{"knowledge_schema": {"broad_category": "Physics \u2192 Particle Physics \u2192 Beyond the Standard Model", "refinement": "This problem involves the calculation of mass corrections in a theoretical framework that includes additional particles and interactions beyond the Standard Model.", "specific_scope": "The focus is on determining the mass of a new scalar particle (H_3) through radiative corrections, considering contributions from various particles and their masses.", "goal": "To derive the expression for the mass of the new scalar particle H_3 based on the vacuum expectation values and the mass contributions from other particles."}, "summary": "This problem pertains to particle physics, specifically in the context of extensions to the Standard Model. It requires calculating the mass of a new scalar particle (H_3) through radiative corrections, which involves contributions from various existing particles and their masses. The expression for the mass is derived based on the vacuum expectation values of the scalar fields involved. The correct answer is the first option, which includes specific coefficients (\u03b2_i) that account for the contributions from different particles."}