Changes between Version 1 and Version 2 of SimpleKinematics


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Timestamp:
Apr 6, 2012, 4:33:02 PM (13 years ago)
Author:
trac
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  • SimpleKinematics

    v1 v2  
    33== Basic kinematics in hadron hadron collisions ==
    44
    5 The rapidity %$y$% and pseudo-rapidity %$\eta$% are defined as:
     5The rapidity $y$ and pseudo-rapidity $\eta$ are defined as:
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    9 where the %$z$% direction is that of the colliding beams.
     9where the $z$ direction is that of the colliding beams.
    1010==== 1. ====
    1111
    12 Verify that for a particle of mass %$m$% :
     12Verify that for a particle of mass $m$ :
    1313
    1414
    … …  
    1616==== 2. ====
    1717
    18 Prove that %$\tanh \eta=\cos \theta$%.
     18Prove that $\tanh \eta=\cos \theta$.
    1919
    2020==== 3. ====
    … …  
    2424
    2525
    26 Find the distribution in %$\eta$%.
     26Find the distribution in $\eta$.
    2727
    2828==== 4. ====
    2929
    30 Prove that rapidity equals pseudo-rapidity, %$\eta=y$% for a relativistic particle %$E\gg m$%.
     30Prove that rapidity equals pseudo-rapidity, $\eta=y$ for a relativistic particle $E\gg m$.
    3131
    3232==== 5. ====
    3333
    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:
     34Prove 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:
    3535
    3636
    … …  
    3838==== 6. ====
    3939
    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 %$Q=M$%.
     40Consider 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 $Q=M$.
    4141
    4242<img width="559" alt="lhcgridx.png" src="%ATTACHURLPATH%/lhcgridx.png" height="796" />
    … …  
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