Changes between Initial Version and Version 1 of WAsymm

Timestamp:

Mar 20, 2012, 4:16:54 PM (13 years ago)

Author:

trac

Comment:

--

WAsymm

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+== Drell-Yan at the Tevatron and the LHC ==
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+==== 1. ====
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+Calculate analytically the tree-level decay rate of the W boson to leptons. The formula for the decay rate is given by
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+where %$\begin{cal}M\end{cal}$% denotes the matrix element describing the decay, %$m$% is the mass of the decaying particle and %$\rm{d}\Phi_2$% is the two-particle phase space measure.
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+You may also have a look at the following Mathematica [http://cp3wks05.fynu.ucl.ac.be/twiki/bin/viewfile/Physics/WAsymm?rev=1;filename=WDecay.nb notebook].
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+==== 2. ====
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+The partonic cross-section near the resonance is described by the Breit-Wigner formula:
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+where %$\Gamma_{\ell\nu}$%, %$\Gamma_{u\bar d}$% and %$\Gamma$% denote the partial and total decay rates of the W (See Exercise 1.), and %$\hat s$% denotes the partonic center of mass energy.\ In the limit where %$m_W\gg \Gamma$%, we can use the narrow width approximation for the cross-section. Use
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+to derive the expression of the cross-section in the narrow width approximation.
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+Fold the partonic cross-section with PDF's to obtain the full cross-section for Drell-Yan production at Tevatron,
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+w here %$u(x)$% and %$d(x)$% denote the PDF's of the %$u$% and %$d$% quarks inside the proton. For this exercise we choose %$ u(x)=6(1-x)^2,\qquad d(x)=3(1-x)^2. $%
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+You may also have a look at the following Mathematica [http://cp3wks05.fynu.ucl.ac.be/twiki/bin/viewfile/Physics/WAsymm?rev=1;filename=DYNarrowWidth.nb notebook].
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+==== 3. ====
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+Use Madgraph/MadEvent to generate %$pp \to W^\pm \to e^\pm \nu_e$% at the Tevatron and the LHC. Compare the cross sections and indentify the qualititative differences.
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+==== 4. ====
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+Consider the rapidity asymmetry %$A_W(y)$% for %$W^\pm$% production at the Tevatron. defined as:
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+Give an estimate of such asymmetry and show that it is proportional to the slope of %$d(x)/u(x)$% evaluated at %$x=M_W/\sqrt{s}$%. Plot the rapidity distributions of the the charged leptons coming from %$W^\pm$% decays at the Tevatron.
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+==== 5. ====
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+Is it possible to define an asymmetry at the LHC too?
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