2C_A/(3\epsilon(4\pi)^2)$; the <background gauge-field renormalization identity> $Z_g=Z_A^{-1/2}$ gives $g_0=\mu^{\epsilon/2}(g+4C_Ag^3/[3\epsilon(4\pi)^2])$. Differentiation at fixed $g_0$ yields the screening coefficient. The mass-independent subtraction includes massive fields until effective-theory threshold matching is performed.
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