Version 1 (modified by trac, 6 years ago) (diff)

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## Drell-Yan at the Tevatron and the LHC

#### 1.

Calculate analytically the tree-level decay rate of the W boson to leptons. The formula for the decay rate is given by

where %% denotes the matrix element describing the decay, %% is the mass of the decaying particle and %% is the two-particle phase space measure.

You may also have a look at the following Mathematica notebook.

#### 2.

The partonic cross-section near the resonance is described by the Breit-Wigner formula:

where %%, %% and %% denote the partial and total decay rates of the W (See Exercise 1.), and %% denotes the partonic center of mass energy.\ In the limit where %%, we can use the narrow width approximation for the cross-section. Use

to derive the expression of the cross-section in the narrow width approximation.

Fold the partonic cross-section with PDF's to obtain the full cross-section for Drell-Yan production at Tevatron,

w here %% and %% denote the PDF's of the %% and %% quarks inside the proton. For this exercise we choose %%

You may also have a look at the following Mathematica notebook.

#### 3.

Use Madgraph/MadEvent to generate %% at the Tevatron and the LHC. Compare the cross sections and indentify the qualititative differences.

#### 4.

Consider the rapidity asymmetry %% for %% production at the Tevatron. defined as:

Give an estimate of such asymmetry and show that it is proportional to the slope of %% evaluated at %%. Plot the rapidity distributions of the the charged leptons coming from %% decays at the Tevatron.

#### 5.

Is it possible to define an asymmetry at the LHC too?