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 Autor Jan Thomsen Titel Search for Supersymmetric Particles based on large Missing Transverse Energy and High Pt Jets at the CMS Experiment Datum 29. November 2007 Anmerkung Diplomarbeit, Institut für Experimentalphysik, Universität Hamburg; Gutachter: Prof. Dr. Peter Schleper, JProf. Dr. Johannes Haller URL http://inspirehep.net/record/894098/files/TS2008_007.pdf Literaturverz. nein Fußnoten nein Fragmente 4

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The SM can be divided into three parts: the fundamental matter particles, which are spin 1/2 fermions; the carriers of the fundamental forces, which are spin 1 bosons: and the Higgs mechanism, which allows particles to obtain mass and predicts a hitherly undiscovered spin 0 Higgs boson. The chapter will finish with presenting the problems of the SM, giving reasons for the need to expand it by new physics, e.g. Supersymmetry. The SM can be divided into three parts: the fundamental matter particles, which are spin 1/2 fermions; the carriers of the fundamental forces, which are spin 1 bosons; and the Higgs mechanism, which allows particles to gather mass and predicts a spin 0 Higgs boson. [...] The chapter will finish with presenting the problems of the SM, giving reasons for the need for expanding it by some new physics.
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Bosons and fermions provide corrections to the Higgs mass with a different sign. If one postulates a partner for each particle, which differs by 1/2 unit in spin, but otherwise has the same quantum numbers, this performs an automatic cancellation of the form

$\delta m^2_H = - \frac{\lambda_F^2}{16\pi^2} (\Lambda;^2+m_F^2) + \frac{\lambda_F^2}{16\pi^2} (\Lambda;^2+m_B^2) + \dots = {\mathcal O} (\frac{\alpha}{4\pi})\vert m_B^2 - m_F^2\vert, \quad \quad (2.25)$

Assuming the Yukawa couplings for fermions and bosons to be equal F = λB). This reduces the corrections to an acceptable level, as long as the masses do not differ much more than about a TeV. The fine tuning and Hierarchy problem, explained before, can therefore be handled in an elegant way. According to this argument Supersymmetric partners of the SM particles should not to be too heavy and can be found at LHC energies.

Bosons and fermions enter the corrections to the Higgs mass with a different sign. If one postulates a partner for each particle, which differs by 1/2 unit in spin, but otherwise has the same quantum numbers, this performs an automatic cancellation of the form:

$\delta m^2_H = - \frac{\lambda_F^2}{16\pi^2} (\Lambda;^2+m_F^2) + \frac{\lambda_F^2}{16\pi^2} (\Lambda;^2+m_B^2) + \dots = {\mathcal O} (\frac{\alpha}{4\pi})\vert m_B^2 - m_F^2\vert, \quad \quad (3.1)$

assuming the Yukawa couplings for fermions and bosons to be equal F = λB). This reduces the corrections to an acceptable level, as long as the masses do not differ much more than about a TeV. The fine tuning problem can therefore be avoided in an elegant way and as supersymmetric partners should not be too heavy there is a good chance to find supersymmetry with the LHC with a center of mass energy of 14 TeV.

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2.2.1 The Minimal Supersymmetric Standard Model(MSSM)

There is a large number of possible supersymmetric theories. All models considered in this analysis are based on the Minimal Supersymmetric Model(MSSM), which is a direct supersymmetrization of the SM, except for the fact that a second Higgs doublet field has to be introduced and R-parity conservation is assumed.

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3.3 Minimal Supersymmetric Model

There is a large number of possible supersymmetric theories. All models considered in this analysis are based on the Minimal Supersymmetric Model (MSSM), which is a

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direct supersymmetrization of the SM, except for the fact that a second Higgs doublet field has to be introduced and R-parity conservation is assumed.

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As left- and right-handed fermions have different gauge transformations (see Section 2.1.5), there are two scalars for each fermion called sfermions. These sfermions form

together with the SM fermions chiral supermultiplets. The notation left or right refers to the SUSY-partner of a left- or right-handed fermion. The superpartner of the SM gauge bosons are spin 1/2 gauginos that also have two helicity states. These gauge-bosons and gauginos form a gauge or vector supermultiplet.

In the SM, baryon- and lepton-numbers are conserved because of gauge invariance. In supersymmetric theories it is possible to construct renormalizable operators that do not conserve these numbers, but are still consistent with SM gauge symmetries and supersymmetry. As the proton has a lifetime of more than 1033 years, terms that violate both baryon and lepton numbers have to be small. With the introduction of R-parity conservation these terms are excluded. R-parity is defined by:

R = (−1)3(B−L)+2S   (2.27)

where B and L are baryon- and lepton-numbers, respectively, and S is the spin. All SM particles have even R-parity, while their superpartners are R-odd. Therefore, there can be no mixing between SM particles and sparticles. Furthermore, the lightest supersymmetric particle (LSP) has to be stable, if R is conserved [13]. This is assumed for this analysis.

[13] D. I. Kazakov, “Beyond the standard model (in search of supersymmetry)”. 2000. hep-ph/0012288.

As left- and right-handed fermions have different gauge transformations, there are two scalars for each fermion called sfermions. These sfermions form together with the SM fermions chiral supermultiplets. The denotation left or right refers to the SUSY-partner of a left- or right-handed fermion. The superpartner of the SM gauge bosons are spin $\frac{1}{2}$ ”gauginos” that also have two helicity states. These gauge-bosons and gauginos form a gauge or vector supermultiplet.

In the SM, baryon- and lepton-numbers are conserved because of gauge invariance. In supersymmetric theories it is possible to construct renormalizable operators that do not conserve these numbers, but are still consistent with SM gauge symmetries and supersymmetry. As the proton has a lifetime of more than 1033 years [22], terms that violate both baryon and lepton numbers have to be small. With the introduction of R-parity conservation these terms are excluded. R-parity is defined by:

R = (−1)3(B−L)+2S   (3.3)

where B and L are baryon- and lepton-numbers, respectively, and S is the spin. All SM particles have even R-parity, while their superpartners are R-odd. Therefore, there can be no mixing between SM particles and sparticles. Furthermore, the lightest supersymmetric particle (LSP) has to be stable, if R is conserved. This is assumed for this analysis.

[22] B.V. Sreekantan. Searches for Proton Decay and Superheavy Magnetic Monopoles. Journal of Astrophysics and Astronomy (ISSN 0250-6335), 1984.

 Anmerkungen Ohne Hinweis auf eine Übernahme. Tatsächlich finden sich die aufgeführten Aussagen zur R-Parität in der angegebenen Quelle (dort S.29). Die Formulierungen stimmen aber wortwörtlich mit denen in Thomsen (2007) überein. Sichter (Graf Isolan)