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[1.] Analyse:Mac/Fragment 003 14 - Diskussion
Bearbeitet: 16. February 2015, 10:46 Graf Isolan
Erstellt: 16. February 2015, 10:45 (Graf Isolan)
Fragment, Mac, SMWFragment, Schutzlevel, Thomsen 2007, Verschleierung, ZuSichten

Typus
Verschleierung
Bearbeiter
Graf Isolan
Gesichtet
No.png
Untersuchte Arbeit:
Seite: 3, Zeilen: 14-19
Quelle: Thomsen 2007
Seite(n): 3, Zeilen: 4-7, 8-9
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.
Anmerkungen

Ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

[2.] Analyse:Mac/Fragment 011 22 - Diskussion
Bearbeitet: 16. February 2015, 11:12 Graf Isolan
Erstellt: 16. February 2015, 10:58 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, SMWFragment, Schutzlevel, Thomsen 2007, ZuSichten

Typus
KomplettPlagiat
Bearbeiter
Graf Isolan
Gesichtet
No.png
Untersuchte Arbeit:
Seite: 11, Zeilen: 22-32
Quelle: Thomsen 2007
Seite(n): 13, Zeilen: 13-23
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.

Anmerkungen

Ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

[3.] Analyse:Mac/Fragment 012 19 - Diskussion
Bearbeitet: 16. February 2015, 10:36 Graf Isolan
Erstellt: 16. February 2015, 10:36 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, SMWFragment, Schutzlevel, Thomsen 2007, ZuSichten

Typus
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Graf Isolan
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Untersuchte Arbeit:
Seite: 12, Zeilen: 19-23
Quelle: Thomsen 2007
Seite(n): 15-16, Zeilen: 15:36-38 - 16:1-2
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.

[Seite 15]

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

[Seite 16]

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.

Anmerkungen

Ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

[4.] Analyse:Mac/Fragment 013 04 - Diskussion
Bearbeitet: 16. February 2015, 10:29 Graf Isolan
Erstellt: 16. February 2015, 00:32 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, SMWFragment, Schutzlevel, Thomsen 2007, ZuSichten

Typus
KomplettPlagiat
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Graf Isolan
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No.png
Untersuchte Arbeit:
Seite: 13, Zeilen: 4-21
Quelle: Thomsen 2007
Seite(n): 15, Zeilen: 18-35
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)

[5.] Analyse:Mac/Fragment 016 07 - Diskussion
Bearbeitet: 23. February 2015, 01:19 Graf Isolan
Erstellt: 23. February 2015, 01:19 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, Niegel 2009, SMWFragment, Schutzlevel, ZuSichten

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Graf Isolan
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No.png
Untersuchte Arbeit:
Seite: 16, Zeilen: 7-12
Quelle: Niegel 2009
Seite(n): 25, Zeilen: 23-28
2.2.3 SUSY Mass Spectrum

In the MSSM, the masses of the SUSY particles can be calculated via the renormalization group equations (RGE), which are derived from the Lagrangian. With a given initial condition at the GUT scale, the solution of the RGE link the values at the GUT scale with the electroweak scale and thus determine the mass matrices of gauginos, squarks and leptons.

2.3.3 SUSY Mass Spectrum

In the MSSM, the masses of the SUSY particles can be calculated via the renormalization group equations (RGE), which are derived from the Lagrangian. With a given initial condition at the GUT scale, the solution of the RGE link the values at the GUT scale with the electroweak scales and thus determine the mass matrices of gauginos, squarks and leptons.

Anmerkungen

Identisch; ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

[6.] Analyse:Mac/Fragment 017 01 - Diskussion
Bearbeitet: 25. February 2015, 13:37 Graf Isolan
Erstellt: 23. February 2015, 01:52 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, Niegel 2009, SMWFragment, Schutzlevel, ZuSichten

Typus
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Graf Isolan
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Untersuchte Arbeit:
Seite: 17, Zeilen: 1ff. (komplett)
Quelle: Niegel 2009
Seite(n): 25-26, Zeilen: 25:29-32 - 26:1-22
Neutralinos and Charginos

Neutralinos and Charginos are the mass eigenstates of the neutral and charged fields, respectively. Their mass eigenstates are mixed states of gauginos and higgsinos:

\chi = \left(\begin{array}{c}\tilde B\\ \tilde W^3\\ \tilde H^0_d\\ \tilde H^0_u\end{array} \right)\quad , \quad \psi =\left(\begin{array}{c}\tilde W^+\\ \tilde H^+\end{array} \right)\quad , \quad\quad (2.35)

where χ and Ψ are the Majorana neutralino and Dirac chargino fields, respectively.

The corresponding neutralino mass matrix can be written as:


\begin{array}{c}
M^{(0)}
\end{array}
=
\left(
\begin{array}{cccc}
M_1 & 0 & -M_Z \cos \beta \sin \theta_W& M_Z \sin \beta \sin \theta_W\\
0 & M_2 &  M_Z \cos \beta \cos \theta_W& -M_Z \sin \beta \cos \theta_W\\
-M_Z \cos \beta \sin \theta_W& M_Z \cos \beta \cos \theta_W  & 0 & -\mu\\
M_Z \sin \beta \sin \theta_W& -M_Z \sin \beta \cos \theta_W & -\mu & 0
\end{array}
\right)
\quad (2.36)

with the gaugino masses M1, M2, the weak mixing angle θW and tan β, the ratio of two Higgs vacuum expectation values. The physical masses of the neutralinos are given by the eigenvalues of this matrix. The neutralino mass eigenstates are denoted as \begin{array}{c}\chi^0_1\end{array}, \begin{array}{c}\chi^0_2\end{array}, \begin{array}{c}\chi^0_3\end{array}, \begin{array}{c}\chi^0_4\end{array} with \begin{array}{c}m_{\chi_1^0}\end{array}\le \begin{array}{c}m_{\chi_2^0}\end{array}\le \begin{array}{c}m_{\chi_3^0}\le \begin{array}{c}m_{\chi_4^0}.\end{array}\end{array}

The mass matrix for the charginos is given by:


\begin{array}{c}
M^{(c)}
\end{array}
=
\left(
\begin{array}{cc}
M_2 & \sqrt{2} M_W \sin \beta \\
\sqrt{2} M_W \cos \beta & \mu
\end{array}
\right ),
\quad (2.37)

which leads to two chargino eigenstates \begin{array}{c}m_{\chi^\pm_{1,2}}\end{array} with the mass eigenvalues


\begin{array}{rl}
m_{\chi^\pm_{1,2}}^2 = & \frac{1}{2} M_2^2 + \frac{1}{2} \mu^2 + \frac{1}{2} M_W^2 \\
& \mp \frac{1}{2} \sqrt{(M_2^2 - \mu^2)^2 + 4 M_W^4 \cos^2 2\beta + 4 M_W^2 (M_2^2 + \mu^2 + 2 M_2 \mu \sin 2\beta)}
\end{array}. \quad (2.38)

The gluino is the only color octet fermion. Since SU(3) is unbroken, the gluino does not mix with other MSSM particles. The mass of the physical particle is defined by the gaugino mass parameter 
\begin{array}{c}
m_{\tilde g} \equiv M_3.
\end{array}

Approximately, the gaugino mass parameters at the electroweak scale are:


\begin{array}{lcll}
M_3 & \simeq & 2.7 m_{1/2} & \quad\quad (2.39) \\
M_2 & \simeq & 0.8 m_{1/2} & \quad\quad (2.40) \\
M_1 & \simeq & 0.4 m_{1/2} & \quad\quad (2.41) 
\end{array}

The physical masses of the neutralinos are obtained by diagonalizing the mass matrix Eq. 2.36. In the mSUGRA model, the lightest neutralino is dominantly bino-like [and the next-to-lightest neutralino is mostly wino-like, with masses close to M1 and M2, respectively.]

[Seite 25]

Neutralinos and Charginos

Neutralinos and Charginos are the mass eigenstates of the neutral and charged fields, respectively. Their mass eigenstates are mixed states of gauginos and higgsinos:

\chi = \left(\begin{array}{c}\tilde B\\ \tilde W^3\\ \tilde H^0_1\\ \tilde H^0_2\end{array} \right)\quad , \psi =\left(\begin{array}{c}\tilde W^+\\ \tilde H^+\end{array} \right)\quad , \quad\quad (2.64)

[Seite 26]

where χ and Ψ are the Majorana neutralino and Dirac chargino fields, respectively.

The corresponding neutralino mass matrix reads as:


\begin{array}{c}
M^{(0)}
\end{array}
=
\left(
\begin{array}{cccc}
M_1 & 0 & -M_Z \cos \beta \sin \theta_W& M_Z \sin \beta \sin \theta_W\\
0 & M_2 &  M_Z \cos \beta \cos \theta_W& -M_Z \sin \beta \cos \theta_W\\
-M_Z \cos \beta \sin \theta_W& M_Z \cos \beta \cos \theta_W  & 0 & -\mu\\
M_Z \sin \beta \sin \theta_W& -M_Z \sin \beta \cos \theta_W & -\mu & 0
\end{array}
\right)
\quad (2.65)

with the gaugino masses M1, M2, the weak mixing angle θW and tan β, the ratio of two Higgs vacuum expectation values. The physical masses of the neutralinos are given by the eigenvalues of this matrix. The neutralino mass eigenstates are denoted as \begin{array}{c}\chi^0_1\end{array}, \begin{array}{c}\chi^0_2\end{array}, \begin{array}{c}\chi^0_3\end{array}, \begin{array}{c}\chi^0_4\end{array} with \begin{array}{c}m_{\chi_1^0}\end{array}\le \begin{array}{c}m_{\chi_2^0}\end{array}\le \begin{array}{c}m_{\chi_3^0}\le \begin{array}{c}m_{\chi_4^0}.\end{array}\end{array}

The mass matrix for the charginos given by:


\begin{array}{c}
M^{(c)}
\end{array}
=
\left(
\begin{array}{cc}
M_2 & \sqrt{2} M_W \sin \beta \\
\sqrt{2} M_W \cos \beta & \mu
\end{array}
\right )
\quad (2.66)

leads to two chargino eigenstates \begin{array}{c}m_{\chi^\pm_{1,2}}\end{array} with the mass eigenvalues


\begin{array}{rl}
m_{\chi^\pm_{1,2}}^2 = & \frac{1}{2} M_2^2 + \frac{1}{2} \mu^2 + \frac{1}{2} M_W^2 \\
& \mp \frac{1}{2} \sqrt{(M_2^2 - \mu^2)^2 + 4 M_W^4 \cos^2 2\beta + 4 M_W^2 (M_2^2 + \mu^2 + 2 M_2 \mu \sin 2\beta)}
\end{array}. \quad (2.67)

The gluino is the only color octet fermion. Since the SU(3) is unbroken, the gluino does not mix with other MSSM particles. The mass of the physical particle is defined by the gaugino mass parameter 
\begin{array}{c}
m_{\tilde g} \equiv M_3.
\end{array}

Approximately, the gaugino mass parameters at the electroweak scale are:


\begin{array}{lcll}
M_3 & \simeq & 2.7 m_{1/2} & \quad\quad (2.68) \\
M_2 & \simeq & 0.8 m_{1/2} & \quad\quad (2.69) \\
M_1 & \simeq & 0.4 m_{1/2} & \quad\quad (2.70) 
\end{array}

The physical masses of the neutralinos are obtained by diagonalizing the mass matrix Eq. 2.65. In the mSUGRA model, the lightest neutralino is dominantly bino-like and the next-to-lightest neutralino is mostly wino-like, with masses close to M1 and M2, respectively.

Anmerkungen

Identisch; ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

[7.] Analyse:Mac/Fragment 018 01 - Diskussion
Bearbeitet: 26. February 2015, 12:04 Graf Isolan
Erstellt: 25. February 2015, 13:37 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, Niegel 2009, SMWFragment, Schutzlevel, ZuSichten

Typus
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Graf Isolan
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Untersuchte Arbeit:
Seite: 18, Zeilen: 1ff. (komplett)
Quelle: Niegel 2009
Seite(n): 26-27, Zeilen: 26:20-24 - 27:1-20
[In the mSUGRA model, the lightest neutralino is dominantly bino-like] and the next-to-lightest neutralino is mostly wino-like, with masses close to M1 and M2, respectively. The mass of the lightest chargino is approximately given by M2. Hence the masses of the next-to-lightest neutralino and the lightest chargino are similar, and approximately two times the mass of the lightest neutralino.

Sleptons and Squarks

The masses of left-handed and right-handed fermions are equal. But their superpartners are bosons and the masses of left-handed and right-handed sfermions can be different:


\begin{array}{lcll}
\tilde m_{e_L}^2 & = & \tilde m^2_{L_i} + m^2_{E_i} + M_Z^2 \cos (2\beta)\left(-{\displaystyle \frac{1}{2}} + \sin^2 \theta_W \right) &\quad \quad (2.42) \\
\\
\tilde m_{\nu_L}^2 & = & \tilde m^2_{L_i} + M_Z^2 \cos (2\beta)\left(\displaystyle{\frac{1}{2}}\right) &\quad \quad (2.43) \\
\\
\tilde m_{e_R}^2 & = & \tilde m^2_{E_i} + m^2_{E_i} - M_Z^2 \cos (2\beta)\left(\sin^2 \theta_W \right) &\quad \quad (2.44) \\
\\
\tilde m_{u_L}^2 & = & \tilde m^2_{Q_i} + m^2_{U_i} + M_Z^2 \cos (2\beta)\left(+ \displaystyle{\frac{1}{2}} + \sin^2 \theta_W \right) &\quad \quad (2.45) \\
\\
\tilde m_{d_L}^2 & = & \tilde m^2_{Q_i} + m^2_{D_i} + M_Z^2 \cos (2\beta)\left(-\displaystyle{\frac{1}{2} + \frac{1}{3}} \sin^2 \theta_W \right) &\quad \quad (2.46) \\
\\
\tilde m_{u_R}^2 & = & \tilde m^2_{U_i} + m^2_{U_i} + M_Z^2 \cos (2\beta)\left(\displaystyle {\frac{2}{3}} \sin^2 \theta_W \right) &\quad \quad (2.47) \\
\\
\tilde m_{d_R}^2 & = & \tilde m^2_{D_i} + m^2_{D_i} - M_Z^2 \cos (2\beta)\left({\displaystyle \frac{1}{3}}\sin^2 \theta_W \right) \quad .&\quad \quad (2.48) 
\end{array}

On the right side of the equations, the terms denoted as \tilde m are calculated with the RGE, the mass terms m are the fermion masses. The index i denotes the three generations.

Furthermore non-negligible Yukawa couplings lead to a mixing between the electroweak eigenstates and the mass eigenstates of the third generation sleptons and squarks. Due to small Yukawa couplings the mixing is negligible for the first and second generation. Therefore the mass eigenstates corresponds to the interaction eigenstates, which have been introduced above. The mass matrices for the third generation can be written as:


\begin{array}{lcll}
{\mathcal M}^{\tilde t} & = & \left( 
\begin{array}{cc}
\tilde m_{t_L}^2 & m_t (A_t - \mu \cot \beta)\\
m_t (A_t - \mu \cot \beta) & \tilde m_{t_R}^2 
\end{array}
\right)
&\quad\quad (2.49)\\
\\
{\mathcal M}^{\tilde b} & = & \left( 
\begin{array}{cc}
\tilde m_{b_L}^2 & m_b (A_b - \mu \tan \beta)\\
m_b (A_b - \mu \tan \beta) & \tilde m_{b_R}^2 
\end{array}
\right)
&\quad\quad (2.50)\\
\\
{\mathcal M}^{\tilde \tau} & = & \left( 
\begin{array}{cc}
\tilde m_{\tau_L}^2 & m_\tau (A_\tau - \mu \tan \beta)\\
m_\tau (A_\tau - \mu \tan \beta) & \tilde m_{\tau_R}^2 
\end{array}
\right)\quad .
&\quad\quad (2.51)
\end{array}

[Seite 26]

In the mSUGRA model, the lightest neutralino is dominantly bino-like and the next-to-lightest neutralino is mostly wino-like, with masses close to M1 and M2, respectively. The mass of the lightest chargino is approximately given by M2. Hence the masses of the next-to-lightest neutralino and the lightest chargino are similar, and approximately two times the mass of the lightest neutralino.

[Seite 27]

Sleptons and Squarks

The masses of left-handed and right-handed fermions are equal. But their superpartners are bosons and the masses of left-handed and right-handed sfermions can be different:


\begin{array}{lcll}
\tilde m_{e_L}^2 & = & \tilde m^2_{L_i} + m^2_{E_i} + M_Z^2 \cos (2\beta)\left(-{\displaystyle \frac{1}{2}} + \sin^2 \theta_W \right) &\quad \quad (2.71) \\
\\
\tilde m_{\nu_L}^2 & = & \tilde m^2_{L_i} + M_Z^2 \cos (2\beta)\left(\displaystyle{\frac{1}{2}}\right) &\quad \quad (2.72) \\
\\
\tilde m_{e_R}^2 & = & \tilde m^2_{E_i} + m^2_{E_i} - M_Z^2 \cos (2\beta)\left(\sin^2 \theta_W \right) &\quad \quad (2.73) \\
\\
\tilde m_{u_L}^2 & = & \tilde m^2_{Q_i} + m^2_{U_i} + M_Z^2 \cos (2\beta)\left(+ \displaystyle{\frac{1}{2}} + \sin^2 \theta_W \right) &\quad \quad (2.74) \\
\\
\tilde m_{d_L}^2 & = & \tilde m^2_{Q_i} + m^2_{D_i} + M_Z^2 \cos (2\beta)\left(-\displaystyle{\frac{1}{2} + \frac{1}{3}} \sin^2 \theta_W \right) &\quad \quad (2.75) \\
\\
\tilde m_{u_R}^2 & = & \tilde m^2_{U_i} + m^2_{U_i} + M_Z^2 \cos (2\beta)\left(\displaystyle {\frac{2}{3}} \sin^2 \theta_W \right) &\quad \quad (2.76) \\
\\
\tilde m_{d_R}^2 & = & \tilde m^2_{D_i} + m^2_{D_i} - M_Z^2 \cos (2\beta)\left({\displaystyle \frac{1}{3}}\sin^2 \theta_W \right)\quad . &\quad \quad (2.77) 
\end{array}

On the right side of the equations, the terms denoted as \tilde m are calculated with the RGE, the mass terms m are the fermion masses. The index i denotes the three generations.

Furthermore non-negligible Yukawa couplings lead to a mixing between the electroweak eigenstates and the mass eigenstates of the third generation sleptons and squarks. Due to small Yukawa couplings the mixing is negligible for the first and second generation. Therefore the mass eigenstates corresponds to the interaction eigenstates, which have been introduced above. The mass matrices for the third generation reads as:


\begin{array}{lcll}
{\mathcal M}^{\tilde t} & = & \left( 
\begin{array}{cc}
\tilde m_{t_L}^2 & m_t (A_t - \mu \cot \beta)\\
m_t (A_t - \mu \cot \beta) & \tilde m_{t_R}^2 
\end{array}
\right)
&\quad\quad (2.78)\\
\\
{\mathcal M}^{\tilde b} & = & \left( 
\begin{array}{cc}
\tilde m_{b_L}^2 & m_b (A_b - \mu \tan \beta)\\
m_b (A_b - \mu \tan \beta) & \tilde m_{b_R}^2 
\end{array}
\right)
&\quad\quad (2.79)\\
\\
{\mathcal M}^{\tilde \tau} & = & \left( 
\begin{array}{cc}
\tilde m_{\tau_L}^2 & m_\tau (A_\tau - \mu \tan \beta)\\
m_\tau (A_\tau - \mu \tan \beta) & \tilde m_{\tau_R}^2 
\end{array}
\right)\quad .
&\quad\quad (2.80)
\end{array}

Anmerkungen

Identisch; ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

[8.] Analyse:Mac/Fragment 053 01 - Diskussion
Bearbeitet: 23. February 2015, 01:21 Graf Isolan
Erstellt: 21. February 2015, 23:07 (Graf Isolan)
BauernOpfer, Dobbs et al 2004, Fragment, Mac, SMWFragment, Schutzlevel, ZuSichten

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Untersuchte Arbeit:
Seite: 53, Zeilen: 1-29
Quelle: Dobbs et al 2004
Seite(n): 25-26, Zeilen: 25:35-39.40-42; 26:1-11.13-21
The time evolution of the event goes from bottom to top in Figure 4.4. Two protons (each indicated by three solid lines to denote their valence quark content) collide and a parton is resolved at scale Q and momentum fraction x in each one. The parton density as function of x and Q^2 is encoded in the parton distribution function which is labeled by f(x,Q^2). The quark and anti-quark annihilate into an s-channel resonance denoted by a wavy line. The resonance then decays into a fermion anti-fermion pair. This part of the event is called the hard subprocess. The generator incorporates higher order QCD effects by allowing the (anti)quarks to branch into qg pairs, while the gluons may branch into q\overline q or gg pairs. The resultant partons may also branch, resulting in a cascade of branchings. This part of the event is labeled parton shower in the figure (showering of or cascade of partons). The event now consists of a number of elementary particles, including quarks, antiquarks, and gluons which are not allowed to exist in isolation, as dictated by colour confinement. Next, the program groups the colored partons into colour-singlet composite hadrons using a phenomenological model referred to as hadronization. The hadronization scale is in the non-perturbative regime and the programs use fairly crude phenomenological models, which contain several non-physical parameters that have to be tuned using experimental data. After hadronization, many short-lived resonances will be present and are their decays simulated by the program. The generators also add features of the underlying event. The beam remnants are the colored remains of the proton which are left behind when the parton which participates in the hard subprocess is pulled out. The motion of the partons inside the proton results in a small (≈ 1 GeV) primordial transverse momentum, which yield a recoil energy of the beam remnants. The beam remnants are colour connected to the hard subprocess and so should be included in the same hadronization system. Multiple parton-parton interactions, wherein more than one pair of partons from the beam protons interact, are also accounted for. In a final step, pile-up from other proton-proton collisions in the same bunch crossing are added to the event [110].

[110] M. A. Dobbs et al., “Les Houches guidebook to Monte Carlo generators for hadron collider physics”. 2004. hep-ph/0403045.

[Seite 25]

The general structure of the final state of an event from an SHG is shown in Figure 5. The time evolution of the event goes from bottom to top. Two protons (each indicated by three solid lines to denote their valence quark content) collide and a parton is resolved at scale Q and momentum fraction x in each one. The phenomenology of the parton resolution is encoded in the parton distribution function f(x,Q^2). [...] The quark and anti-quark annihilate into an s-channel resonance denoted by a wavy line. The resonance then decays into a fermion anti-fermion pair. This part of the event is called the hard subprocess.

[Seite 26]

As briefly outlined there, the SHG incorporates higher order QCD effects by allowing the (anti)quarks to branch into \stackrel{(-)}{q} g pairs, while the gluons may branch into q\overline q or gg pairs. The resultant partons may also branch, resulting in a shower or cascade of partons.17 This part of the event is labelled parton shower in the figure. Showering of the initial state partons is also included in the SHG’s, but is not shown in the figure for simplicity. The event now consists of a number of elementary particles, including quarks, antiquarks, and gluons which are not allowed to exist in isolation, as dictated by colour confinement. Next, the program groups the coloured partons into colour-singlet composite hadrons using a phenomenological model referred to as hadronization. The hadronization scale is in the non-perturbative regime and the programs use fairly crude phenomenological models, which contain several non-physical parameters that are tuned using experimental data. [...] After hadronization, many short-lived resonances will be present and are decayed by the program.

The SHG’s also add in features of the underlying event. The beam remnants are the coloured remains of the proton which are left behind when the parton which participates in the hard subprocess is ‘pulled out’. The motion of the partons inside the proton results in a small (≈ 1 GeV) primordial transverse momentum, against which the beam remnants recoil. The beam remnants are colour connected to the hard subprocess and so should be included in the same hadronization system. Multiple parton-parton interactions, wherein more than one pair of partons from the beam protons interact, are also accounted for. In a final step, pile-up from other proton-proton collisions in the same bunch crossing are added to the event.


17 Though the discussion of parton showers presented here is restricted to QCD showers, an identical prescription can be applied to electromagnetic showers and is used in SHG’s to incorporate higher order QED corrections.

Anmerkungen

Die Quelle wird zwar genannt, Art und Umfang der vollständig wortwörtlichen Übernahme bleiben aber gänzlich ungekennzeichnet.

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Fragmente (Verdächtig / Keine Wertung)

Kein Fragment



Fragmente (Kein Plagiat)

Kein Fragment



Fragmente (Verwaist)

1 Fragment

[1.] Analyse:Mac/Fragment 019 01 - Diskussion
Bearbeitet: 27. February 2015, 13:06 Graf Isolan
Erstellt: 27. February 2015, 13:06 (Graf Isolan)
Fragment, KomplettPlagiat, Mac, Niegel 2009, SMWFragment, Schutzlevel, Unfertig

Typus
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Graf Isolan
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Untersuchte Arbeit:
Seite: 19, Zeilen: 1-4
Quelle: Niegel 2009
Seite(n): 27, Zeilen: 21-24
The mass eigenstates of the third generation are:

[...]

The mass eigenstates of the third generation are:
Anmerkungen

Schließt die auf den Vorderseiten begonnene identische Übernahme ab.

Sichter
(Graf Isolan)


Quellen

Quelle Autor Titel Verlag Jahr Lit.-V. FN
Mac/Niegel 2009 Martin Florian Niegel Search for Supersymmetry in Trimuon Final States with the CMS Detector 2009 ja ja
Mac/Thomsen 2007 Jan Thomsen Search for Supersymmetric Particles based on large Missing Transverse Energy and High Pt Jets at the CMS Experiment 2007 nein nein


Übersicht

Typus Gesichtet ZuSichten Unfertig Σ
KP0617
VS0101
ÜP0000
BO0101
KW0000
KeinP0000
Σ0819

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