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Alec Aivazis renamed kinematics more.tex to kinematics_angle.tex
almost 10 years ago
Commit id: 37f17b213af5f1984370f633559cf530b32a7b59
deletions | additions
diff --git a/kinematics_angle.tex b/kinematics_angle.tex
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index 0000000..0ffcca2
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+++ b/kinematics_angle.tex
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\subsubsection{Neutrino Decay Angle}
To understand what happens during the decay in the frame of reference of the lab, we need to boost in the beam direction, taken to be in the z-direction. The Lorentz Boost in the z-direction is given by:
\begin{equation}
\begin{bmatrix}
ct' \\
x' \\
y' \\
z' \\
\end{bmatrix} = \begin{bmatrix}
\gamma & 0 & 0 & - \beta \gamma \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
-\beta \gamma & 0 & 0 & \gamma \\
\end{bmatrix} \begin{bmatrix}
ct \\
x \\
y \\
z \\
\end{bmatrix}
\end{equation}
Where the boost factor $\gamma$ is given by
\begin{equation}
\gamma = \frac{E_{\pi}}{m_{\pi}}
\end{equation}
