# Calculation of right-handed fraction of leptons (pi decay)

1. Jul 15, 2017

### black1corn

1. The problem statement, all variables and given/known data
I would like to understand whether reocurring formulas in the example solutions to my homework problems hold in general and ideally where they're derived from. (I'm new here; if there's there a way to embed formulas in f.i. latex code please tell me.)
As an example problem: pi^- can decay via electrons or muons. Phase space considerations lead to a branching ratio of w = 3.3 (electrons would be produced much more likely). The goal of the execise is to correct this ratio to the one measured in experiments (R = 1.3e-4), considering that W bosons couple only to left-handed particles and right-handed anti-particles.
The solution is given by:
2. Relevant equations
R = 3.3 * \frac{1-\beta_e}{1-\beta_\mu}
3. The attempt at a solution

From angular momentum conservation it's clear to me that lepton and corresponding anti-neutrino both have to be right-handed as for pi^-: J^P=0^-. It's intuitively clear to me that the (suppressed) right-handed fraction of leptons is smaller and thus an amount of 1-\beta (=1-p/E) makes sence for the momenta in question. What I don't know/am able to find out is whether generally the amount of left-handed particles is \beta and the right-handed amount 1-\beta and how these formulas were originally found.

Any clarification on this would be greatly appreciated.

2. Jul 17, 2017