{"knowledge_schema": {"broad_category": "Physics \u2192 Cosmology \u2192 Particle Interactions", "refinement": "This problem deals with high-energy gamma-ray interactions with the Cosmic Microwave Background (CMB) photons, specifically focusing on pair production processes.", "specific_scope": "The context involves calculating the threshold energy for gamma rays to interact with CMB photons to produce electron-positron pairs, considering the average energy of CMB photons.", "goal": "Determine the energy threshold at which gamma rays would have their lifetimes constrained due to interactions with CMB photons."}, "summary": "This problem is rooted in the field of physics, particularly in cosmology and particle interactions. It examines the interaction between high-energy gamma rays and Cosmic Microwave Background photons, specifically the process of pair production (\u03b3\u03b3 \u2192 e\u207ae\u207b). The task is to calculate the energy threshold for gamma rays that would lead to significant interactions with CMB photons, thereby constraining their lifetimes in the universe. The average energy of CMB photons is given as 10\u207b\u00b3 eV, and the correct answer for the threshold energy of gamma rays is 2.6 \u00d7 10\u2075 GeV."}