Version 2 (modified by trac, 8 years ago) (diff)

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## Basic kinematics in hadron hadron collisions

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

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