Changes between Version 1 and Version 2 of SimpleKinematics
 Timestamp:
 04/06/12 16:33:02 (7 years ago)
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SimpleKinematics
v1 v2 3 3 == Basic kinematics in hadron hadron collisions == 4 4 5 The rapidity %$y$% and pseudorapidity %$\eta$%are defined as:5 The rapidity $y$ and pseudorapidity $\eta$ are defined as: 6 6 7 7 8 8 9 where the %$z$%direction is that of the colliding beams.9 where the $z$ direction is that of the colliding beams. 10 10 ==== 1. ==== 11 11 12 Verify that for a particle of mass %$m$%:12 Verify that for a particle of mass $m$ : 13 13 14 14 … … 16 16 ==== 2. ==== 17 17 18 Prove that %$\tanh \eta=\cos \theta$%.18 Prove that $\tanh \eta=\cos \theta$. 19 19 20 20 ==== 3. ==== … … 24 24 25 25 26 Find the distribution in %$\eta$%.26 Find the distribution in $\eta$. 27 27 28 28 ==== 4. ==== 29 29 30 Prove that rapidity equals pseudorapidity, %$\eta=y$% for a relativistic particle %$E\gg m$%.30 Prove that rapidity equals pseudorapidity, $\eta=y$ for a relativistic particle $E\gg m$. 31 31 32 32 ==== 5. ==== 33 33 34 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:34 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: 35 35 36 36 … … 38 38 ==== 6. ==== 39 39 40 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 %$Q=M$%.40 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 $Q=M$. 41 41 42 42 <img width="559" alt="lhcgridx.png" src="%ATTACHURLPATH%/lhcgridx.png" height="796" /> … … 64 64 65 65 66