Mandelstam variables consider the relativistic two-body scattering a+b→c+d with corresponding 4-vectors pa, p pc, and pp the masses of the corresponding objects are m,', mb, me, and mb. you can set the speed of light as c l if you would like. the mandelstam variables are useful lorentz invariants: t = (pa-pc) u = (pa-po) (a) show that s + t + u = mhng + mる+ m2, . [ 10 points] (b) show that the total center of mass energy is given by s. [10 points] (c) the lhc collides protons in the lab frame with an energy of 6.5 tev against other protons with an energy of 6.5 tev (so that 's = 13 tev) one of the things looked for is the production of new z bosons. what is the most massive z' that the lhc could directly observe? [10 points] (d) why can the photon not decay? [10 points] hint 1: prove that the mass of a decaying particle must exceed the masses of the particles produced in its decay. in other words, if a decays into b+c, show that m,> mmc. hint 2: evaluate in the center of mass frame.