Subatomic Physics

11.5. The Muon Decay 347
Linac Pion channel
p � � �
p �
J �
Pion
target � �
� �
J �
p �
Muon
target
Figure 11.7: A positive pion is selected in the pion channel and comes to rest in the pion target.
The pion decay results in a fully polarized muon. The muon escapes from the pion target and
comes to rest in the muon target. Its spin points in the direction from which it came. The decay
electron is then observed.
Conservation laws determine much of what happens: Conservation of the lepton
and muon numbers requires the neutral particle to be a muon neutrino. Momentum
conservation demands that the muon and the muon neutrino have equal and
opposite momenta in the c.m. of the decaying pion. The muon neutrino has its
spin opposite to its momentum, as shown in Fig. 7.2. Since the pion has spin 0,
angular momentum conservation insists that the positive muon must be fully polarized,
with its spin pointing opposite to its momentum. The muons escape from
the pion target; some are stopped in the muon target, and their decay positron can
be detected. With proper choice of the muon target, the decaying muon is still
polarized, and its spin J points into the direction from which it came.
The processes just described and shown in Fig. 11.7 permit a number of measurements
that all give information concerning the weak interaction. We shall discuss
three aspects here, parity nonconservation, the lifetime of the muon, and the spectrum
of the decay electrons.
Parity Nonconservation As Fig. 11.7 is drawn, it shows the breakdown of parity
in two different places. The muon is expected to be polarized because the neutrino
emitted together with it is polarized. A longitudinally polarized muon violates
parity conservation, as was explained in Section 9.3. A measurement of the polarization
of the muon thus demonstrates that parity is not conserved in the weak
decay of the pion. Such a polarization has been detected. (12) The second place
where parity nonconservation shows up is in the decay of the muon. As sketched
in Fig. 11.7, the muon spin points into a well-defined direction, and the probability
of positron emission can now be determined with respect to this direction. This
experiment is analogous to the one discussed in Section 9.3 and shown in Fig. 9.6.
Indeed, as in the Wu–Ambler experiment, it was found that the positron is prefer-
12 G. Backenstoss, B. D. Hyams, G. Knop, P. C. Marin, and U. Stierlin, Phys. Rev. Lett. 6, 415
(1961); M. Bardon, P. Franzini, and J. Lee, Phys. Rev. Lett. 7, 23 (1961); TWIST collaboration,
Phys. Rev. D 71, 071101 (2005).
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