{"knowledge_schema": {"broad_category": "Theoretical Physics \u2192 Quantum Field Theory \u2192 Renormalization", "refinement": "This problem involves analyzing the mass dimensions of parameters in an interaction Lagrangian to assess the renormalizability of the theory.", "specific_scope": "The focus is on the interaction term involving fermionic fields and gauge fields, specifically the mass dimension of the coupling constant \u03ba in the context of the Lagrangian \u2112_int = \u03ba\u03c8\u0305\u03c3_\u03bc\u03bd\u03c8 F^\u03bc\u03bd.", "goal": "Determine the mass dimension of \u03ba and evaluate whether the theory is renormalizable based on this dimension."}, "summary": "In this problem, we analyze the interaction Lagrangian \u2112_int = \u03ba\u03c8\u0305\u03c3_\u03bc\u03bd\u03c8 F^\u03bc\u03bd to determine the mass dimension of the coupling constant \u03ba. By considering the mass dimensions of the fields involved, we find that the mass dimension of \u03ba is -1. This negative mass dimension indicates that the theory is not renormalizable, as renormalizability typically requires coupling constants to have non-negative mass dimensions."}