this is for holding javascript data
Alec Aivazis edited nova.tex
almost 10 years ago
Commit id: 826e020bc6dcbf44cf0460a595734c68a1e85719
deletions | additions
diff --git a/nova.tex b/nova.tex
index a241a77..73f8201 100644
--- a/nova.tex
+++ b/nova.tex
...
P(\nu_{\mu} \rightarrow \nu_{e}) = f \left(\sin^2 \theta_{23} \sin^2 2\theta_{13}, \frac{\Delta_{31}}{\Delta_{31} \mp a L} \sin(\Delta_{31} \mp aL), \sin \delta_{CP}\right)
\end{equation}
where $i$ and $j$ carry values 1,2,3 and stand for electron, muon, and tau quantities respectively; $\theta_{ij}$ is the "mixing angle" between the various flavors; $\Delta_{ij} = \Delta m_{ij}^2 L / 4E $; L is the length over which the oscillations occur; $a = G_F N_e \sqrt{2} \simeq (4000 \rm{km})^{-1}$; the $\delta_{CP}$ is a measure of the amount by which charge and parity conversation are allowed to be violated; the $\mp$ correspond to neutrinos and antineutrinos respectively. It is important to note that the aL term comes about because of the initial momentum of the neutrinos in the beam and allows for close study of the mass hierarchy since its closely related to
$\Delta_{ij}$. $\Delta_{ij}$ .