Natural Science Forum / Physics / Particle Physics / October 2004

his is known as "helicity suppression", and it's calculation was
an early triumph of the left-handed "V-A" weak interaction. It's
discussed in most HEP textbooks.  It's in section 6.8 of my
(very old) Perkins, for example.

The pion has zero spin, which means that to conserve angular momentum,
the two decay fermions, which are going in opposite directions, must
have the *same* helicity.  The weak interaction can only couple to
lefthanded particle (right handed antiparticle) *chiral* states.  The
closer that  a particle is going to the speed of light, the closer the
chiral states are to pure helicity states.  Let's say you have
pi+ -> f+  +  nu_f, where f+ is either a mu+ or an e+, and nu_f is
the corresponding  neutrino.  The nu_f is going at the speed of light
for all practical purposes, so it's going to be a pure left
handed helicity state. That means that the fermion has to
*also* have a left handed helicity, but it's and *antiparticle*
so it's a right-handed chiral state (ie, it's the "wrong"
helicity).  Because the electron much lighter than the muon,
it is going much closer to the speed of light, so the coupling
between the right-handed chiral state and the left handed
helicity state is much smaller.

The calculated ratio of the decay is 1.275E-4, which
matches experiment quite nicely.

-E