U-Channel

$\underline{\textbf{Navigation}}$

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u-Channel

The u quantity is does not have a clear cut interpretation like the s and t channels

$u \equiv \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_1^{'*}}\right)^2$

$u \equiv\left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2$

$u \equiv \mathbf P_1^{*2}-2 \mathbf P_1^* \mathbf P_2^{'*}+ \mathbf P_2^{'*2}$

$u \equiv 2m_1^2-2E_1^*E_2^{'*}+2 \vec p \ _1^* \vec p \ _2^{'*}$

In the center of mass frame of reference,

$E^* \equiv E_1^*=E_1^{'*} = E_2^*=E_2^{'*} = E_1^*=E_2^*$

and

$|p^*| \equiv | \vec p \ _1^*|=| \vec p \ _1^{'*}| =| \vec p \ _2^*|=| \vec p \ _2^{'*}|$

and $\theta_1=-\theta_2$ is the angle between $\vec p \ _1^*$ and $\vec p \ _2^{'*}$

$u \equiv 2m_1^*-2E_1^{*2}-2 |p |^{*2}cos\ \theta$

Using the relativistic term for Energy

$E^2=\vec p \ ^2+m^2$

$u \equiv -2 p \ ^{*2}(1+cos\ \theta)$

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$\underline{\textbf{Navigation}}$

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