[math]\displaystyle{ \underline{\textbf{Navigation}} }[/math]
[math]\displaystyle{ \vartriangleleft }[/math]
[math]\displaystyle{ \triangle }[/math]
[math]\displaystyle{ \vartriangleright }[/math]
t Channel
The t quantity is known as the square of the 4-momentum transfer
[math]\displaystyle{ t \equiv \left({\mathbf P_1^*}- {\mathbf P_1^{'*}}\right)^2=\left({\mathbf P_2^{*}}- {\mathbf P_2^{'*}}\right)^2 }[/math]
[math]\displaystyle{ t \equiv \left({\mathbf P_1^*}- {\mathbf P_1^{'*}}\right)^2 }[/math]
[math]\displaystyle{ t \equiv \mathbf P_1^{*2}-2 \mathbf P_1^* \mathbf P_1^{'*}+ \mathbf P_1^{'*2} }[/math]
[math]\displaystyle{ t \equiv 2m_1^2-2E_1^*E_1^{'*}+2 \vec p \ _1^* \vec p \ _1^{'*} }[/math]
In the center of mass frame of reference,
[math]\displaystyle{ E^* \equiv E_1^*=E_1^{'*} = E_2^*=E_2^{'*} = E_1^*=E_2^* }[/math]
and
[math]\displaystyle{ |p^*| \equiv | \vec p \ _1^*|=| \vec p \ _1^{'*}| =| \vec p \ _2^*|=| \vec p \ _2^{'*}| }[/math]
and [math]\displaystyle{ \theta_1 }[/math] is the angle between [math]\displaystyle{ \vec p \ _1^* }[/math] and [math]\displaystyle{ \vec p \ _1^{'*} }[/math]
[math]\displaystyle{ t \equiv 2m_1^*-2E_1^{*2}+2 |p |^{*2}cos\ \theta }[/math]
Using the relativistic term for Energy
[math]\displaystyle{ E^2=\vec p \ ^2+m^2 }[/math]
[math]\displaystyle{ t \equiv -2 p \ ^{*2}(1-cos\ \theta) }[/math]
[math]\displaystyle{ \underline{\textbf{Navigation}} }[/math]
[math]\displaystyle{ \vartriangleleft }[/math]
[math]\displaystyle{ \triangle }[/math]
[math]\displaystyle{ \vartriangleright }[/math]
