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Asymptotic Freedom

At short distances (high energies), the strong force becomes weaker, allowing quarks to behave almost as free particles.
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The statement of the theorem

Define the running coupling constant αs(Q2)\alpha_s(Q^2) via the renormalization group equation (RGE) in QCD. The beta function β(αs)=μdαsdμ\beta(\alpha_s) = \mu \frac{d \alpha_s}{d \mu} is calculated as: β(αs)=−αs2(113Nc−23Nf)14π+O(αs3)\beta(\alpha_s) = -\alpha_s^2 \left( \frac{11}{3} N_c - \frac{2}{3} N_f \right) \frac{1}{4\pi} + O(\alpha_s^3) where Nc=3N_c=3 is the number of colors and NfN_f is the number of active flavors. As the energy scale μ→∞\mu \to \infty (or distance r→0r \to 0), β(αs)<0\beta(\alpha_s) < 0, leading to αs(Q2)→0\alpha_s(Q^2) \to 0.