# Pion decay in electron and neutrino

1. Apr 25, 2009

### mur79

Hi,
I have a question about this decay: $$\pi^- \rightarrow e^- \overline{\nu_e}$$
there is a factor:

$$1 - \frac{v_e}{c}$$

what are these values, $$v_e,c$$, and why this quantity is equal to:

$$\frac{m^2_e}{m^2_\pi + m^2_e}$$?

Thank you
Ciccio

2. Apr 25, 2009

### mur79

Sorry but I don't understand why the latex don't work...

the decay is

pi- -> e- anti-nu(e)

the factor is: 1-v/c

and I don't understand what are v and c...
and why that quantity is equal to: (m_e)^2 / [(m_pi)^2 + (m_e)^2]

Thank you
Ciccio

3. Apr 26, 2009

### clem

v is the electron velocity and c the speed of light.
In special relativity, v/c=pc/E, where p is the momentum and E the total energy.
Some more algebra is required to get the final result.