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Mass Generation

The mechanism by which quarks acquire mass, primarily through the interaction with the gluon field, remains a central open question.
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The statement of the theorem

The effective mass meffm_{\text{eff}} acquired by a quark field ψ\psi due to interactions with the gluon background field AμA_{\mu} is determined by the self-energy diagram Σ(p2)\Sigma(p^2). In the context of the QCD vacuum, the mass term is generated via the vacuum expectation value of the field strength tensor, leading to an effective Lagrangian term: Lmass=−12mqψˉψ\mathcal{L}_{\text{mass}} = -\frac{1}{2} m_q \bar{\psi} \psi where mqm_q is the running quark mass, calculated from the pole of the full propagator S−1(p)=p−m0−Σ(p)S^{-1}(p) = p - m_0 - \Sigma(p). The mechanism involves chiral symmetry breaking.
Source: Wikipedia