Difference between revisions of "Summary of 4-momentum components"

From New IAC Wiki
Jump to navigation Jump to search
(Created page with "===Summary of 4-momentum calculations=== {| class="wikitable" align="center" | style="background: red" | <math>For\ 0 \ge \phi \ge \frac{-\pi}{2}\ Radians</math> |- | <cente…")
(No difference)

Revision as of 19:52, 31 May 2017

Summary of 4-momentum calculations

[math]For\ 0 \ge \phi \ge \frac{-\pi}{2}\ Radians[/math]
x=POSITIVE
y=NEGATIVE
[math]For\ 0 \le \phi \le \frac{\pi}{2}\ Radians[/math]
x=POSITIVE
y=POSITIVE
[math]For\ \frac{-\pi}{2} \ge \phi \ge -\pi\ Radians[/math]
x=NEGATIVE
y=NEGATIVE
[math]For\ \frac{\pi}{2} \le \phi \le \pi\ Radians[/math]
x=NEGATIVE
y=POSITIVE


4 momentum calculations for different frames of reference
Electron Initial Lab Frame Moller electron Initial Lab Frame Moller electron Final Lab Frame Moller electron Center of Mass Frame Electron Center of Mass Frame Electron Final Lab Frame
[math]p_{1}\equiv 11000 MeV[/math] [math]p_{2}\equiv 0[/math] [math]p_{2}'\equiv INPUT[/math] [math]p_{2}^*=\sqrt{E_{2}^{*2}-m^2}[/math] [math]p_{1}^*=\sqrt{E_{2}^{*2}-m^2}[/math] [math]p_{1}'=\sqrt{E_{1}^{'\ 2}-m^2}[/math]
[math]\theta_{1}\equiv 0[/math] [math]\theta_{2}\equiv 0[/math] [math]\theta_{2}'\equiv INPUT[/math] [math]\theta_{2}^*=\arccos \left(\frac{p_{2(z)}^*}{p_2^*} \right)[/math] [math]\theta_{1}^*=\pi-\theta_{2}^*[/math] [math]\theta_{1}'= \arccos \left(\frac{p_{1(z)}'}{p_{1}'} \right)[/math]
[math]E_{1}=\sqrt{p_1^2+m^2}[/math] [math]E_{2}\equiv m[/math] [math]E_{2}'=\sqrt{p_{2}^{'\ 2}+m^2}[/math] [math]E_{2}^*=\sqrt{\frac{m(m+E_1)}{2}}[/math] [math]E_{1}^*=\sqrt{\frac{m(m+E_1)}{2}}[/math] [math]E_{1}'\equiv E'-E_{2}'[/math]
[math]p_{1(x)}\equiv 0[/math] [math]p_{2(x)}\equiv 0[/math] [math]p_{2(x)}'=\sqrt{p_{2}^{'\ 2}-p_{2(z)}^{'\ 2}} cos(\phi '_2)[/math] [math]p_{2(x)}^*\equiv p_{2(x)}'[/math] [math]p_{1(x)}^*\equiv-p_{2(x)}^*[/math] [math]p_{1(x)}'\equiv p_{1(x)}^*[/math]
[math]p_{1(y)}\equiv 0[/math] [math]p_{2(y)}\equiv 0[/math] [math]p_{2(y)}'=\sqrt{p_{2}^{'\ 2}-p_{2(x)}^{'\ 2}-p_{2(z)}^{'\ 2}}[/math] [math]p_{2(y)}^*\equiv p_{2(y)}'[/math] [math]p_{1(y)}^*\equiv -p_{2(y)}^*[/math] [math]p_{1(y)}'\equiv p_{2(y)}^*[/math]
[math]p_{1(z)}\equiv p_1[/math] [math]p_{2(z)}\equiv 0[/math] [math]p_{2(z)}'\equiv p_{2}'\ cos(\theta'_2)[/math] [math]p_{2(z)}^*=-\sqrt{p_{2}^{*\ 2}-p_{2(x)}^{*\ 2}-p_{2(y)}^{*\ 2}}[/math] [math]p_{1(z)}^*\equiv -p_{2(z)}^*[/math] [math]p_{1(z)}'=\sqrt{p_{1}^{'\ 2}-p_{(1(x)}^{'\ 2}-p_{1(y)}^{'\ 2}}[/math]