Subatomic Physics

348 The Weak Interaction
entially emitted parallel to the spin of the incoming muon, indicating that parity is
also violated in the muon decay. (13)
Muon Lifetime The experimental arrangement for determining the muon lifetime
has already been described in chapter 4. In Fig. 4.22, the logic elements are
shown, and it is easy to see how they fit into the setup of Fig. 11.7. Observation
of the number of electrons detected in counter D as a function of the delay time
between counters B and D gives a curve of the form shown in Fig. 5.15, and the
slope of the curve determines the muon lifetime. For most estimates it is sufficient
to remember that the muon mean life is 2.2 µsec.
Figure 11.8: Electron spectrum from unpolarized muons.
[B. A. Sherwood, Phys. Rev. 156, 1475 (1967).] The
momentum is measured in units of the maximum electron
momentum.
Electron Spectrum To investigate
the electron spectrum,
the number of electrons
is measured as a function of
momentum. To determine the
momentum, the electron path
in a magnetic field is observed.
One possibility to detect the
electrons is to use wire spark
chambers the result of which
is shown in Fig. 11.8. Another
detection scheme using
drift chambers has recently
led to spectacular precision
and was shown in chapter 4
(see Fig. 4.16). (14)
Some similarity to the electron spectrum in nuclear beta decay, Fig. 11.1, exists but
the drop-off at high electron momenta is much steeper. The electron spectrum is
no longer determined by the phase-space factor alone and comparison with theory
provides information on the form of the weak Hamiltonian.
11.6 The Weak Current of Leptons
In the previous section, some of the salient features of the muon decay have been
discussed. The τ decay is similar, but there are many more open channels. These
data and some additional information will now be used to construct the weak Hamiltonian,
Eq. (11.25), in more detail. In particular, we shall have to find the form of
the weak current, J l w , as far as we can with our limited tools. The first fact to be
used is the uncanny similarity between electron and muon, a fact often stated by
13 R.L.Garwin,L.M.Lederman,andM.Weinrich,Phys. Rev. 105, 1415 (1957); J. L. Friedman
andV.L.Telegdi,Phys. Rev. 105, 1681 (1957).
14 TWIST Collaboration, Phys. Rev. Lett. 94, 101805 (2005).