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Quantum Chromodynamics (QCD)

QCD is the quantum field theory describing the strong interaction between quarks and gluons, forming the basis of the Standard Model.
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The statement of the theorem

Define the QCD Lagrangian density LQCD\mathcal{L}_{QCD} for NfN_f flavors of quarks ψi\psi_i and the gluon field GμaG^a_{\mu}: LQCD=∑i=1Nfψˉi(iγμDμ−mi)ψi−14GμaGaμ\mathcal{L}_{QCD} = \sum_{i=1}^{N_f} \bar{\psi}_i (i \gamma^{\mu} D_{\mu} - m_i) \psi_i - \frac{1}{4} G^a_{\mu} G^{a\mu} where the covariant derivative DμD_{\mu} is defined as Dμ=∂μ−igsTaGμaD_{\mu} = \partial_{\mu} - i g_s T^a G^a_{\mu}. The gluon field strength tensor GμνaG^a_{\mu\nu} is given by: Gμνa=∂μGνa−∂νGμa+gsfabcGμbGνcG^a_{\mu\nu} = \partial_{\mu} G^a_{\nu} - \partial_{\nu} G^a_{\mu} + g_s f^{abc} G^b_{\mu} G^c_{\nu} The coupling constant gsg_s runs with the energy scale μ\mu according to the renormalization group equation, exhibiting asymptotic freedom: μdgsdμ=β(gs)=−gs316π2(11−23Nf)\mu \frac{d g_s}{d \mu} = \beta(g_s) = - \frac{g_s^3}{16\pi^2} (11 - \frac{2}{3} N_f).