Initial BSc commit
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figures/antikt-comparision.png
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figures/cms_coordinates.png
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figures/sm_wikipedia.svg
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figures/sm_wikipedia.svg
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|
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<title>Standard Model of Elementary Particles</title>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
|
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|
||||
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|
||||
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
|
||||
.st42 {fill:#55CC22; font-size:54px; font-weight:bold;} /* color for leptons */
|
||||
.st43 {fill:#CC99FF; font-size:54px; font-weight:bold;} /* color for quarks */
|
||||
.st44 {fill:#FF6C6C; font-size:54px; font-weight:bold;} /* color for gauge bosons */
|
||||
.st44b{fill:#FF6C6C; font-size:36px; font-weight:bold;} /* color for vector bosons */
|
||||
.st45 {fill:#EEBB33; font-size:54px; font-weight:bold;} /* color for scalar bosons */
|
||||
.st46 {fill:#77AADD; font-size:54px; font-weight:bold;} /* color for tensor bosons */
|
||||
.st46b{fill:#77AADD; font-size:36px; font-weight:bold;} /* color for hypothetical bosons */
|
||||
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|
||||
|
||||
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|
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|
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|
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|
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<stop offset="1" stop-color="#AA77DD" />
|
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|
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|
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|
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|
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<stop offset="1" stop-color="#66CC33" />
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|
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|
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<linearGradient id="lgb_gauge" gradientUnits="userSpaceOnUse" x1="45" y1="-15" x2="200" y2="250">
|
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<stop offset="0" stop-color="#FF9977" />
|
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<stop offset="1" stop-color="#DD5544" />
|
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</linearGradient>
|
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|
||||
<linearGradient id="lgb_scalar" gradientUnits="userSpaceOnUse" x1="45" y1="-15" x2="200" y2="250">
|
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<stop offset="0" stop-color="#EEE677" />
|
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<stop offset="1" stop-color="#EEBB33" />
|
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</linearGradient>
|
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|
||||
<linearGradient id="lgb_tensor" gradientUnits="userSpaceOnUse" x1="45" y1="-15" x2="200" y2="250">
|
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<stop offset="0" stop-color="#99CCFF" />
|
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<stop offset="1" stop-color="#6699CC" />
|
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|
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|
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|
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<linearGradient id="lgp_quark" gradientUnits="userSpaceOnUse" x1="120" y1="60" x2="165" y2="140">
|
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<stop offset="0" stop-color="#EEBBFF" />
|
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<stop offset="1" stop-color="#AA77DD" />
|
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</linearGradient>
|
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|
||||
<linearGradient id="lgp_lepton" gradientUnits="userSpaceOnUse" x1="120" y1="60" x2="165" y2="140">
|
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<stop offset="0" stop-color="#AAEE77" />
|
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<stop offset="1" stop-color="#66CC33" />
|
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|
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|
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<linearGradient id="lgp_gauge" gradientUnits="userSpaceOnUse" x1="120" y1="60" x2="165" y2="140">
|
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|
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<stop offset="1" stop-color="#DD5544" />
|
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|
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|
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<linearGradient id="lgp_scalar" gradientUnits="userSpaceOnUse" x1="120" y1="60" x2="165" y2="140">
|
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<stop offset="1" stop-color="#EEBB33" />
|
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|
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<linearGradient id="lgp_tensor" gradientUnits="userSpaceOnUse" x1="120" y1="60" x2="165" y2="140">
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|
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|
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|
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<g id="tilequ">
|
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|
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<use xlink:href="#ball" class="st20" />
|
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|
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|
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<g id="tilele">
|
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<use xlink:href="#box" stroke="url(#lgb_lepton)" />
|
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<use xlink:href="#ball" class="st26" />
|
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</g>
|
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|
||||
<g id="tilegb">
|
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<use xlink:href="#box" stroke="url(#lgb_gauge)" />
|
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<use xlink:href="#ball" class="st32" />
|
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|
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|
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<g id="tilesb">
|
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<use xlink:href="#box" stroke="url(#lgb_scalar)" />
|
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<use xlink:href="#ball" class="st36" />
|
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|
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|
||||
<g id="tiletb">
|
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<use xlink:href="#box" stroke="url(#lgb_tensor)" />
|
||||
<use xlink:href="#ball" class="st37" />
|
||||
</g>
|
||||
|
||||
</defs>
|
||||
|
||||
<text class="head1" x="50%" y="95">Standard Model of Elementary Particles</text>
|
||||
|
||||
<g transform="translate(-20 0)">
|
||||
<title>Forces</title>
|
||||
<path
|
||||
id="fstrong"
|
||||
class="st0"
|
||||
d="M240.8,322.6c-30.4,0-55,24.6-55,55v250c0,30.4,24.6,55,55,55h500c30.4,0,55-24.6,55-55 c0-107.7,87.3-195,195-195h10c30.4,0,55-24.6,55-55c0-30.4-24.6-55-55-55H240.8" />
|
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<path
|
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class="st0"
|
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d="M240.8,312.6c-35.9,0-65,29.1-65,65v510c0,35.9,29.1,65,65,65h500c35.9,0,65-29.1,65-65 c0-107.7,82.8-195,185-195h10c35.9,0,65-29.1,65-65c0-35.9-29.1-65-65-65h-10c-102.2,0-185-82.8-185-185c0-35.9-29.1-65-65-65H240.8 "
|
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|
||||
<path
|
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class="st0"
|
||||
d="M240.8,302.6c-41.4,0-75,33.6-75,75v760c0,41.4,33.6,75,75,75h760c41.4,0,75-33.6,75-75v-250 c0-41.4-33.6-75-75-75h-10c-96.6,0-175-78.4-175-175v-260c0-41.4-33.6-75-75-75H240.8"
|
||||
id="fweak" />
|
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|
||||
|
||||
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|
||||
<title>Fermions</title>
|
||||
<rect class="st2" x="100" y="137.6" width="740" height="80" rx="30" ry="30" />
|
||||
<text x="470" y="166" font-size="30" font-weight="bold" text-anchor="middle">three generations of matter<tspan x="470" dy="36px">(fermions)</tspan></text>
|
||||
<g class="st41" transform="translate(100 255)">
|
||||
<text x="120">I</text>
|
||||
<text x="370">II</text>
|
||||
<text x="620">III</text>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
<g>
|
||||
<title>Bosons</title>
|
||||
<rect class="st2" x="860" y="137.6" width="500" height="80" rx="30" ry="30" />
|
||||
<text x="1110" y="166" font-size="30" font-weight="bold" text-anchor="middle">interactions / force carriers<tspan x="1110" dy="36px">(bosons)</tspan></text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(85 20)" class="st39" font-size="24" text-anchor="end">
|
||||
<title>mass, charge, spin</title>
|
||||
<text y="295">mass</text>
|
||||
<text y="335">charge</text>
|
||||
<text y="375">spin</text>
|
||||
</g>
|
||||
|
||||
<g>
|
||||
<title>Quarks</title>
|
||||
<text class="st43" transform="translate(70 770) rotate(-90)">QUARKS</text>
|
||||
|
||||
<g transform="translate(100 275)">
|
||||
<title>up</title>
|
||||
|
||||
<use xlink:href="#tilequ" />
|
||||
<text class="psymr" x="120" y="120">u</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃2.2 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">⅔</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">up</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(100 525)">
|
||||
<title>down</title>
|
||||
|
||||
<use xlink:href="#tilequ" />
|
||||
<text class="psymr" x="120" y="120">d</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃4.7 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">−⅓</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">down</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(350 275)">
|
||||
<title>charm</title>
|
||||
|
||||
<use xlink:href="#tilequ" />
|
||||
<text class="psymr" x="120" y="120">c</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃1.28 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">⅔</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">charm</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(350 525)">
|
||||
<title>strange</title>
|
||||
|
||||
<use xlink:href="#tilequ" />
|
||||
<text class="psymr" x="120" y="120">s</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃96 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">−⅓</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">strange</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(600 275)">
|
||||
<title>top</title>
|
||||
|
||||
<use xlink:href="#tilequ" />
|
||||
<text class="psymr" x="120" y="120">t</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃173.1 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">⅔</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">top</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(600 525)">
|
||||
<title>bottom</title>
|
||||
|
||||
<use xlink:href="#tilequ" />
|
||||
<text class="psymr" x="120" y="120">b</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃4.18 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">−⅓</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">bottom</text>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
<g>
|
||||
<title>Leptons</title>
|
||||
<text class="st42" transform="translate(70 1270) rotate(-90)">LEPTONS</text>
|
||||
|
||||
<g transform="translate(100 790)">
|
||||
<title>electron</title>
|
||||
|
||||
<use xlink:href="#tilele" />
|
||||
<text class="psymr" x="120" y="120">e</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃0.511 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">−1</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">electron</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(100 1040)">
|
||||
<title>electron neutrino</title>
|
||||
|
||||
<use xlink:href="#tilele" />
|
||||
<text class="psymg" x="120" y="110">ν<tspan class="sub">e</tspan></text>
|
||||
|
||||
<text class="pmass" x="015" y="040"><2.2 eV/c²</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pnam2" x="120" y="200"><tspan dy="-20">electron</tspan><tspan x="120" dy="040">neutrino</tspan></text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(350 790)">
|
||||
<title>muon</title>
|
||||
|
||||
<use xlink:href="#tilele" />
|
||||
<text class="psymg" x="120" y="120">μ</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃105.66 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">−1</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">muon</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(350 1040)">
|
||||
<title>muon neutrino</title>
|
||||
|
||||
<use xlink:href="#tilele" />
|
||||
<text class="psymg" x="120" y="110">ν<tspan class="sub">μ</tspan></text>
|
||||
|
||||
<text class="pmass" x="015" y="040"><0.17 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pnam2" x="120" y="200"><tspan dy="-20">muon</tspan><tspan x="120" dy="040">neutrino</tspan></text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(600 790)">
|
||||
<title>tau</title>
|
||||
|
||||
<use xlink:href="#tilele" />
|
||||
<text class="psymg" x="120" y="120">τ</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃1.7768 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">−1</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pname" x="120" y="200">tau</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(600 1040)">
|
||||
<title>tau neutrino</title>
|
||||
|
||||
<use xlink:href="#tilele" />
|
||||
<text class="psymg" x="120" y="110">ν<tspan class="sub">τ</tspan></text>
|
||||
|
||||
<text class="pmass" x="015" y="040"><18.2 MeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">½</text>
|
||||
<text class="pnam2" x="120" y="200"><tspan dy="-20">tau</tspan><tspan x="120" dy="040">neutrino</tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
<g>
|
||||
<title>Gauge Bosons</title>
|
||||
<text class="st44" transform="translate(1170 1270) rotate(-90)">GAUGE BOSONS</text>
|
||||
<text class="st44b" transform="translate(1210 1270) rotate(-90)">VECTOR BOSONS</text>
|
||||
|
||||
<g transform="translate(860 275)">
|
||||
<title>gluon</title>
|
||||
|
||||
<use xlink:href="#tilegb" />
|
||||
<text class="psymr" x="120" y="120">g</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">0</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">1</text>
|
||||
<text class="pname" x="120" y="200">gluon</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(860 525)">
|
||||
<title>photon</title>
|
||||
|
||||
<use xlink:href="#tilegb" />
|
||||
<text class="psymg" x="120" y="120">γ</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">0</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">1</text>
|
||||
<text class="pname" x="120" y="200">photon</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(860 790)">
|
||||
<title>Z boson</title>
|
||||
|
||||
<use xlink:href="#tilegb" />
|
||||
<text class="psymr" x="120" y="120">Z</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃91.19 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">1</text>
|
||||
<text class="pname" x="120" y="200">Z boson</text>
|
||||
</g>
|
||||
|
||||
<g transform="translate(860 1040)">
|
||||
<title>W boson</title>
|
||||
|
||||
<use xlink:href="#tilegb" />
|
||||
<text class="psymr" x="120" y="120">W</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃80.39 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">±1</text>
|
||||
<text class="pspin" x="015" y="120">1</text>
|
||||
<text class="pname" x="120" y="200">W boson</text>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
<g>
|
||||
<title>Scalar Bosons</title>
|
||||
<text class="st45" transform="translate(1350 530) rotate(-90)" text-anchor="end">SCALAR BOSONS</text>
|
||||
|
||||
<g transform="translate(1120 275)">
|
||||
<title>Higgs</title>
|
||||
|
||||
<use xlink:href="#tilesb" />
|
||||
<text class="psymr" x="120" y="120">H</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">≃124.97 GeV/c²</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">0</text>
|
||||
<text class="pname" x="120" y="200">higgs</text>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
<g style="display:none;">
|
||||
<title>Tensor Bosons</title>
|
||||
<text class="st46" transform="translate(1610 530) rotate(-90)" text-anchor="end">TENSOR BOSONS</text>
|
||||
<text class="st46b" transform="translate(1555 530) rotate(-90)" text-anchor="end">HYPOTHETICAL</text>
|
||||
|
||||
<g transform="translate(1380 275)">
|
||||
<title>Graviton</title>
|
||||
|
||||
<use xlink:href="#tiletb" />
|
||||
<text class="psymr" x="120" y="120">G</text>
|
||||
|
||||
<text class="pmass" x="015" y="040">0</text>
|
||||
<text class="pchar" x="015" y="080">0</text>
|
||||
<text class="pspin" x="015" y="120">2</text>
|
||||
<text class="pname" x="120" y="200">graviton</text>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 17 KiB |
144
structure.md
Normal file
144
structure.md
Normal file
|
|
@ -0,0 +1,144 @@
|
|||
# Abstract
|
||||
|
||||
# Theoretical background
|
||||
|
||||
## Standard model
|
||||
|
||||
- issues
|
||||
|
||||
### q*
|
||||
|
||||
- common conclusion from composite models
|
||||
|
||||
## LHC
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
### CMS
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
#### Jets
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
# Search for excited quarks
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
## Method of analysis
|
||||
|
||||
- dominant background: QCD (gg-gg e.g. - two jets)
|
||||
- division in QCD bg and signal
|
||||
|
||||
### Signal/Background modelling
|
||||
|
||||
- expected: bg smooth falling
|
||||
|
||||
## Event selection
|
||||
|
||||
- division in pre/post selection
|
||||
- preselection for trigger efficiency and general physical cuts
|
||||
- post selection to apply different taggers
|
||||
|
||||
### Preselection
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
### Tagger
|
||||
|
||||
- Cut on softdropmass
|
||||
|
||||
#### Tau21
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
#### DeepBoosted
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
### Optimization
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
## Data MC Comparision
|
||||
|
||||
.
|
||||
|
||||
### Sideband
|
||||
|
||||
.
|
||||
|
||||
## Uncertainties (?)
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
# Results
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
## 2016
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
### previous research
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
## 2016 + 2017 + 2018
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
.
|
||||
|
||||
# Summary
|
||||
BIN
structure.pdf
Normal file
BIN
structure.pdf
Normal file
Binary file not shown.
416
thesis.md
Normal file
416
thesis.md
Normal file
|
|
@ -0,0 +1,416 @@
|
|||
---
|
||||
author: David Leppla-Weber
|
||||
title: Search for excited quark states decaying to qW/qZ
|
||||
lang: en-GB
|
||||
header-includes: |
|
||||
\usepackage[onehalfspacing]{setspace}
|
||||
\usepackage{siunitx}
|
||||
\usepackage{tikz-feynman}
|
||||
\pagenumbering{gobble}
|
||||
abstract: |
|
||||
This is my very long abstract.
|
||||
|
||||
Blubb
|
||||
documentclass: article
|
||||
geometry:
|
||||
- top=2.5cm
|
||||
- left=3cm
|
||||
- right=2.5cm
|
||||
- bottom=2.5cm
|
||||
papersize: a4
|
||||
mainfont: Times New Roman
|
||||
fontsize: 12pt
|
||||
toc: true
|
||||
---
|
||||
\newpage
|
||||
\pagenumbering{arabic}
|
||||
|
||||
# Introduction
|
||||
|
||||
\newpage
|
||||
|
||||
# Theoretical background
|
||||
|
||||
This chapter presents a short summary of the theoretical background relevant to this thesis. It first gives an
|
||||
introduction to the standard model itself and some of the issues it raises. It then goes on to explain the processes of
|
||||
quantum chromodynamics and the theory of q*, which will be the main topic of this thesis.
|
||||
|
||||
## Standard model
|
||||
|
||||
The Standard Model of physics proofed very successful in describing three of the four fundamental interactions currently
|
||||
known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully included in
|
||||
this theory.
|
||||
|
||||
The Standard Model divides all particles into spin-$\frac{n}{2}$ fermions and spin-n bosons, where n could be any
|
||||
integer but so far is only known to be one for fermions and either one (gauge bosons) or zero (scalar bosons) for
|
||||
bosons. The fermions are further divided into quarks and leptons. Each of those exists in six so called flavours.
|
||||
Furthermore, quarks and leptons can also be divided into three generations, each of which contains two particles.
|
||||
In the lepton category, each generation has one charged lepton and one neutrino, that has no charge. Also, the mass of
|
||||
the neutrinos is not yet known, so far, only an upper bound has been established. A full list of particles known to the
|
||||
standard model can be found in [@fig:sm]. Furthermore, all fermions have an associated anti particle with reversed
|
||||
charge. Therefore it is not clear, whether it makes sense to differ between particle and anti particle for chargeless
|
||||
particles such as photons and neutrinos.
|
||||
|
||||
{width=50% #fig:sm}
|
||||
|
||||
The gauge bosons, namely the photon, $W^\pm$ bosons, $Z^0$ boson, and eight gluons, are mediators of the different
|
||||
forces of the standard model.
|
||||
|
||||
The photon is responsible for the electromagnetic force and therefore interacts with all
|
||||
electrically charged particles. It itself carries no electromagnetic charge and has no mass. Possible interactions are
|
||||
either scattering or absorption.
|
||||
|
||||
The $W^\pm$ and $Z^0$ bosons mediate the weak force. All quarks and leptons carry a flavour, which is a conserved value.
|
||||
Only the weak interaction breaks this conservation, a quark or lepton can therefore, by interacting with a $W^\pm$
|
||||
boson, change its flavour. The probabilities of this happening are determined by the Cabibbo-Kobayashi-Maskawa matrix:
|
||||
|
||||
\begin{equation}
|
||||
V_{CKM} =
|
||||
\begin{pmatrix}
|
||||
|V_{ud}| & |V_{us}| & |V_{ub}| \\
|
||||
|V_{cd}| & |V_{cs}| & |V_{cb}| \\
|
||||
|V_{td}| & |V_{ts}| & |V_{tb}|
|
||||
\end{pmatrix}
|
||||
=
|
||||
\begin{pmatrix}
|
||||
0.974 & 0.225 & 0.004 \\
|
||||
0.224 & 0.974 & 0.042 \\
|
||||
0.008 & 0.041 & 0.999
|
||||
\end{pmatrix}
|
||||
\end{equation}
|
||||
|
||||
The probability of a quark changing its flavour from $i$ to $j$ is given by the square of the absolute value of the
|
||||
matrix element $V_{ij}$. It is easy to see, that the change of flavour in the same generation is way more likely than
|
||||
any other flavour change.
|
||||
|
||||
The strong interaction or quantum chromodynamics (QCD) describe the strong interaction of particles. It applies to all
|
||||
particles carrying colour (e.g. quarks). The force is mediated by the gluons. Those bosons carry colour as well,
|
||||
although they don't carry just one colour but rather a combination of a colour and an anticolour, and can therefore
|
||||
interact with themselves. As a result of this, processes, where a gluon decays into two gluons are possible. Furthermore
|
||||
the strong force, binding to colour carrying particles, increases with their distance r making it at a certain point
|
||||
more energetically efficient to form a new quark - antiquark pair than separating two particles even further. This
|
||||
effect is known as colour confinement. Due to this effect, colour carrying particles can't be observed directly but
|
||||
rather form so called jets that cause hadronic showers in the detector. An effect called Hadronisation.
|
||||
|
||||
### Quantum Chromodynamic background {#sec:qcdbg}
|
||||
|
||||
In this thesis, a decay that produces two jets will be analysed. Therefore it will be hard to distinguish the signal
|
||||
processes from any QCD effects. Those also produce two jets in the endstate, as can be seen in [@fig:qcdfeynman]. They
|
||||
are also happening very often in a proton proton collision. This is caused by the structure of the proton. It does not
|
||||
only consist of the three quarks, called valence quarks, but also of a lot of quark-antiquark pairs connected by
|
||||
gluons, called the sea quarks. Therefore in a proton - proton collision, interactions of gluons and quarks are the main
|
||||
processes causing a very strong QCD background.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\feynmandiagram [horizontal=v1 to v2] {
|
||||
q1 [particle=\(q\)] -- [fermion] v1 -- [gluon] g1 [particle=\(g\)],
|
||||
v1 -- [gluon] v2,
|
||||
q2 [particle=\(q\)] -- [fermion] v2 -- [gluon] g2 [particle=\(g\)],
|
||||
};
|
||||
\feynmandiagram [horizontal=v1 to v2] {
|
||||
g1 [particle=\(g\)] -- [gluon] v1 -- [gluon] g2 [particle=\(g\)],
|
||||
v1 -- [gluon] v2,
|
||||
g3 [particle=\(g\)] -- [gluon] v2 -- [gluon] g4 [particle=\(g\)],
|
||||
};
|
||||
\caption{Two examples of QCD processes resulting in two jets.} \label{fig:qcdfeynman}
|
||||
\end{figure}
|
||||
|
||||
### Shortcomings of the Standard Model
|
||||
|
||||
While being very successful in describing mostly all of the effects we can observe in particle colliders so far, the
|
||||
Standard Model still has several shortcomings.
|
||||
|
||||
- **Gravity**: as already noted, the standard model doesn't include gravity as a force.
|
||||
- **Dark Matter**: observations of the rotational velocity of galaxies can't be explained by the matter known, dark
|
||||
matter up to date is our best theory to explain those.
|
||||
- **Matter-antimatter assymetry**: The amount of matter vastly outweights the amount of
|
||||
antimatter in the observable universe. This can't be explained by the standard model, which predicts a similar amount
|
||||
of matter and antimatter.
|
||||
- **Symmetries between particles**: Why do exactly three generations of fermions exist? Why is the charge of a quark
|
||||
exactly one third of the charge of a lepton? How are the masses of the particles related? Those questions cannot be
|
||||
answered by the standard model.
|
||||
- **Hierarchy problem**:
|
||||
|
||||
## Excited quark states
|
||||
|
||||
One category of theories that try to solve some of the shortcomings of the standard model are the composite quark
|
||||
models. Those state, that quarks consist of some particles unknown to us so far. This could explain the symmetries
|
||||
between the different fermions. A common prediction of those models are excited quark states (q\*, q\*\*, q\*\*\*...),
|
||||
similar to atoms, that can be excited by the absorption of a photon and can then decay again under emission of a photon
|
||||
with an energy corresponding to the excited state.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\feynmandiagram [large, horizontal=qs to v] {
|
||||
a -- qs -- b,
|
||||
qs -- [fermion, edge label=\(q*\)] v,
|
||||
q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
|
||||
q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
|
||||
};
|
||||
\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also
|
||||
decaying to two quarks.} \label{fig:qsfeynman}
|
||||
\end{figure}
|
||||
|
||||
This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the single excited quark state
|
||||
q\* which can decay to a quark and any boson. An example of a q\* decaying to a quark and a W boson can be seen in
|
||||
[@fig:qsfeynman]. As the boson will also quickly decay to for example two quarks, those events will be hard to
|
||||
distinguish from the QCD background described in [@sec:qcdbg]. To reconstruct the mass of the q\* particle, the dijet
|
||||
invariant mass, the mass of the two jets in the final state, can be calculated by adding their four momenta, vectors
|
||||
consisting of the energy and momentum of a particle, together. From the four momentum it's easy to derive the mass by
|
||||
solving $E=\sqrt{p^2 + m^2}$ for m.
|
||||
|
||||
\newpage
|
||||
|
||||
# Experimental Setup
|
||||
|
||||
Following on, the experimental setup used to gather the data analysed in this thesis will be described.
|
||||
|
||||
## Large Hadron Collider
|
||||
|
||||
The Large Hadron Collider is the world's largest and most powerful particle accelerator [@website]. It has a perimeter
|
||||
of 27 km and can collide protons at a centre of mass energy of 13 TeV. It is home to several experiments, the biggest of
|
||||
those are ATLAS and the Compact Muon Solenoid (CMS). Both are general-purpose detectors to investigate the particles
|
||||
that form during particle collisions.
|
||||
|
||||
The luminosity L is a quantity to be able to calculate the number of events per second generated in a LHC collision by
|
||||
$N_{event} = L\sigma_{event}$ with $\sigma_{event}$ being the cross section of the event.
|
||||
The luminosity of the LHC for a Gaussian beam distribution can be described as follows:
|
||||
|
||||
\begin{equation}
|
||||
L = \frac{N_b^2 n_b f_{rev} \gamma_r}{4 \pi \epsilon_n \beta^*}F
|
||||
\end{equation}
|
||||
|
||||
Where $N_b$ is the number of particles per bunch, $n_b$ the number of bunches per beam, $f_{rev}$ the revolution
|
||||
frequency, $\gamma_r$ the relativistic gamma factor, $\epsilon_n$ the normalised transverse beam emittance, $\beta^*$
|
||||
the beta function at the collision point and F the geometric luminosity reduction factor due to the crossing angle at
|
||||
the interaction point:
|
||||
\begin{equation}
|
||||
F = \left(1+\left( \frac{\theta_c\sigma_z}{2\sigma^*}\right)^2\right)^{-1/2}
|
||||
\end{equation}
|
||||
|
||||
At the maximum luminosity of $10^{34}\si{\per\square\centi\metre\per\s}$, $N_b = 1.15 \cdot 10^{11}$, $n_b = 2808$,
|
||||
$f_{rev} = \SI{11.2}{\kilo\Hz}$, $\beta^* = \SI{0.55}{\m}$, $\epsilon_n = \SI{3.75}{\micro\m}$ and $F = 0.85$.
|
||||
|
||||
To quantify the amount of data collected by one of the experiments at LHC, the integrated luminosity is introduced as
|
||||
$L_{int} = \int L dt$. In 2016 the CMS captured data of a total integrated luminosity of $\SI{35.92}{\per\femto\barn}$.
|
||||
In 2017 it collected $\SI{41.53}{\per\femto\barn}$ and in 2018 $\SI{59.74}{\per\femto\barn}$.
|
||||
|
||||
## Compact Muon Solenoid
|
||||
|
||||
The data used in this thesis was captured by the Compact Muon Solenoid (CMS). It is one of the biggest experiments at
|
||||
the Large Hadron Collider. It can detect all elementary particles of the standard model except neutrinos. For that, it
|
||||
has an onion like setup. The particles produced in a collision first go through a tracking system. They then pass an
|
||||
electromegnetic as well as a hadronic calorimeter. This part is surrounded by a supercondcting solenoid that generates a
|
||||
magenetic field of 3.8 T. Outside of the solenoid are big muon chambers.
|
||||
|
||||
### Coordinate conventions
|
||||
|
||||
Per convention, the z axis points along the beam axis, the y axis upwards and the x axis horizontal towards the LHC
|
||||
centre. Furthermore, the azimuthal angle $\phi$, which describes the angle in the x - y plane, the polar angle $\theta$,
|
||||
which describes the angle in the y - z plane and the pseudorapidity $\eta$, which is defined as $\eta =
|
||||
-ln\left(tan\frac{\theta}{2}\right)$ are introduced. The coordinates are visualised in [@fig:cmscoords].
|
||||
|
||||
{#fig:cmscoords width=60%}
|
||||
|
||||
### The tracking system
|
||||
|
||||
The tracking system is built of two parts, first a pixel detector and then silicon strip sensors. It is used to
|
||||
reconstruct the tracks of charged particles, measuring their charge sign, direction and momentum. It is as close to the
|
||||
collision as possible to be able to identify secondary vertices.
|
||||
|
||||
### The electromagnetic calorimeter
|
||||
|
||||
The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal.
|
||||
When passed by particles, it produces light in proportion to the particle's energy. This light is measured by
|
||||
photodetectors that convert this scintillation light to an electrical signal. To measure a particles energy, it has to
|
||||
leave its whole energy in the ECAL, which is true for photons and electrons, but not for other particles such as
|
||||
hadrons (particles formed of quarks) and muons. They too leave some energy in the ECAL.
|
||||
|
||||
### The hadronic calorimeter
|
||||
|
||||
The hadronic calorimeter (HCAL) is used to detect high energy hadronic particles. It surrounds the ECAL and is made of
|
||||
alternating layers of active and absorber material. While the absorber material with its high density causes the hadrons
|
||||
to shower, the active material then detects those showers and measures their energy, similar to how the ECAL works.
|
||||
|
||||
### The solenoid
|
||||
|
||||
The solenoid, giving the detector its name, is one of the most important feature. It creates a magnetic field of 3.8 T
|
||||
and therefore makes it possible to measure momentum of charged particles by bending their tracks.
|
||||
|
||||
### The muon system
|
||||
|
||||
Outside of the solenoid there is only the muon system. It consists of three types of gas detectors, the drift tubes,
|
||||
cathode strip chambers and resistive plate chambers. The system is divided into a barrel part and two endcaps. Together
|
||||
they cover $0 < |\eta| < 2.4$. The muons are the only detected particles, that can pass all the other systems
|
||||
without a significant energy loss.
|
||||
|
||||
### The Particle Flow algorithm
|
||||
|
||||
The particle flow algorithm is used to identify and reconstruct all the particles arising from the proton - proton
|
||||
collision by using all the information available from the different sub-detectors of the CMS. It does so by
|
||||
extrapolating the tracks through the different calorimeters and associating clusters they cross with them. The set of
|
||||
the track and its clusters is then no more used for the detection of other particles. This is first done for muons and
|
||||
then for charged hadrons, so a muon can't give rise to a wrongly identified charged hadron. Due to Bremsstrahlung photon
|
||||
emission, electrons are harder to reconstruct, for them a specific track reconstruction algorithm is used [TODO].
|
||||
After identifying charged hadrons, muons and electrons, all remaining clusters within the HCAL correspond to neutral
|
||||
hadrons and within ECAL to photons. If the list of particles and their corresponding deposits is established, it can be
|
||||
used to determine the particles four momentums. From that, the missing transverse energy can be calculated and tau
|
||||
particles can be reconstructed by their decay products.
|
||||
|
||||
### Jet clustering
|
||||
|
||||
Because of the hadronisation it is not possible to uniquely identify the originating particle of a jet. Nonetheless,
|
||||
several algorithms exist to help with this problem. The algorithm used in this thesis is the anti-$k_t$ clustering
|
||||
algorithm. It arises from a generalization of several other clustering algorithms, namely the $k_t$, Cambridge/Aachen
|
||||
and SISCone clustering algorithms.
|
||||
|
||||
The anti-$k_t$ clustering algorithm associates hard particles with their soft particles surrounding them within a radius
|
||||
R in the $\eta$ - $\phi$ plane forming cone like jets. If two jets overlap, the jets shape is changed according to its
|
||||
hardness. A softer particles jet will change its shape more than a harder particles. A visual comparision of four
|
||||
different clustering algorithms can be seen in [@fig:antiktcomparision].
|
||||
|
||||
{#fig:antiktcomparision}
|
||||
|
||||
\newpage
|
||||
|
||||
# Method of analysis
|
||||
|
||||
As described in …, an excited quark q\* can decay to a quark and any boson. The branching ratios are calculated to be as
|
||||
follows:
|
||||
|
||||
The majority of excited quarks will decay to a quark and a gluon, but as this is virtually impossible to distinguish
|
||||
from QCD effects (for example from the qg->qg processes), this analysis will focus on the processes q\*->qW and q\*->qZ.
|
||||
In this case, due to jet substructure studies, it is possible to establish a discriminator between QCD background and
|
||||
jets originating in a W/Z decay. They still make up roughly 20 % of the signal events to study and therefore seem like a
|
||||
good choice.
|
||||
|
||||
To find signal events in the data, this thesis looks at the dijet invariant mass distribution. It is assumed to only consist
|
||||
of QCD background and signal events, other backgrounds are neglected. If the q\* particle exists, this distribution
|
||||
should show a peak at its invariant mass. This peak will be looked for with statistical methods explained later on.
|
||||
|
||||
## Signal/Background modelling
|
||||
|
||||
To be able to first make sure the setup is working as intended, simulated samples are of background and signal are used.
|
||||
For that, Monte Carlo simulations are used. The different particle interactions that take in a proton - proton collision
|
||||
are simulated using the probabilities provided by the Standard Model. Later on, also detector effects are applied to
|
||||
make sure, they look like real data coming from the CMS detector. The q\* signal samples are simulated by the
|
||||
probabilities given by the q\* theory and assuming a cross section of $\SI{1}{\per\pico\barn}$.
|
||||
|
||||
The invariant mass distribution of the QCD background sample is fitted using the following function with three
|
||||
parameters p0, p1, p2:
|
||||
\begin{equation}
|
||||
\frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}}
|
||||
\end{equation}
|
||||
Whereas $m_{jj}$ is the invariant mass of the dijet and $p_0$ is a normalisation parameter. Two and four parameter
|
||||
functions have also been studied but found to not fit the background as good as this one.
|
||||
|
||||
The signal is fitted using a double sided crystal ball function. A gaussian and a poisson have also been studied but
|
||||
found to not fit the signal sample very well.
|
||||
|
||||
\newpage
|
||||
|
||||
# Preselection and data quality
|
||||
|
||||
To separate the background from the signal, several cuts have to be introduced. The selection of events is divided in
|
||||
two parts. The first one (the preselection) adds some cuts for trigger efficiency as well as general physics motivated
|
||||
cuts. It is not expected to already provide a good separation of background and signal. In the second part, different
|
||||
taggers will be used as a discriminator between QCD background and signal events. After the preselection, it is made
|
||||
sure, that the simulated samples represent the real data well.
|
||||
|
||||
## Preselection
|
||||
|
||||
From a decaying q\* particle, we expect two jets in the endstate. Therefore a cut of number of jets $\ge$ 2 is added.
|
||||
More jets are also possible because of jets originating in QCD effects such as gluon - gluon interactions. The second
|
||||
cut is on $\Delta\eta$. The q\* particle is expected to be very heavy and therefore almost stationary. Its decay
|
||||
products should therefore be close to back to back, which means a low $\Delta\eta$. To maintain comparability, the
|
||||
same cut as in previous research of $\Delta\eta \le 1.3$ will be used. The last cut in the preselection is on the dijet
|
||||
invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important for a high trigger efficiency. To summarise, the
|
||||
following cuts are applied during preselection:
|
||||
|
||||
1. Number of jets $\ge$ 2
|
||||
1. $\Delta\eta \le 1.3$
|
||||
1. $m_{jj} \ge \SI{1050}{\giga\eV}$
|
||||
|
||||
## Data - Monte Carlo Comparision
|
||||
|
||||
To ensure high data quality, the MC QCD background sample is now being compared to the actual data of the corresponding
|
||||
year collected by the CMS detector. This is done for the years 2016, 2017 and 2018. The distributions are normalised on
|
||||
the invariant mass distribution. For most distributions, no significant difference is seen between data and simulation.
|
||||
In 2018, way more events have a high number of primary vertices in the real data than in the simulated sample. This is
|
||||
being investigated by a CMS workgroup already but should not affect this analysis.
|
||||
|
||||
### Sideband
|
||||
|
||||
The sideband is introduced to make sure there are no unwanted side effects of the used cuts. It adds a cut, that makes
|
||||
sure, no data in the sideband is used for the actual analysis. As sideband, the region where the mass of one of the two
|
||||
jets with the highest transverse momentum ($p_t$) is more than 105 GeV. Because the decay of a q\* to a vector boson is
|
||||
being investigated, one of the two jets should have a mass between 105 GeV and 35 GeV. Therefore events with jets that
|
||||
are heavier than 105 GeV will not be used for this analysis which makes them a good sideband to use.
|
||||
|
||||
# Event substructure selection
|
||||
|
||||
This selection is responsible for distinguishing between QCD and signal events by using a tagger to identify jets coming
|
||||
from a vector boson. Two different taggers will be used to later compare the results. The decay analysed includes either
|
||||
a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut on the
|
||||
softdropmass of a jet. The softdropmass is calculated by removing wide angle soft particles from the jet to counter the
|
||||
effects of contamination from initial state radiation, underlying event and multiple hadron scattering. The softdropmass
|
||||
of at least one of the two leading jets is expected to be within $\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$.
|
||||
|
||||
## N-Subjettiness
|
||||
|
||||
The N-subjettiness $\tau_n$ is defined as
|
||||
|
||||
\begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta
|
||||
R_{N,k} \} \end{equation}
|
||||
|
||||
with k going over the constituent particles in a given jet, $p_{T,k}$ being their transverse momenta and $\Delta R_{J,k}
|
||||
= \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}$ being the distance of a candidate subjet J and a constituent particle k in the
|
||||
rapidity-azimuth plane. It quantifies to what degree a jet can be regarded as a jet composed of $N$ subjets.
|
||||
It has been shown, that $\tau_{21} = \tau_2/\tau_1$ is a good discriminator between QCD events
|
||||
and events originating from the decay of a boosted vector boson.
|
||||
|
||||
The $\tau_{21}$ cut is applied to the one of the two highest $p_t$ jets passing the softdropmasswindow. If both of them
|
||||
pass, it is applied to the one with higher $p_t$.
|
||||
|
||||
## DeepBoosted
|
||||
|
||||
The deep boosted tagger uses a trained neural network to identify decays originitating in a vector boson. It is supposed
|
||||
to give better efficiencies than the older N-Subjettiness method.
|
||||
|
||||
## Optimization
|
||||
|
||||
To figure out the best value to cut on the discriminators introduced by the two taggers, a value to quantify how good a
|
||||
cut is has to be introduced. For that, the significance calculated by $\frac{S}{\sqrt{B}}$ will be used. S stands for
|
||||
the amount of signal events and B for the amount of background events in a given interval. This value assumes a gaussian
|
||||
error on the background so it will be calculated for the 2 TeV masspoint where enough background events exist to justify
|
||||
this assumption. The value therefore represents how good the signal can be distinguished from the background in units of
|
||||
the standard deviation of the background. As interval, a 10 % margin around the masspoint is chosen.
|
||||
|
||||
As a result, the $\tau_{21}$ cut is placed at $\le 0.35$ and the VvsQCD cut is placed at $\ge 0.83$.
|
||||
|
||||
\newpage
|
||||
|
||||
# Signal extraction
|
||||
|
||||
## Uncertainties
|
||||
|
||||
\newpage
|
||||
|
||||
# Results
|
||||
|
||||
|
||||
## 2016
|
||||
|
||||
### previous research
|
||||
|
||||
|
||||
## 2016 + 2017 + 2018
|
||||
|
||||
|
||||
# Summary
|
||||
BIN
thesis.pdf
Normal file
BIN
thesis.pdf
Normal file
Binary file not shown.
357
thesis.tex
Normal file
357
thesis.tex
Normal file
|
|
@ -0,0 +1,357 @@
|
|||
% Options for packages loaded elsewhere
|
||||
\PassOptionsToPackage{unicode}{hyperref}
|
||||
\PassOptionsToPackage{hyphens}{url}
|
||||
%
|
||||
\documentclass[
|
||||
12pt,
|
||||
british,
|
||||
a4paper,
|
||||
]{article}
|
||||
\usepackage{lmodern}
|
||||
\usepackage{amssymb,amsmath}
|
||||
\usepackage{ifxetex,ifluatex}
|
||||
\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
|
||||
\usepackage[T1]{fontenc}
|
||||
\usepackage[utf8]{inputenc}
|
||||
\usepackage{textcomp} % provide euro and other symbols
|
||||
\else % if luatex or xetex
|
||||
\usepackage{unicode-math}
|
||||
\defaultfontfeatures{Scale=MatchLowercase}
|
||||
\defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
|
||||
\setmainfont[]{Times New Roman}
|
||||
\fi
|
||||
% Use upquote if available, for straight quotes in verbatim environments
|
||||
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
|
||||
\IfFileExists{microtype.sty}{% use microtype if available
|
||||
\usepackage[]{microtype}
|
||||
\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
|
||||
}{}
|
||||
\makeatletter
|
||||
\@ifundefined{KOMAClassName}{% if non-KOMA class
|
||||
\IfFileExists{parskip.sty}{%
|
||||
\usepackage{parskip}
|
||||
}{% else
|
||||
\setlength{\parindent}{0pt}
|
||||
\setlength{\parskip}{6pt plus 2pt minus 1pt}}
|
||||
}{% if KOMA class
|
||||
\KOMAoptions{parskip=half}}
|
||||
\makeatother
|
||||
\usepackage{xcolor}
|
||||
\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
|
||||
\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
|
||||
\hypersetup{
|
||||
pdftitle={Search for excited quark states decaying to qW/qZ},
|
||||
pdfauthor={David Leppla-Weber},
|
||||
pdflang={en-GB},
|
||||
hidelinks,
|
||||
pdfcreator={LaTeX via pandoc}}
|
||||
\urlstyle{same} % disable monospaced font for URLs
|
||||
\usepackage[top=2.5cm,left=3cm,right=2.5cm,bottom=2.5cm]{geometry}
|
||||
\usepackage{listings}
|
||||
\newcommand{\passthrough}[1]{#1}
|
||||
\lstset{defaultdialect=[5.3]Lua}
|
||||
\lstset{defaultdialect=[x86masm]Assembler}
|
||||
\setlength{\emergencystretch}{3em} % prevent overfull lines
|
||||
\providecommand{\tightlist}{%
|
||||
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
|
||||
\setcounter{secnumdepth}{5}
|
||||
\usepackage[onehalfspacing]{setspace}
|
||||
\usepackage{siunitx}
|
||||
\usepackage{tikz-feynman}
|
||||
\tikzfeynmanset{compat=1.0.0}
|
||||
\pagenumbering{gobble}
|
||||
\ifxetex
|
||||
% Load polyglossia as late as possible: uses bidi with RTL langages (e.g. Hebrew, Arabic)
|
||||
\usepackage{polyglossia}
|
||||
\setmainlanguage[variant=british]{english}
|
||||
\else
|
||||
\usepackage[shorthands=off,main=british]{babel}
|
||||
\fi
|
||||
\usepackage[]{biblatex}
|
||||
|
||||
\title{Search for excited quark states decaying to qW/qZ}
|
||||
\author{David Leppla-Weber}
|
||||
\date{}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
\begin{abstract}
|
||||
This is my very long abstract.
|
||||
|
||||
Blubb
|
||||
\end{abstract}
|
||||
|
||||
{
|
||||
\setcounter{tocdepth}{3}
|
||||
\tableofcontents
|
||||
}
|
||||
\newpage
|
||||
\pagenumbering{arabic}
|
||||
|
||||
\hypertarget{introduction}{%
|
||||
\section{Introduction}\label{introduction}}
|
||||
|
||||
\newpage
|
||||
|
||||
\hypertarget{theoretical-background}{%
|
||||
\section{Theoretical background}\label{theoretical-background}}
|
||||
|
||||
This chapter presents a short summary of the theoretical background
|
||||
relevant to this thesis. It first gives introduction to the standard
|
||||
model itself and some of the issues it raises. It then goes on to
|
||||
explain the processes of quantum chromodynamics and the theory of q*,
|
||||
which will be the main topic of this thesis.
|
||||
|
||||
\hypertarget{standard-model}{%
|
||||
\subsection{Standard model}\label{standard-model}}
|
||||
|
||||
The Standard Model of physics proofed very successful in describing
|
||||
three of the four fundamental interactions currently known: the
|
||||
electromagnetic, weak and strong interaction. The fourth, gravity, could
|
||||
not yet be successfully included in this theory.
|
||||
|
||||
The Standard Model divides all particles into spin-\(\frac{n}{2}\)
|
||||
fermions and spin-n bosons, where n could be any integer but so far is
|
||||
only known to be one for fermions and either one (gauge bosons) or zero
|
||||
(scalar bosons) for bosons. The fermions are further divided into quarks
|
||||
and leptons, both of which exist in three generations.
|
||||
|
||||
\begin{itemize}
|
||||
\tightlist
|
||||
\item
|
||||
issues
|
||||
\end{itemize}
|
||||
|
||||
\hypertarget{quantum-chromodynamics}{%
|
||||
\subsection{Quantum Chromodynamics}\label{quantum-chromodynamics}}
|
||||
|
||||
The quantum chromodynamics (QCD) describe the strong interaction of
|
||||
particles. It applies to all particles carrying colour (e.g.~quarks).
|
||||
The force is mediated by the gluons. Those bosons carry colour as well
|
||||
and can therefore interact with themselves. As a result of this,
|
||||
processes, where a gluon decays into two gluons are possible.
|
||||
Furthermore the strong force, binding to colour carrying particles,
|
||||
increases with their distance r making it impossible to separate two
|
||||
bound particles and causing the effect of hadronisation, which describes
|
||||
the process of hadrons forming out of individual, colour carrying,
|
||||
particles.
|
||||
|
||||
\hypertarget{excited-quark-states}{%
|
||||
\subsection{Excited quark states}\label{excited-quark-states}}
|
||||
|
||||
One category of theories that try to solve some of the shortcomings of
|
||||
the standard model are the composite quark models. Those state, that
|
||||
quarks consist of some particles unknown to us so far. A common
|
||||
prediction of those models are excited quark states (q*, q**,
|
||||
q***\ldots). This thesis will search data of the years 2016, 2017 and
|
||||
2018 for the single excited quark state q* which decays to a quark and
|
||||
any boson. As the boson will also quickly decay to for example two
|
||||
quarks, those events will be hard to distinguish from the QCD background
|
||||
described in \ldots.
|
||||
|
||||
\feynmandiagram [horizontal=a to b] {
|
||||
i1 -- [fermion] a -- [fermion] i2,
|
||||
a -- [photon] b,
|
||||
f1 -- [fermion] b -- [fermion] f2,
|
||||
};
|
||||
|
||||
\hypertarget{experimental-setup}{%
|
||||
\section{Experimental Setup}\label{experimental-setup}}
|
||||
|
||||
Following on, the experimental setup used to gather the data analysed in
|
||||
this thesis will be described.
|
||||
|
||||
\hypertarget{large-hadron-collider}{%
|
||||
\subsection{Large Hadron Collider}\label{large-hadron-collider}}
|
||||
|
||||
The Large Hadron Collider is the world's largest and most powerful
|
||||
particle accelerator \autocite{website}. It has a perimeter of 27 km and
|
||||
can collide protons at a centre of mass energy of 13 TeV. It is home to
|
||||
several experiments, the biggest of those are ATLAS and CMS. Both are
|
||||
general-purpose detectors to investigate the particles that form during
|
||||
particle collisions.
|
||||
|
||||
\hypertarget{cms}{%
|
||||
\subsection{CMS}\label{cms}}
|
||||
|
||||
\hypertarget{the-particle-flow-algorithm}{%
|
||||
\subsubsection{The Particle Flow
|
||||
algorithm}\label{the-particle-flow-algorithm}}
|
||||
|
||||
\hypertarget{jet-clustering}{%
|
||||
\subsubsection{Jet clustering}\label{jet-clustering}}
|
||||
|
||||
Because of the hadronisation it is not possible to uniquely identify the
|
||||
originating particle of a jet. Nonetheless, several algorithms exist to
|
||||
help with this problem. The algorithm used in this thesis is the
|
||||
anti-\(k_t\) clustering algorithm. It arises from a generalization of
|
||||
several other clustering algorithms, namely the \(k_t\),
|
||||
Cambridge/Aachen and SISCone clustering algorithms.
|
||||
|
||||
The anti-\(k_t\) clustering algorithm associates hard particles with
|
||||
their soft particles surrounding them within a radius R in the \(\eta\)
|
||||
- \(\phi\) plane forming cone like jets. If two jets overlap, the jets
|
||||
shape is changed according to its hardness. A softer particles jet will
|
||||
change its shape more than a harder particles. A visual comparision of
|
||||
four different clustering algorithms can be seen in \ldots.
|
||||
|
||||
\hypertarget{method-of-analysis}{%
|
||||
\section{Method of analysis}\label{method-of-analysis}}
|
||||
|
||||
As described in \ldots, an excited quark q* can decay to a quark and any
|
||||
boson. The branching ratios are calculated to be as follows:
|
||||
|
||||
The majority of excited quarks will decay to a quark and a gluon, but as
|
||||
this is virtually impossible to distinguish from QCD effects (for
|
||||
example from the qg-\textgreater qg processes), this analysis will focus
|
||||
on the processes q\emph{-\textgreater qW and q}-\textgreater qZ. As the
|
||||
vector bosons quickly decay mainly into two quarks, it will still be
|
||||
hard to discriminate between signal and qcd background events, but due
|
||||
to jet substructure studies it is well possible to establish a
|
||||
discriminator.
|
||||
|
||||
\begin{itemize}
|
||||
\tightlist
|
||||
\item
|
||||
dominant background: QCD (gg-gg e.g.~- two jets)
|
||||
\item
|
||||
division in QCD bg and signal
|
||||
\end{itemize}
|
||||
|
||||
\hypertarget{signalbackground-modelling}{%
|
||||
\subsection{Signal/Background
|
||||
modelling}\label{signalbackground-modelling}}
|
||||
|
||||
Following on, as background a QCD Monte Carlo sample will be used and as
|
||||
signal a Monte Carlo sample of q* decaying to qW/qZ.
|
||||
|
||||
The background is fitted using the following function with three
|
||||
parameters p0, p1, p2: \begin{equation}
|
||||
\frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}} \end{equation}
|
||||
Whereas \(m_{jj}\) is the invariant mass of the dijet and \(p_0\) is a
|
||||
normalisation parameter. Two and four parameter functions have also been
|
||||
studied but found to not fit the background as good as this one.
|
||||
|
||||
The signal is fitted using a double sided crystal ball function. A
|
||||
gaussian and a poisson have also been studied but found to not fit the
|
||||
signal sample very well.
|
||||
|
||||
\hypertarget{event-selection}{%
|
||||
\section{Event selection}\label{event-selection}}
|
||||
|
||||
The selection of events is divided in two parts. First, the preselection
|
||||
is optimized for high trigger efficiency and makes some physically
|
||||
motivated cuts. After that, a jet substructure selection uses different
|
||||
taggers to discriminate between QCD and signal events.
|
||||
|
||||
\hypertarget{preselection}{%
|
||||
\subsection{Preselection}\label{preselection}}
|
||||
|
||||
The preselection introduces the following cuts:
|
||||
|
||||
\begin{enumerate}
|
||||
\def\labelenumi{\arabic{enumi}.}
|
||||
\tightlist
|
||||
\item
|
||||
Number of jets \(\ge\) 2
|
||||
\item
|
||||
\(\Delta\eta \le 1.3\)
|
||||
\item
|
||||
\(m_{jj} \ge \SI{1050}{\giga\eV}\)
|
||||
\end{enumerate}
|
||||
|
||||
In the final state, at least two jets are expected. One directly
|
||||
originating from the decaying q* particle, the other one from the
|
||||
decaying vector boson. The resonance mass of the q* particle is expected
|
||||
to be very high, therefore it will be almost stationary and decay into
|
||||
two particles that are approximately back to back. That is ensured by
|
||||
the \(\Delta\eta\) cut. The last cut of the invariant dijet mass is to
|
||||
improve trigger efficiency.
|
||||
|
||||
\hypertarget{datamc-comparision}{%
|
||||
\subsection{Data/MC Comparision}\label{datamc-comparision}}
|
||||
|
||||
To ensure high data quality, the MC QCD background sample is now being
|
||||
compared to the actual data of the corresponding data. This is done for
|
||||
all three years of data available in Run2.
|
||||
|
||||
\hypertarget{event-substructure-selection}{%
|
||||
\section{Event substructure
|
||||
selection}\label{event-substructure-selection}}
|
||||
|
||||
This selection is responsible for distinguishing between QCD and signal
|
||||
events by using a tagger to identify jets coming from a vector boson.
|
||||
Two taggers different taggers will be used to later compare the results.
|
||||
For each tagger, a softdropmass is introduced.
|
||||
|
||||
\hypertarget{sideband}{%
|
||||
\subsection{Sideband}\label{sideband}}
|
||||
|
||||
The sideband is introduced to make sure there are no unwanted side
|
||||
effects of the used cut. It adds a cut, that makes sure, no data in the
|
||||
sideband is used for the actual analysis. Later on, a cut on the
|
||||
softdropmass will be used. The sideband is the softdropmass cut
|
||||
reversed.
|
||||
|
||||
\hypertarget{n-subjettiness}{%
|
||||
\subsection{N-Subjettiness}\label{n-subjettiness}}
|
||||
|
||||
The N-subjettiness \(\tau_n\) is defined as
|
||||
|
||||
\begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta
|
||||
R_{N,k} \} \end{equation}
|
||||
|
||||
with k going over the constituent particles in a given jet, \(p_{T,k}\)
|
||||
being their transverse momenta and
|
||||
\(\Delta R_{J,k} = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}\) being the
|
||||
distance of a candidate subjet J and a constituent particle k in the
|
||||
rapidity-azimuth plane. It has been shown, that
|
||||
\(\tau_{21} = \tau_2/\tau_1\) is a good discriminator between QCD events
|
||||
and events originating from the decay of a boosted vector boson.
|
||||
|
||||
\hypertarget{deepboosted}{%
|
||||
\subsection{DeepBoosted}\label{deepboosted}}
|
||||
|
||||
The deep boosted tagger uses a trained neural network to identify decays
|
||||
originitating in a vector boson. It is supposed to give better
|
||||
efficiencies than the older N-Subjettiness method.
|
||||
|
||||
\hypertarget{optimization}{%
|
||||
\subsection{Optimization}\label{optimization}}
|
||||
|
||||
To figure out the best value to cut on the discriminators introduced by
|
||||
the two taggers, a value to quantify how good a cut is has to be
|
||||
introduced. For that, the significance calculated by
|
||||
\(\frac{S}{\sqrt{B}}\) will be used. S stands for the amount of signal
|
||||
events and B for the amount of background events in a given interval.
|
||||
This value assumes a gaussian error on the background so it will be
|
||||
calculated for the 2 TeV masspoint where enough background events exist
|
||||
to justify this assumption. The value therefore represents how good the
|
||||
signal can be distinguished from the background in units of the standard
|
||||
deviation of the background. As interval, a 10 \% margin around the
|
||||
masspoint is chosen.
|
||||
|
||||
As a result, the \(\tau_{21}\) cut is placed at \(\le 0.35\) and the
|
||||
VvsQCD cut is placed at \(\ge 0.83\).
|
||||
|
||||
\hypertarget{signal-extraction}{%
|
||||
\section{Signal extraction}\label{signal-extraction}}
|
||||
|
||||
\hypertarget{uncertainties}{%
|
||||
\subsection{Uncertainties}\label{uncertainties}}
|
||||
|
||||
\hypertarget{results}{%
|
||||
\section{Results}\label{results}}
|
||||
|
||||
\hypertarget{section}{%
|
||||
\subsection{2016}\label{section}}
|
||||
|
||||
\hypertarget{previous-research}{%
|
||||
\subsubsection{previous research}\label{previous-research}}
|
||||
|
||||
\hypertarget{section-1}{%
|
||||
\subsection{2016 + 2017 + 2018}\label{section-1}}
|
||||
|
||||
\printbibliography[title=Summary]
|
||||
|
||||
\end{document}
|
||||
Loading…
Reference in New Issue
Block a user