Changes between Version 1 and Version 2 of WAsymm
 Timestamp:
 04/06/12 16:33:02 (7 years ago)
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WAsymm
v1 v2 9 9 10 10 11 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 twoparticle phase space measure.11 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 twoparticle phase space measure. 12 12 13 13 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]. … … 19 19 20 20 21 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 crosssection. Use21 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 crosssection. Use 22 22 23 23 … … 29 29 30 30 31 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(1x)^2,\qquad d(x)=3(1x)^2. $%31 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(1x)^2,\qquad d(x)=3(1x)^2. $ 32 32 33 33 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]. … … 35 35 ==== 3. ==== 36 36 37 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.37 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. 38 38 39 39 ==== 4. ==== 40 40 41 Consider the rapidity asymmetry %$A_W(y)$% for %$W^\pm$%production at the Tevatron. defined as:41 Consider the rapidity asymmetry $A_W(y)$ for $W^\pm$ production at the Tevatron. defined as: 42 42 43 43 44 44 45 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.45 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. 46 46 47 47 ==== 5. ==== … … 74 74 75 75 76