# Analyse:Mac/Fragment 018 01

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 Typus KomplettPlagiat Bearbeiter Graf Isolan Gesichtet
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)