[math]\displaystyle{ \underline{\textbf{Navigation}} }[/math]
[math]\displaystyle{ \vartriangleleft }[/math]
[math]\displaystyle{ \triangle }[/math]
[math]\displaystyle{ \vartriangleright }[/math]
u-Channel
The u quantity is does not have a clear cut interpretation like the s and t channels
[math]\displaystyle{ u \equiv \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_1^{'*}}\right)^2 }[/math]
[math]\displaystyle{ u \equiv\left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2 }[/math]
[math]\displaystyle{ u \equiv \mathbf P_1^{*2}-2 \mathbf P_1^* \mathbf P_2^{'*}+ \mathbf P_2^{'*2} }[/math]
[math]\displaystyle{ u \equiv 2m_1^2-2E_1^*E_2^{'*}+2 \vec p \ _1^* \vec p \ _2^{'*} }[/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=-\theta_2 }[/math] is the angle between [math]\displaystyle{ \vec p \ _1^* }[/math] and [math]\displaystyle{ \vec p \ _2^{'*} }[/math]
[math]\displaystyle{ u \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{ u \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]
