== Two Jet Kinematics ==
At the LHC, partons in the incoming beams (beam energy $E_b$=7 !TeV) collide with a momementum fraction $x_{1,2}$ and produce two jets with negligible mass, transverse momentum $p_T$ and rapidities $y_{3,4}$.
==== 1. ====
Show that $x_1 = \frac{p_T}{\sqrt{s}} ( e^{y_3}+ e^{y_4}), x_2 = \frac{p_T}{\sqrt{s}} ( e^{-y_3}+ e^{-y_4})\,. $
==== 2. ====
Show that the invariant mass of the jet-jet system is
and the centre-of-mass scattering angle is given by
==== 3. ====
Discuss the regions of $x_{1,2}, M_{JJ}$ and $\theta^*$ that can be studied at the LHC with a jet trigger of $p_T > 35 $ GeV and $||y_{3,4}||<3$.
==== 4. ====
Use MadGraph/MadEvent to obtain the relative contribution of $gg,qg+\bar q g,qq+q\bar q$ initial states to the jet $E_T$ distribution as function of the $E_T$ $(10