{"knowledge_schema": {"broad_category": "Physics \u2192 Quantum Field Theory \u2192 Renormalization", "refinement": "This problem involves analyzing the mass dimensions of coupling constants in a quantum field theory Lagrangian, specifically focusing on an interaction term involving a scalar field and a fermion field.", "specific_scope": "The interaction term \u2112_int = \u03bb\u03d5^3 \u03c8 requires determining the mass dimension of the coupling constant \u03bb to assess the renormalizability of the theory.", "goal": "Calculate the mass dimension of \u03bb and evaluate whether the theory is renormalizable based on that dimension."}, "summary": "In this problem, we analyze the mass dimension of the coupling constant \u03bb in the interaction term of a Lagrangian involving a scalar field (\u03d5) and a fermion field (\u03c8). By determining the mass dimensions of the fields involved, we find that [\u03bb]_M = -1. This negative mass dimension indicates that the theory is not renormalizable, as coupling constants with negative mass dimensions typically lead to divergences that cannot be controlled through renormalization."}