PHY357S: Monday, 17 March 1997

Problem 1

The partial widths for the decay of the Z⁰ boson into fermion-antifermion pairs are = 84.0 MeV, = 167.2 MeV, = 300.6 MeV, = 383.3 MeV, and =375.9 MeV. (The mass of the b quark causes a slight phase space suppression relative to decays into d and s quarks.)

(a) Calculate the fraction of Z⁰ decays which are into quark-antiquark pairs.

(b) Calculate the peak cross section for e⁺e^-ÆZ⁰Æhadrons. (The Z⁰ mass is 91.188 GeV.)

(c) If there was a fourth kind of light neutrino, n₄, the partial width for decays would also be = 167.2 MeV. Show that the existence of a fourth type of ight neutrino is not consistent with the observed cross section for electron-positron production of hadrons at the peak of the Z⁰, s_peak(e⁺e^-ÆZ⁰Æhadrons )=41.488±0.078nb.

Problem 2

(a) Rederive Frauenfelder & Henley equation 11.5 for a small finite neutrino mass, 0<m_n<<m_e.

(b) Use the best current values for G_F, the t lepton mass, and the t lepton lifetime (1.16639¥10^-5 GeV^-2, 1777 MeV, and 291¥10^-15s) to calculate the branching fraction for decays.

(c) Show that the reaction n_me^-Æ n_me^- is forbidden if only weak interaction charged currents exist, but n_ee^-Æ n_ee^- is allowed.

Problem 3

(a) The neutron and antineutron are neutral antiparticles, just as the and are. Why do the neutron and antineutron not mix like the and ? (See F&H Section 9.7.)

(b) Only about half of the electron neutrinos expected from ⁸B in the sun are observed. (See F&H Section 19.3.) Do the neutrino oscillation limits of Figure 11.11 exclude n_e´n_m oscillations as a possible solition to this "Solar Neutrino Problem"? For simplicity you may assume all the⁸B solar neutrinos have an energy of E_max//2, and do not consider the possibility of matter enhanced oscillations mentioned in the last paragraph of Section 19.3.