Suppose that the reaction e⁺e⁻ → Z⁰H⁰ was to be studied at a centre-of-mass energy of 500 GeV in a collider operating for 10⁷s per year. Given that the cross-section at this energy is approximately 65 fb, what instantaneous luminosity (in units of cm⁻²s⁻¹) would be needed to collect 2000 events in one year if the detection efficiency is 10%? To what extent would selecting events with b-quark jets present increase the statistical error and enhance the e⁺e⁻ → Z⁰H⁰ signal relative to the background reaction e⁺e⁻ → Z⁰Z⁰? The branching ratio for Z⁰ → bb̅ is about 15% (see Problem 10.7).