https://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&feed=atom&action=historyChapter I - Revision history2024-03-28T09:39:44ZRevision history for this page on the wikiMediaWiki 1.35.3https://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=4687&oldid=prevStanb@nikhef.nl at 13:17, 19 July 20052005-07-19T13:17:54Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><H1>Chapter&nbsp;1&nbsp;&nbsp;The Top Quark</H1><!--SEC END --></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><H1>Chapter&nbsp;1&nbsp;&nbsp;The Top Quark</H1><!--SEC END --></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>During the past thirty years, physicists have been building comprehensive and accurate models to describe the universe at sub-nuclear level. The result is an elegant set of theories collectively known as the Standard Model (usually abbreviated as SM). These theories provide powerful tools; their predictive power has been confirmed in many experiments worldwide.<BR></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>During the past thirty years<ins class="diffchange diffchange-inline">'''I actually think its not only the last 30 years, but the last century'''</ins>, physicists have been building comprehensive and accurate models to describe the universe at sub-nuclear level. The result is an elegant set of theories collectively known as the Standard Model (usually abbreviated as SM). These theories provide powerful tools; their predictive power has been confirmed in many experiments worldwide.<BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The inspiring principle of the Standard Model is <EM>gauge symmetry</EM>. This principle states that the description of all physical phenomena does not vary if the Lagrangian equations describing the phenomena are subjected to a special set of local transformations --- the <EM>local gauge transformations</EM>. In analogy with classical mechanics, local gauge invariance in the interaction Lagrangian is associated with conserved currents and boson fields, which act as the medium of the interaction. A great success for gauge theories (and thus for the Standard Model) was the prediction of the properties of intermediate vector bosons <I>W</I><FONT SIZE=2><SUP>&plusmn;</SUP></FONT> and <I>Z</I><FONT SIZE=2><SUP>0</SUP></FONT>, which mediate the weak interaction, and which were discovered at CERN in 1983 [2, 3, 4, 5].<BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The inspiring principle of the Standard Model is <EM>gauge symmetry</EM>. This principle states that the description of all physical phenomena does not vary if the Lagrangian equations describing the phenomena are subjected to a special set of local transformations --- the <EM>local gauge transformations</EM>. In analogy with classical mechanics, local gauge invariance in the interaction Lagrangian is associated with conserved currents and boson fields, which act as the medium of the interaction. A great success for gauge theories (and thus for the Standard Model) was the prediction of the properties of intermediate vector bosons <I>W</I><FONT SIZE=2><SUP>&plusmn;</SUP></FONT> and <I>Z</I><FONT SIZE=2><SUP>0</SUP></FONT>, which mediate the weak interaction, and which were discovered at CERN in 1983 [2, 3, 4, 5].<BR></div></td></tr>
</table>Stanb@nikhef.nlhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=413&oldid=prevBarison at 10:18, 19 July 20052005-07-19T10:18:41Z<p></p>
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</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=410&oldid=prevBarison at 10:15, 19 July 20052005-07-19T10:15:42Z<p></p>
<a href="https://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=410&oldid=409">Show changes</a>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=409&oldid=prevBarison at 18:26, 18 July 20052005-07-18T18:26:51Z<p></p>
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<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:Sign-wt.gif]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:Sign-wt.gif ]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.7: Experimental signature of single top production in the associated production channel.</DIV><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.7: Experimental signature of single top production in the associated production channel.</DIV><BR></div></td></tr>
</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=408&oldid=prevBarison at 18:01, 18 July 20052005-07-18T18:01:50Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></TR></TABLE></DIV> where <FONT FACE=symbol>Da</FONT> contains the leading logarithmic contributions from the light fermion loops, <FONT FACE=symbol>Dr</FONT> contains the <I>m</I><FONT SIZE=2><SUB><I>t</I></SUB><SUP>2</SUP></FONT> dependence from top/bottom loops and (&Delta; <I>r</I>)<FONT SIZE=2><I><SUB>rem</SUB></I></FONT> contains the non-leading terms where <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> plays a role [7]. Thus, a precise measurement of <I>M<FONT SIZE=2><SUB>W</SUB></FONT></I> and <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> --- the other physical parameters <FONT FACE=symbol>a</FONT> and <I>M<FONT SIZE=2><SUB>Z</SUB></FONT></I> have a smaller impact --- can give us, through the evaluation of &Delta; <I>r</I>, an estimate on <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I>, as shown in Figure&nbsp;1.1.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></TR></TABLE></DIV> where <FONT FACE=symbol>Da</FONT> contains the leading logarithmic contributions from the light fermion loops, <FONT FACE=symbol>Dr</FONT> contains the <I>m</I><FONT SIZE=2><SUB><I>t</I></SUB><SUP>2</SUP></FONT> dependence from top/bottom loops and (&Delta; <I>r</I>)<FONT SIZE=2><I><SUB>rem</SUB></I></FONT> contains the non-leading terms where <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> plays a role [7]. Thus, a precise measurement of <I>M<FONT SIZE=2><SUB>W</SUB></FONT></I> and <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> --- the other physical parameters <FONT FACE=symbol>a</FONT> and <I>M<FONT SIZE=2><SUB>Z</SUB></FONT></I> have a smaller impact --- can give us, through the evaluation of &Delta; <I>r</I>, an estimate on <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I>, as shown in Figure&nbsp;1.1.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:Tmass_higgs.gif ]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:Tmass_higgs.gif]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.1: &chi;<FONT SIZE=2><SUP>2</SUP></FONT>-likelihood for the mass of the Higgs boson, depending on the value of the top quark mass. The most probable value corresponds to the minimum &chi;<FONT SIZE=2><SUP>2</SUP></FONT>. The graph shows the shift in <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> for the new Tevatron analyses (dotted line) compared to the previous Tevatron measurements (full line). The band around the full line shows the uncertainties in the theoretical model. Figure taken from [6].</DIV><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.1: &chi;<FONT SIZE=2><SUP>2</SUP></FONT>-likelihood for the mass of the Higgs boson, depending on the value of the top quark mass. The most probable value corresponds to the minimum &chi;<FONT SIZE=2><SUP>2</SUP></FONT>. The graph shows the shift in <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> for the new Tevatron analyses (dotted line) compared to the previous Tevatron measurements (full line). The band around the full line shows the uncertainties in the theoretical model. Figure taken from [6].</DIV><BR></div></td></tr>
</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=406&oldid=prevBarison at 17:59, 18 July 20052005-07-18T17:59:42Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></TR></TABLE></DIV> where <FONT FACE=symbol>Da</FONT> contains the leading logarithmic contributions from the light fermion loops, <FONT FACE=symbol>Dr</FONT> contains the <I>m</I><FONT SIZE=2><SUB><I>t</I></SUB><SUP>2</SUP></FONT> dependence from top/bottom loops and (&Delta; <I>r</I>)<FONT SIZE=2><I><SUB>rem</SUB></I></FONT> contains the non-leading terms where <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> plays a role [7]. Thus, a precise measurement of <I>M<FONT SIZE=2><SUB>W</SUB></FONT></I> and <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> --- the other physical parameters <FONT FACE=symbol>a</FONT> and <I>M<FONT SIZE=2><SUB>Z</SUB></FONT></I> have a smaller impact --- can give us, through the evaluation of &Delta; <I>r</I>, an estimate on <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I>, as shown in Figure&nbsp;1.1.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></TR></TABLE></DIV> where <FONT FACE=symbol>Da</FONT> contains the leading logarithmic contributions from the light fermion loops, <FONT FACE=symbol>Dr</FONT> contains the <I>m</I><FONT SIZE=2><SUB><I>t</I></SUB><SUP>2</SUP></FONT> dependence from top/bottom loops and (&Delta; <I>r</I>)<FONT SIZE=2><I><SUB>rem</SUB></I></FONT> contains the non-leading terms where <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> plays a role [7]. Thus, a precise measurement of <I>M<FONT SIZE=2><SUB>W</SUB></FONT></I> and <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> --- the other physical parameters <FONT FACE=symbol>a</FONT> and <I>M<FONT SIZE=2><SUB>Z</SUB></FONT></I> have a smaller impact --- can give us, through the evaluation of &Delta; <I>r</I>, an estimate on <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I>, as shown in Figure&nbsp;1.1.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center><del class="diffchange diffchange-inline"><!--</del>[[Image:Tmass_higgs.gif]]<del class="diffchange diffchange-inline">--></del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:Tmass_higgs.gif ]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.1: &chi;<FONT SIZE=2><SUP>2</SUP></FONT>-likelihood for the mass of the Higgs boson, depending on the value of the top quark mass. The most probable value corresponds to the minimum &chi;<FONT SIZE=2><SUP>2</SUP></FONT>. The graph shows the shift in <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> for the new Tevatron analyses (dotted line) compared to the previous Tevatron measurements (full line). The band around the full line shows the uncertainties in the theoretical model. Figure taken from [6].</DIV><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.1: &chi;<FONT SIZE=2><SUP>2</SUP></FONT>-likelihood for the mass of the Higgs boson, depending on the value of the top quark mass. The most probable value corresponds to the minimum &chi;<FONT SIZE=2><SUP>2</SUP></FONT>. The graph shows the shift in <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> for the new Tevatron analyses (dotted line) compared to the previous Tevatron measurements (full line). The band around the full line shows the uncertainties in the theoretical model. Figure taken from [6].</DIV><BR></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66" >Line 66:</td>
<td colspan="2" class="diff-lineno">Line 66:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Among the Tevatron studies, the most interesting concerns the mass of the top quark: the combined measurements [9] of the <B>CDF</B> and <B>D&Oslash;</B> experiments at the Tevatron at Run&nbsp;I resulted in a top mass of 178.0&plusmn;4.3&nbsp;GeV (see Figure&nbsp;1.2). Such a large mass is quite extraordinary in the the quark hierarchy: the top quark is roughly 35 times more massive than the b quark.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Among the Tevatron studies, the most interesting concerns the mass of the top quark: the combined measurements [9] of the <B>CDF</B> and <B>D&Oslash;</B> experiments at the Tevatron at Run&nbsp;I resulted in a top mass of 178.0&plusmn;4.3&nbsp;GeV (see Figure&nbsp;1.2). Such a large mass is quite extraordinary in the the quark hierarchy: the top quark is roughly 35 times more massive than the b quark.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:World_avg.gif]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:World_avg.gif ]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.2: Combined measurement of the top quark mass at the Tevatron during Run&nbsp;I. The Run&nbsp;I average includes measurements from lepton-plus-jets and di-leptonic decay channels for both CDF and D&Oslash;, plus the CDF jets-only channel. Figure taken from&nbsp;[9].</DIV><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.2: Combined measurement of the top quark mass at the Tevatron during Run&nbsp;I. The Run&nbsp;I average includes measurements from lepton-plus-jets and di-leptonic decay channels for both CDF and D&Oslash;, plus the CDF jets-only channel. Figure taken from&nbsp;[9].</DIV><BR></div></td></tr>
</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=405&oldid=prevBarison at 17:58, 18 July 20052005-07-18T17:58:41Z<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:58, 18 July 2005</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l28" >Line 28:</td>
<td colspan="2" class="diff-lineno">Line 28:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></TR></TABLE></DIV> where <FONT FACE=symbol>Da</FONT> contains the leading logarithmic contributions from the light fermion loops, <FONT FACE=symbol>Dr</FONT> contains the <I>m</I><FONT SIZE=2><SUB><I>t</I></SUB><SUP>2</SUP></FONT> dependence from top/bottom loops and (&Delta; <I>r</I>)<FONT SIZE=2><I><SUB>rem</SUB></I></FONT> contains the non-leading terms where <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> plays a role [7]. Thus, a precise measurement of <I>M<FONT SIZE=2><SUB>W</SUB></FONT></I> and <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> --- the other physical parameters <FONT FACE=symbol>a</FONT> and <I>M<FONT SIZE=2><SUB>Z</SUB></FONT></I> have a smaller impact --- can give us, through the evaluation of &Delta; <I>r</I>, an estimate on <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I>, as shown in Figure&nbsp;1.1.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></TR></TABLE></DIV> where <FONT FACE=symbol>Da</FONT> contains the leading logarithmic contributions from the light fermion loops, <FONT FACE=symbol>Dr</FONT> contains the <I>m</I><FONT SIZE=2><SUB><I>t</I></SUB><SUP>2</SUP></FONT> dependence from top/bottom loops and (&Delta; <I>r</I>)<FONT SIZE=2><I><SUB>rem</SUB></I></FONT> contains the non-leading terms where <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> plays a role [7]. Thus, a precise measurement of <I>M<FONT SIZE=2><SUB>W</SUB></FONT></I> and <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> --- the other physical parameters <FONT FACE=symbol>a</FONT> and <I>M<FONT SIZE=2><SUB>Z</SUB></FONT></I> have a smaller impact --- can give us, through the evaluation of &Delta; <I>r</I>, an estimate on <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I>, as shown in Figure&nbsp;1.1.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center>[[Image:Tmass_higgs.gif]]</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><BLOCKQUOTE><DIV ALIGN=center><HR WIDTH="80%" SIZE=2></DIV><DIV ALIGN=center><ins class="diffchange diffchange-inline"><!--</ins>[[Image:Tmass_higgs.gif]]<ins class="diffchange diffchange-inline">--></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><BR></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.1: &chi;<FONT SIZE=2><SUP>2</SUP></FONT>-likelihood for the mass of the Higgs boson, depending on the value of the top quark mass. The most probable value corresponds to the minimum &chi;<FONT SIZE=2><SUP>2</SUP></FONT>. The graph shows the shift in <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> for the new Tevatron analyses (dotted line) compared to the previous Tevatron measurements (full line). The band around the full line shows the uncertainties in the theoretical model. Figure taken from [6].</DIV><BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><DIV ALIGN=center>Figure 1.1: &chi;<FONT SIZE=2><SUP>2</SUP></FONT>-likelihood for the mass of the Higgs boson, depending on the value of the top quark mass. The most probable value corresponds to the minimum &chi;<FONT SIZE=2><SUP>2</SUP></FONT>. The graph shows the shift in <I>M<FONT SIZE=2><SUB>H</SUB></FONT></I> for the new Tevatron analyses (dotted line) compared to the previous Tevatron measurements (full line). The band around the full line shows the uncertainties in the theoretical model. Figure taken from [6].</DIV><BR></div></td></tr>
</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=404&oldid=prevBarison at 17:47, 18 July 20052005-07-18T17:47:03Z<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:47, 18 July 2005</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l101" >Line 101:</td>
<td colspan="2" class="diff-lineno">Line 101:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\sigma(s,m_t) =</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\sigma(s,m_t) =</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\sum_ \int_0^1 dx_1 \int_0^1 dx_2 \,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\sum_<ins class="diffchange diffchange-inline">{i,j} </ins>\int_0^1 dx_1 \int_0^1 dx_2 \,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f_i(x_i,\mu^2_f) \, f_j(x_j,\mu^2_f) \;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f_i(x_i,\mu^2_f) \, f_j(x_j,\mu^2_f) \;</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\<del class="diffchange diffchange-inline">h</del>(\<del class="diffchange diffchange-inline">h</del>,m_t,\alpha_s(\mu^2_r))</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\<ins class="diffchange diffchange-inline">hat\sigma_{ij}</ins>(\<ins class="diffchange diffchange-inline">hat{s}</ins>,m_t,\alpha_s(\mu^2_r))</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This equation descends from the following assumption: the QCD scattering process can be expressed by independent --- <EM>factorised</EM> --- terms. Consider the scattering of two protons: they are complex objects, made of several components called <EM>partons</EM>. The fractional momentum <I>x</I> carried by the partons inside the protons is described by probability density called <EM>Parton Distribution Functions</EM> --- <B>PDF</B>, indicated by <I>f</I>(<I>x</I>,&micro;<FONT SIZE=2><SUB><I>f</I></SUB><SUP>2</SUP></FONT>) in the equation. However, when we consider the scattering process, we assume that the scattering partons are independent from the protons that contained them; then, we have <EM>factorised</EM> the matrix element of the scattering of the two partons from the PDFs that contained the partons. By doing so, we choose an energy scale &micro;<FONT SIZE=2><I><SUB>f</SUB></I></FONT>, the <EM>factorisation scale</EM> that separates the description of the parton as a statistic variable from the description of a pointlike particle in the scattering process. In the factorization scheme, the partonic cross section for <I>tt</I> production <FONT FACE=symbol>s</FONT> depends only on the square of the partonic center of mass energy <I>s</I>=<I>x<FONT SIZE=2><SUB>i</SUB></FONT>x<FONT SIZE=2><SUB>j</SUB></FONT>s</I>, the top mass <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> and the running strong coupling constant <FONT FACE=symbol>a</FONT><FONT SIZE=2><I><SUB>s</SUB></I></FONT>(&micro;<FONT SIZE=2><SUB><I>r</I></SUB><SUP>2</SUP></FONT>). The coupling constant is evaluated at the <EM>renormalisation scale</EM> &micro;<FONT SIZE=2><I><SUB>r</SUB></I></FONT>, that sets the energy limit above which the hard scattering is assumed to be independent from hadronisation effects.<BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This equation descends from the following assumption: the QCD scattering process can be expressed by independent --- <EM>factorised</EM> --- terms. Consider the scattering of two protons: they are complex objects, made of several components called <EM>partons</EM>. The fractional momentum <I>x</I> carried by the partons inside the protons is described by probability density called <EM>Parton Distribution Functions</EM> --- <B>PDF</B>, indicated by <I>f</I>(<I>x</I>,&micro;<FONT SIZE=2><SUB><I>f</I></SUB><SUP>2</SUP></FONT>) in the equation. However, when we consider the scattering process, we assume that the scattering partons are independent from the protons that contained them; then, we have <EM>factorised</EM> the matrix element of the scattering of the two partons from the PDFs that contained the partons. By doing so, we choose an energy scale &micro;<FONT SIZE=2><I><SUB>f</SUB></I></FONT>, the <EM>factorisation scale</EM> that separates the description of the parton as a statistic variable from the description of a pointlike particle in the scattering process. In the factorization scheme, the partonic cross section for <I>tt</I> production <FONT FACE=symbol>s</FONT> depends only on the square of the partonic center of mass energy <I>s</I>=<I>x<FONT SIZE=2><SUB>i</SUB></FONT>x<FONT SIZE=2><SUB>j</SUB></FONT>s</I>, the top mass <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> and the running strong coupling constant <FONT FACE=symbol>a</FONT><FONT SIZE=2><I><SUB>s</SUB></I></FONT>(&micro;<FONT SIZE=2><SUB><I>r</I></SUB><SUP>2</SUP></FONT>). The coupling constant is evaluated at the <EM>renormalisation scale</EM> &micro;<FONT SIZE=2><I><SUB>r</SUB></I></FONT>, that sets the energy limit above which the hard scattering is assumed to be independent from hadronisation effects.<BR></div></td></tr>
</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=403&oldid=prevBarison at 17:42, 18 July 20052005-07-18T17:42:20Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:42, 18 July 2005</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l104" >Line 104:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f_i(x_i,\mu^2_f) \, f_j(x_j,\mu^2_f) \;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f_i(x_i,\mu^2_f) \, f_j(x_j,\mu^2_f) \;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\h(\h,m_t,\alpha_s(\mu^2_r))</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\h(\h,m_t,\alpha_s(\mu^2_r))</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">\</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This equation descends from the following assumption: the QCD scattering process can be expressed by independent --- <EM>factorised</EM> --- terms. Consider the scattering of two protons: they are complex objects, made of several components called <EM>partons</EM>. The fractional momentum <I>x</I> carried by the partons inside the protons is described by probability density called <EM>Parton Distribution Functions</EM> --- <B>PDF</B>, indicated by <I>f</I>(<I>x</I>,&micro;<FONT SIZE=2><SUB><I>f</I></SUB><SUP>2</SUP></FONT>) in the equation. However, when we consider the scattering process, we assume that the scattering partons are independent from the protons that contained them; then, we have <EM>factorised</EM> the matrix element of the scattering of the two partons from the PDFs that contained the partons. By doing so, we choose an energy scale &micro;<FONT SIZE=2><I><SUB>f</SUB></I></FONT>, the <EM>factorisation scale</EM> that separates the description of the parton as a statistic variable from the description of a pointlike particle in the scattering process. In the factorization scheme, the partonic cross section for <I>tt</I> production <FONT FACE=symbol>s</FONT> depends only on the square of the partonic center of mass energy <I>s</I>=<I>x<FONT SIZE=2><SUB>i</SUB></FONT>x<FONT SIZE=2><SUB>j</SUB></FONT>s</I>, the top mass <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> and the running strong coupling constant <FONT FACE=symbol>a</FONT><FONT SIZE=2><I><SUB>s</SUB></I></FONT>(&micro;<FONT SIZE=2><SUB><I>r</I></SUB><SUP>2</SUP></FONT>). The coupling constant is evaluated at the <EM>renormalisation scale</EM> &micro;<FONT SIZE=2><I><SUB>r</SUB></I></FONT>, that sets the energy limit above which the hard scattering is assumed to be independent from hadronisation effects.<BR></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This equation descends from the following assumption: the QCD scattering process can be expressed by independent --- <EM>factorised</EM> --- terms. Consider the scattering of two protons: they are complex objects, made of several components called <EM>partons</EM>. The fractional momentum <I>x</I> carried by the partons inside the protons is described by probability density called <EM>Parton Distribution Functions</EM> --- <B>PDF</B>, indicated by <I>f</I>(<I>x</I>,&micro;<FONT SIZE=2><SUB><I>f</I></SUB><SUP>2</SUP></FONT>) in the equation. However, when we consider the scattering process, we assume that the scattering partons are independent from the protons that contained them; then, we have <EM>factorised</EM> the matrix element of the scattering of the two partons from the PDFs that contained the partons. By doing so, we choose an energy scale &micro;<FONT SIZE=2><I><SUB>f</SUB></I></FONT>, the <EM>factorisation scale</EM> that separates the description of the parton as a statistic variable from the description of a pointlike particle in the scattering process. In the factorization scheme, the partonic cross section for <I>tt</I> production <FONT FACE=symbol>s</FONT> depends only on the square of the partonic center of mass energy <I>s</I>=<I>x<FONT SIZE=2><SUB>i</SUB></FONT>x<FONT SIZE=2><SUB>j</SUB></FONT>s</I>, the top mass <I>m<FONT SIZE=2><SUB>t</SUB></FONT></I> and the running strong coupling constant <FONT FACE=symbol>a</FONT><FONT SIZE=2><I><SUB>s</SUB></I></FONT>(&micro;<FONT SIZE=2><SUB><I>r</I></SUB><SUP>2</SUP></FONT>). The coupling constant is evaluated at the <EM>renormalisation scale</EM> &micro;<FONT SIZE=2><I><SUB>r</SUB></I></FONT>, that sets the energy limit above which the hard scattering is assumed to be independent from hadronisation effects.<BR></div></td></tr>
</table>Barisonhttps://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=402&oldid=prevBarison at 17:41, 18 July 20052005-07-18T17:41:25Z<p></p>
<a href="https://wiki.nikhef.nl/atlas/index.php?title=Chapter_I&diff=402&oldid=401">Show changes</a>Barison