{"knowledge_schema": {"broad_category": "Theoretical Physics \u2192 Quantum Field Theory \u2192 Renormalization", "refinement": "This problem involves analyzing the mass dimensions of parameters in a Lagrangian and determining the renormalizability of the theory based on these dimensions.", "specific_scope": "The focus is on the Lagrangian involving fermionic fields and gauge fields, specifically examining the mass dimension of the coupling constant \u03ba and the implications for renormalizability.", "goal": "Determine the mass dimension of \u03ba and assess whether the theory is renormalizable based on this dimension."}, "summary": "In this problem, we analyze the mass dimension of the coupling constant \u03ba in the given Lagrangian and evaluate the renormalizability of the theory. The mass dimension of \u03ba is found to be -1, which suggests that the theory is not renormalizable. Therefore, the correct answer is that the mass dimension [\u03ba]_M=-1 and the theory is not renormalizable."}