Difference between revisions of "Limits based on Mandelstam Variables"

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In the center of mass frame, the momentum of the particles interacting are equal and opposite, i.e. <math>p_1=-p_2</math>.  However, the 4-momentum still retains an energy component, which as a scalar quantity, can not be countered by another particle's direction of motion.
 
In the center of mass frame, the momentum of the particles interacting are equal and opposite, i.e. <math>p_1=-p_2</math>.  However, the 4-momentum still retains an energy component, which as a scalar quantity, can not be countered by another particle's direction of motion.
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<center><math>{\mathbf P}\equiv \left(\begin{matrix} E\\ p_x \\ p_y \\ p_z \end{matrix} \right)</math></center>

Revision as of 20:17, 1 June 2017

Limits based on Mandelstam Variables

[math]\Longrightarrow \left({\mathbf P_1^*}+ {\mathbf P_2^{*}}\right)^2=\left({\mathbf P_1^{'*}}+ {\mathbf P_2^{'*}}\right)^2\equiv s[/math]


In the center of mass frame, the momentum of the particles interacting are equal and opposite, i.e. [math]p_1=-p_2[/math]. However, the 4-momentum still retains an energy component, which as a scalar quantity, can not be countered by another particle's direction of motion.


[math]{\mathbf P}\equiv \left(\begin{matrix} E\\ p_x \\ p_y \\ p_z \end{matrix} \right)[/math]
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