"Asymmetric B factories" like the Belle facility in Japan are designed to produce pairs of B mesons (mass about 5 GeV each) from the head- on collision of a highly relativistic electron beam against a highly relativistic positron beam (about 7 GeV and 4 GeV at Belle; recall the electron mass is 0.5 MeV). For the purpose of this problem, the reaction is e+ + e + B+ B and let's assume that the reaction occurs at threshold; the B and B are produced at rest in the center of mass frame. You can, of course, treat the electron and positron as massless in what follows. (a) If the energy of the two beams is E1 and E2 and the mass of the B (and B) is MB, what is the relation between E1, E2 and MB for this to occur?

"Asymmetric B factories" like the Belle facility in Japan are designed to produce pairs of B mesons (mass about 5 GeV each) from the head- on collision of a highly relativistic electron beam against a highly relativistic positron beam (about 7 GeV and 4 GeV at Belle; recall the electron mass is 0.5 MeV). For the purpose of this problem, the reaction is e+ + e + B+ B and let's assume that the reaction occurs at threshold; the B and B are produced at rest in the center of mass frame. You can, of course, treat the electron and positron as massless in what follows. (a) If the energy of the two beams is E1 and E2 and the mass of the B (and B) is MB, what is the relation between E1, E2 and MB for this to occur?