wiki:2Jets

Version 1 (modified by trac, 7 years ago) (diff)

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Two Jet Kinematics

At the LHC, partons in the incoming beams (beam energy %$E_b$%=7 !TeV) collide with a momementum fraction %$x_{1,2}$% and produce two jets with negligible mass, transverse momentum %$p_T$% and rapidities %$y_{3,4}$%.

1.

Show that %$x_1 = \frac{p_T}{\sqrt{s}} ( e^{y_3}+ e^{y_4}), x_2 = \frac{p_T}{\sqrt{s}} ( e^{-y_3}+ e^{-y_4})\,. $%

2.

Show that the invariant mass of the jet-jet system is

and the centre-of-mass scattering angle is given by

3.

Discuss the regions of %$x_{1,2}, M_{JJ}$% and %$\theta^*$% that can be studied at the LHC with a jet trigger of %

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The command:

'/usr/bin/pdflatex -interaction=nonstopmode 471817320cd78786a1b6825171c4bc3d9f15bd35.tex'
failed with the following output:
"This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)\n restricted \\write18 enabled.\nentering extended mode\n(./471817320cd78786a1b6825171c4bc3d9f15bd35.tex\nLaTeX2e <2011/06/27>\nBabel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo\naded.\n(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls\nDocument Class: article 2007/10/19 v1.4h Standard LaTeX document class\n(/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo))\n(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty\n(/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def\n(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu)\n(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu)\n(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu)))\n\n! LaTeX Error: File `cmap.sty' not found.\n\nType X to quit or <RETURN> to proceed,\nor enter new name. (Default extension: sty)\n\nEnter file name: \n! Emergency stop.\n<read *> \n         \nl.4 \\usepackage\n               {type1ec}^^M\n!  ==> Fatal error occurred, no output PDF file produced!\nTranscript written on 471817320cd78786a1b6825171c4bc3d9f15bd35.log.\n"

% GeV and %
TracMath macro processor has detected an error. Please fix the problem before continuing.


The command:

'/usr/bin/pdflatex -interaction=nonstopmode 92206bf2723e398b91bf5829eaf3a6c0655076a2.tex'
failed with the following output:
"This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)\n restricted \\write18 enabled.\nentering extended mode\n(./92206bf2723e398b91bf5829eaf3a6c0655076a2.tex\nLaTeX2e <2011/06/27>\nBabel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo\naded.\n(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls\nDocument Class: article 2007/10/19 v1.4h Standard LaTeX document class\n(/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo))\n(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty\n(/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def\n(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu)\n(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu)\n(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu)))\n\n! LaTeX Error: File `cmap.sty' not found.\n\nType X to quit or <RETURN> to proceed,\nor enter new name. (Default extension: sty)\n\nEnter file name: \n! Emergency stop.\n<read *> \n         \nl.4 \\usepackage\n               {type1ec}^^M\n!  ==> Fatal error occurred, no output PDF file produced!\nTranscript written on 92206bf2723e398b91bf5829eaf3a6c0655076a2.log.\n"

%.

4.

Use MadGraph/MadEvent to obtain the relative contribution of %$gg,qg+\bar q g,qq+q\bar q$% initial states to the jet %$E_T$% distribution as function of the %$E_T$% %

TracMath macro processor has detected an error. Please fix the problem before continuing.


The command:

'/usr/bin/pdflatex -interaction=nonstopmode cbd31dea0a3c6194a2e9fdb1be4381e68290ad9a.tex'
failed with the following output:
"This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)\n restricted \\write18 enabled.\nentering extended mode\n(./cbd31dea0a3c6194a2e9fdb1be4381e68290ad9a.tex\nLaTeX2e <2011/06/27>\nBabel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo\naded.\n(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls\nDocument Class: article 2007/10/19 v1.4h Standard LaTeX document class\n(/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo))\n(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty\n(/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def\n(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu)\n(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu)\n(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu)))\n\n! LaTeX Error: File `cmap.sty' not found.\n\nType X to quit or <RETURN> to proceed,\nor enter new name. (Default extension: sty)\n\nEnter file name: \n! Emergency stop.\n<read *> \n         \nl.4 \\usepackage\n               {type1ec}^^M\n!  ==> Fatal error occurred, no output PDF file produced!\nTranscript written on cbd31dea0a3c6194a2e9fdb1be4381e68290ad9a.log.\n"

% at the Tevatron Run II (%$p\bar p$% collisions at 1.96 TeV) and the LHC (%$pp$% collisions at 14 TeV).

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