Homework #2

Each problem is worth 10 points

1. The mass of the Z-boson is approximately 90 GeV. Estimate the range of weak interaction, carried via the Z-boson exchange. [Hint: use the Heisenberg uncertainty principle.]

2. The Z-boson has a width of 2.5 GeV. Calculate its lifetime in seconds.

3. Using the symmetry of wave function argument, show that a spin 1 r⁰ meson can not decay into a pair of identical spinless p⁰ mesons. [Hint: relate the symmetry of the wave function of two pions with their angular momentum.]

4. Perkins 1.7.

5. What's the helicity of the muon in the p⁺ ® m⁺ + n_m decay? [Hint: pion has spin 0.]

The following problems explore materials of the next week class and reading assignment

6. Electromagnetic (EM) showers stop abruptly when the energy of the secondary particles drop below the energy, E_c, at which e⁺e^- pair production is the dominant source of energy loss. How thick (in cm) one would want to build an electromagnetic calorimeter made out of lead in order for it to contain completely EM showers originated by a 100 GeV electron. How different is the answer for a 1000 GeV electron? Density of the lead is 11.4 g/cm³; Use Table 11.2 to get other properties of the lead, pertinent to this problem. [Hint: see Perkins Section 11.5.3 for discussion of the EM shower development.]

7. Protons are accelerated in a circular accelerator. Maximum bending magnetic field that can be used to keep the protons on a circular orbit is 5 T. Find the maximum energy one can accelerate the protons to if the diameter of the accelerator ring is 1 mile..

8. Resolution of an electromagnetic calorimeter DE/E = 0.15/sqrt(E [GeV]). The Z-boson invariant mass (91 GeV) is reconstructed by measuring the energy of the electrons from the Z ® e⁺e^- decay in the calorimeter. Assuming that the Z-boson is produced at rest in the lab frame find the observed width of the Z-peak due to finite calorimeter resolution. Would such a calorimeter have sufficient resolution to allow for a measurement of the "internal" width of the Z-boson of G = 1/t = 2.5 GeV, which corresponds to a Gaussian shape with s » 1 GeV?

This page was last modified January 26, 2005
 by Greg Landsberg