Version 1 (modified by trac, 7 years ago) (diff)

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The rapidity %% and pseudo-rapidity %% are defined as:

where the %% direction is that of the colliding beams.

#### 1.

Verify that for a particle of mass %% :

Prove that %%.

#### 3.

Consider a set of particles produced uniformly in longitudinal phase space

Find the distribution in %%.

#### 4.

Prove that rapidity equals pseudo-rapidity, %% for a relativistic particle %%.

#### 5.

Prove that for Lorentz transformation (boost) in the beam (%%) directions, the rapidity %% of every particle is shifted by a constant %%, related to the boost velocity. Find the relation between %% and %% for a generic boost:

#### 6.

Consider a generic particle %% of mass %% (such as a Z boson or a Higgs) produced on shell at the LHC , with zero transverse momentum, %%. Find the relevant values of %% of the initial partons that can be accessed by producing such a particle. Compare your results with that of Fig.1, considering the scale %%.

<img width="559" alt="lhcgridx.png" src="%ATTACHURLPATH%/lhcgridx.png" height="796" />

Fig.1