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The center-of-mass energy of two particles colliding near the horizon of amaximally rotating black hole can be arbitrarily high if the angular momentumof either of the incident particles is fine-tuned, which we call a criticalparticle. We study particle emission from such high-energy collision andreaction in the equatorial plane fully analytically. We show that theunconditional upper limit of the energy of the emitted particle is given by218.6% of that of the injected critical particle, irrespective of the detailsof the reaction and this upper limit can be realized for massless particleemission. The upper limit of the energy extraction efficiency for this emissionas a collisional Penrose process is given by 146.6%, which can be realized inthe collision of two massive particles with optimized mass ratio. Moreover, weanalyze perfectly elastic collision, Compton scattering, and pair annihilationand show that net positive energy extraction is really possible for these threereactions. The Compton scattering is most efficient among them and theefficiency can reach 137.2%. On the other hand, our result is qualitativelyconsistent with the earlier claim that the mass and energy of the emittedparticle are at most of order the total energy of the injected particles andhence we can observe neither super-heavy nor super-energetic particles.

Upper limits of particle emission from high-energy collision and reaction near a maximally rotating Kerr black hole