The Leptons — Question 10

Question 10

Charged-current detection identifies the incident neutrino flavor

In a simplified detector, $\nu_\mu+n\to\mu^-+p$ and $\bar\nu_\mu+p\to\mu^++n$ are the only selected channels. A sample contains 600 negative-muon events and 100 positive-muon events. Efficiencies are .600 and .500. Exposures and cross sections are assumed equal.

1. Infer the neutrino-to-antineutrino incident-flux ratio.

2. Check charge and muon-family number for each channel, and explain the limitation if cross sections differ.

Question 10 - Solution

Charged-current detection identifies the incident neutrino flavor

(a) Method and calculation

$$\boxed{N_\nu\propto600/.600=1000,\quad N_{\bar\nu}\propto100/.500=200}.$$$$\boxed{\Phi_\nu/\Phi_{\bar\nu}=5.00}\quad\text{under equal cross sections and exposures}.$$

(b) Interpretation and further calculation

$$\nu_\mu n:\ Q=0=-1+1,\ L_\mu=1=1;\quad\bar\nu_\mu p:\ Q=1=1+0,\ L_\mu=-1=-1.$$$$\boxed{\frac{\Phi_\nu}{\Phi_{\bar\nu}}=\frac{C_-/\epsilon_-}{C_+/\epsilon_+}\frac{\sigma_{\bar\nu}}{\sigma_\nu}}\quad\text{for equal target exposures}.$$

Physical check

The sign of the charged muon tags neutrino versus antineutrino in these selected channels. Equal cross sections are a teaching assumption, not a general fact.