Difference between revisions of "Final Lab Frame Moller Electron 4-momentum components in XZ Plane"
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Figure 3: Definition of Moller electron variables in the Lab Frame in the x-z plane.
Using
should always be positive with respect to the total momentum since cosine is an even function.
This is effectively a ratio of momentum in the z direction versus total momentum.
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− | <center><math>\ | + | <center><math>\underline{\textbf{Navigation}}</math> |
[[Limits_based_on_Mandelstam_Variables|<math>\vartriangleleft </math>]] | [[Limits_based_on_Mandelstam_Variables|<math>\vartriangleleft </math>]] | ||
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+ | Since, | ||
+ | <center><math>\frac{p^'_{2(z)}}{p^'_{2}}=cos(\theta '_2)</math></center> | ||
+ | |||
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+ | <center><math>\Longrightarrow p^'_{2(z)}</math> should always be positive with respect to the total momentum since cosine is an even function.</center> | ||
+ | |||
+ | |||
+ | <center><math>\cos -x=\cos x</math></center> | ||
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+ | <center>This is effectively a ratio of momentum in the z direction versus total momentum. </center> | ||
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{| class="wikitable" align="center" | {| class="wikitable" align="center" | ||
− | | style="background: red" | <math>0^\circ \le \theta '_2 \le | + | | style="background: red" | <math>0^\circ \le \theta '_2 \le 90^\circ \equiv 0 \le \theta '_2 \le \pi \ Radians</math> |
|} | |} | ||
− | + | At <math>\theta=0^{\circ} \quad \cos{0}=1 \Rightarrow p=p_z</math> and all motion is in the z direction. | |
− | + | ||
+ | |||
+ | At <math>\theta=90^{\circ} \quad \cos{90}=0 \Rightarrow p=\sqrt{p_x^2+p_y^2}</math> The motion is in the x-y plane. | ||
+ | |||
+ | |||
+ | |||
+ | ---- | ||
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+ | |||
+ | |||
+ | <center><math>\underline{\textbf{Navigation}}</math> | ||
+ | [[Limits_based_on_Mandelstam_Variables|<math>\vartriangleleft </math>]] | ||
+ | [[VanWasshenova_Thesis#Final_Lab_Frame_Moller_Electron_4-momentum_components|<math>\triangle </math>]] | ||
+ | [[Special_Case_of_Equal_Mass_Particles|<math>\vartriangleright </math>]] | ||
− | + | </center> |
Latest revision as of 18:54, 15 May 2018
Final Lab Frame Moller Electron 4-momentum components in XZ Plane
Since,
Checking on the sign resulting from the cosine function, we are limited to:
At
and all motion is in the z direction.
At The motion is in the x-y plane.