Pion decay in electron and neutrino

[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

 

[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

 

[Meir Achuz]

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.