Final Exam (129A), Dec 13, 5–8 pm
1. Explain the branching fractions of the W-boson. [15]
2. A very high-energy cosmic ray proton would absorb the cosmic-microwave
background photons to become a Delta resonance, which quickly decays into
a nucleon and a pion, thereby losing its energy. Assuming all CMBR photons
have the energy E=kT , what is the maximum proton energy for this not
to happen? (There is a puzzling report that we see cosmic rays above this
so-called GZK cutoff.) [10]
3. KamLAND experiment reported 54 reactor anti-electron-neutrino event for
86.8±5.6 events (5.6 is the systematic error) expected without neutrino
oscillation. Assume all reactors are at the distance of 180 km and the neu-
trino energy of Eν∼3 MeV. (1) What is the reaction used to detect reactor
anti-electro-neutrino? [5] (2) If ∆m2is relatively high and the oscillation is
averaged out, what is the preferred value of sin22θwith statistical and sys-
tematic errors? [5] (3) In order for a sizable oscillation effect to be present
as observed, estimate what the minimum value of ∆m2is in eV2. [5]
4. 21cm line of hydrogen hyperfine transition is important in measuring the
rotation curve of galaxies. In order to see emission lines, excited states must
be present. Why are there excited hyperfine states in the cold space? [10]
5. Existence of matter but no antimatter in Universe suggests that the baryon
and lepton numbers are actually violated, and hence proton may decay.
Grand unified theories indeed predict it. List five possible decay modes
of the proton consistent with all other conservation laws. [15]
6. Using Kresonances, identify states on the leading Regge trajectory [5], ob-
tain the Regge slope [5], and the force between the quark and the anti-quark
in Newton [5].
7. Experiments at LEP-II e+e−collider searched for the Higgs boson, found
a hint, but finished with a lower bound of 114.4 GeV (95% CL). Draw the
Feynman diagram which could have been relevant for the Higgs boson pro-
duction at LEP-II. [5]
8. Using the Friedmann equation ˙
R
R2=8π
3GNρ, the first law of thermody-
namics d(ρR3) = −pd(R3), and the equation of state p=wρ, determine the
evolution of the scale parameter R(t) for Universe dominated by relativistic
matter w= 1/3, non-relativistic matter w= 0, and the cosmological con-
stant w=−1. Show that the Universe accelerates ¨
R > 0 only for the last
case. [15]