# Changes between Version 1 and Version 2 of SimpleKinematics

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Timestamp:
04/06/12 16:33:02 (8 years ago)
Comment:

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 v1 == Basic kinematics in hadron hadron collisions == The rapidity %$y$% and pseudo-rapidity %$\eta$% are defined as: The rapidity $y$ and pseudo-rapidity $\eta$ are defined as: where the %$z$% direction is that of the colliding beams. where the $z$ direction is that of the colliding beams. ==== 1. ==== Verify that for a particle of mass %$m$% : Verify that for a particle of mass $m$ : ==== 2. ==== Prove that %$\tanh \eta=\cos \theta$%. Prove that $\tanh \eta=\cos \theta$. ==== 3. ==== Find the distribution in %$\eta$%. Find the distribution in $\eta$. ==== 4. ==== Prove that rapidity equals pseudo-rapidity, %$\eta=y$% for a relativistic particle %$E\gg m$%. Prove that rapidity equals pseudo-rapidity, $\eta=y$ for a relativistic particle $E\gg m$. ==== 5. ==== Prove that for Lorentz transformation (boost) in the beam (%$z$%) directions, the rapidity %$y$% of every particle is shifted by a constant %$y_0$%, related to the boost velocity. Find the relation between %$\beta$% and %$y_0$% for a generic boost: Prove that for Lorentz transformation (boost) in the beam ($z$) directions, the rapidity $y$ of every particle is shifted by a constant $y_0$, related to the boost velocity. Find the relation between $\beta$ and $y_0$ for a generic boost: ==== 6. ==== Consider a generic particle %$X$% of mass %$M$% (such as a Z boson or a Higgs) produced on shell at the LHC , with zero transverse momentum, %$pp \to X$%. Find the relevant values of %$x_1,x_2$% of the initial partons that can be accessed by producing such a particle. Compare your results with that of Fig.1, considering the scale %$Q=M$%. Consider a generic particle $X$ of mass $M$ (such as a Z boson or a Higgs) produced on shell at the LHC , with zero transverse momentum, $pp \to X$. Find the relevant values of $x_1,x_2$ of the initial partons that can be accessed by producing such a particle. Compare your results with that of Fig.1, considering the scale $Q=M$.