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t Channel
The t quantity is known as the square of the 4-momentum transfer
t≡(P∗1−P′∗1)2=(P∗2+P′∗2)2
t≡(P∗1−P′∗1)2
t≡P∗21−2P∗1P′∗1+P′∗21
t≡2m21−2E∗1E′∗1+2→p ∗1→p ′∗1
In the center of mass frame of reference,
E∗≡E∗1=E′∗1=E∗2=E′∗2=E∗1=E∗2
and
|p∗|≡|→p ∗1|=|→p ′∗1|=|→p ∗2|=|→p ′∗2|
and θ1 is the angle between →p ∗1and→p ′∗1
t≡2m∗1−2E∗21+2|p|∗2cos θ
Using the relativistic term for Energy
E2=→p 2+m2
t≡−2p ∗21(1−cos θ)
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