Changes between Initial Version and Version 1 of SimpleKinematics

Timestamp:

Mar 20, 2012, 4:17:01 PM (13 years ago)

Author:

trac

Comment:

--

SimpleKinematics

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+== Basic kinematics in hadron hadron collisions ==
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+The rapidity %$y$% and pseudo-rapidity %$\eta$% are defined as:
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+where the %$z$% direction is that of the colliding beams.
+==== 1. ====
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+Verify that for a particle of mass %$m$% :
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+==== 2. ====
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+Prove that %$\tanh \eta=\cos \theta$%.
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+==== 3. ====
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+Consider a set of particles produced uniformly in longitudinal phase space
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+Find the distribution in %$\eta$%.
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+==== 4. ====
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+Prove that rapidity equals pseudo-rapidity, %$\eta=y$% for a relativistic particle %$E\gg m$%.
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+==== 5. ====
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+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:
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+==== 6. ====
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+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 %$Q=M$%.
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+<img width="559" alt="lhcgridx.png" src="%ATTACHURLPATH%/lhcgridx.png" height="796" />
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+Fig.1
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