# Difference between revisions of "Limits based on Mandelstam Variables"

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<center><math>cos\ \theta = 1 \qquad cos\ \theta = -1</math></center> | <center><math>cos\ \theta = 1 \qquad cos\ \theta = -1</math></center> | ||

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+ | <center><math>|Rightarrow \theta_{t=0} = arccos \ 1=0^{\circ} \qquad \theta_{u=0} = arccos \ -1=180^{\circ}</math></center> |

## Revision as of 23:57, 9 June 2017

# Limits based on Mandelstam Variables

Since the Mandelstam variables are the scalar product of 4-momenta, which are invariants, they are invariants as well. The sum of these invariant variables must also be invariant as well. Find the sum of the 3 Mandelstam variables when the two particles have equal mass in the center of mass frame gives:

Since

This implies

In turn, this implies

At the condition both t and u are equal to zero, we find