- #1

lLehner95

- 7

- 1

- Homework Statement
- Hello, i'm trying to solve this exercise: to produce neutrino beams, ##\pi## and ##K## meson decays are used. Mesons are produced with a ratio ##n_{K}/n_{\pi}=1/10##. Mesons momentum is ##p_{0}=100 GeV/c##. Calculate the longitudinal neutrino momentum distribution.

- Relevant Equations
- In the lab frame of reference:

##p_{T}=p^{*}sin\theta^{*}##

##p_{L}=\gamma p^{*}cos\theta^{*}+\beta\gamma E^{*}=\frac{E}{M}p^{*}cos\theta^{*}+\frac{p}{M}E^{*}##

In the center of mass frame of reference i found that ##p^{*}=\frac{[(M^{2}-m_{\nu}^{2}-m_{K}^{2})^{2}-4m_{\nu}^{2}m_{K}^{2})]^{1/2}}{2M}##.

I don't know how to find the momentum distribution ##p_{L}(\theta)## considering that i have 2 different mesons with a specific number ratio ##n_{K}/n_{\pi}=1/10##. How can i combine them?

I don't know how to find the momentum distribution ##p_{L}(\theta)## considering that i have 2 different mesons with a specific number ratio ##n_{K}/n_{\pi}=1/10##. How can i combine them?