# Changes between Version 1 and Version 2 of WAsymm

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Timestamp:
04/06/12 16:33:02 (7 years ago)
Comment:

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 v1 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. 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. 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]. 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 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 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 %$u(x)=6(1-x)^2,\qquad d(x)=3(1-x)^2.$% 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 $u(x)=6(1-x)^2,\qquad d(x)=3(1-x)^2.$ 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]. ==== 3. ==== 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. 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. ==== 4. ==== Consider the rapidity asymmetry %$A_W(y)$% for %$W^\pm$% production at the Tevatron. defined as: Consider the rapidity asymmetry $A_W(y)$ for $W^\pm$ production at the Tevatron. defined as: 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. 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. ==== 5. ====