Version 1 (modified by 12 years ago) ( diff ) | ,
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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})\,. $%
2.
Show that the invariant mass of the jet-jet system is
and the centre-of-mass scattering angle is given by
3.
y_{3,4} | <3$%. |
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 %$E_T$% %$(10<E_T<E_{\rm max}/4)$% at the Tevatron Run II (%$p\bar p$% collisions at 1.96 TeV) and the LHC (%$pp$% collisions at 14 TeV).
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