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Mandelstam variables

Last updated Aug 5, 2023

The Mandelstam variables are lorentz invariant kinematic variables used mostly in $2\to 2$ processes:

Definition: Mandelstam variables

The Mandelstam variables for a $2\to 2$ process are defined as $$s = (p_1 + p_2)^2 = (p_3 + p_4)^2$$ $$t = (p_1 - p_3)^2 = (p_2 - p_4)^2$$ $$u = (p_1- p_4)^2 = (p_2 - p_3)^2$$ they satisfy $$s + t + u = \sum m^2_j$$

With the different Mandelstam variables there are diagrams associated (u-, t-, and s-channel) which have the respective variable as invariant mass of the propagator.

We can compute Matrix elements in the CM-frame and then express them in a lorentz invariant way to switch to any other frame.